sqrtexp (problem 3.4.4)

Time bar (total: 7.3s)

analyze205.0ms (2.8%)

Algorithm
search
Search
ProbabilityValidUnknownPreconditionInfiniteDomainCan'tIter
0%0%100%0%0%0%0%0
0%0%100%0%0%0%0%1
0%0%100%0%0%0%0%2
50%50%50%0%0%0%0%3
50%50%50%0%0%0%0%4
50%50%50%0%0%0%0%5
50%50%50%0%0%0%0%6
53.1%53.1%46.9%0%0%0%0%7
53.1%53.1%46.9%0%0%0%0%8
53.9%53.9%46.1%0%0%0%0%9
54.1%54.1%45.9%0%0%0%0%10
54.2%54.2%45.8%0%0%0%0%11
54.2%54.2%45.7%0%0%0%0%12
Compiler

Compiled 14 to 11 computations (21.4% saved)

Precisions
Click to see histograms. Total time spent on operations: 93.0ms
ival-exp: 26.0ms (28% of total)
ival-sub: 20.0ms (21.5% of total)
ival-sqrt: 20.0ms (21.5% of total)
ival-mult: 18.0ms (19.4% of total)
ival-div: 6.0ms (6.5% of total)
const: 3.0ms (3.2% of total)
backward-pass: 1.0ms (1.1% of total)

sample2.3s (32.1%)

Results
1.5s5277×1valid
221.0ms2979×0valid
196.0ms2687×0unsamplable
Precisions
Click to see histograms. Total time spent on operations: 1.5s
ival-exp: 777.0ms (51.4% of total)
ival-sub: 199.0ms (13.2% of total)
ival-mult: 179.0ms (11.9% of total)
ival-sqrt: 144.0ms (9.5% of total)
ival-div: 106.0ms (7% of total)
backward-pass: 79.0ms (5.2% of total)
const: 26.0ms (1.7% of total)
Bogosity

preprocess231.0ms (3.2%)

Algorithm
egg-herbie
Rules
2108×*-lowering-*.f32
2108×*-lowering-*.f64
1708×--lowering--.f32
1708×--lowering--.f64
1500×fnmsub-define
Iterations

Useful iterations: 5 (0.0ms)

IterNodesCost
01929
14827
27727
312527
423420
543518
695418
7377718
0108
1248
2318
3458
4767
51415
63015
78525
849845
082455
Stop Event
iter limit
node limit
node limit
Calls
Call 1
Inputs
(sqrt (/ (- (exp (* 2 x)) 1) (- (exp x) 1)))
Outputs
(sqrt (/ (- (exp (* 2 x)) 1) (- (exp x) 1)))
(sqrt.f64 (+.f64 #s(literal 1 binary64) (exp.f64 x)))
Call 2
Inputs
(sqrt (/ (- (exp (* 2 x)) 1) (- (exp x) 1)))
(sqrt (/ (- (exp (* 2 (neg x))) 1) (- (exp (neg x)) 1)))
(neg (sqrt (/ (- (exp (* 2 (neg x))) 1) (- (exp (neg x)) 1))))
Outputs
(sqrt (/ (- (exp (* 2 x)) 1) (- (exp x) 1)))
(sqrt (+ 1 (exp x)))
(sqrt (/ (- (exp (* 2 (neg x))) 1) (- (exp (neg x)) 1)))
(sqrt (+ 1 (recip (exp x))))
(neg (sqrt (/ (- (exp (* 2 (neg x))) 1) (- (exp (neg x)) 1))))
(neg (sqrt (+ 1 (recip (exp x)))))

explain204.0ms (2.8%)

FPErrors
Click to see full error table
Ground TruthOverpredictionsExampleUnderpredictionsExampleSubexpression
1630-0-(-.f64 (exp.f64 (*.f64 #s(literal 2 binary64) x)) #s(literal 1 binary64))
1630-0-(-.f64 (exp.f64 x) #s(literal 1 binary64))
00-0-x
00-0-(exp.f64 x)
00-0-(/.f64 (-.f64 (exp.f64 (*.f64 #s(literal 2 binary64) x)) #s(literal 1 binary64)) (-.f64 (exp.f64 x) #s(literal 1 binary64)))
00-0-#s(literal 2 binary64)
00-0-(sqrt.f64 (/.f64 (-.f64 (exp.f64 (*.f64 #s(literal 2 binary64) x)) #s(literal 1 binary64)) (-.f64 (exp.f64 x) #s(literal 1 binary64))))
00-0-(*.f64 #s(literal 2 binary64) x)
00-0-#s(literal 1 binary64)
01(342.477943638321)0-(exp.f64 (*.f64 #s(literal 2 binary64) x))
Results
122.0ms316×1valid
34.0ms196×0valid
Compiler

Compiled 107 to 32 computations (70.1% saved)

Precisions
Click to see histograms. Total time spent on operations: 103.0ms
ival-exp: 43.0ms (41.7% of total)
ival-mult: 15.0ms (14.6% of total)
ival-div: 12.0ms (11.6% of total)
ival-sub: 11.0ms (10.7% of total)
ival-sqrt: 11.0ms (10.7% of total)
backward-pass: 10.0ms (9.7% of total)
const: 1.0ms (1% of total)

eval0.0ms (0%)

Compiler

Compiled 6 to 5 computations (16.7% saved)

prune1.0ms (0%)

Alt Table
Click to see full alt table
StatusAccuracyProgram
100.0%
(sqrt.f64 (+.f64 #s(literal 1 binary64) (exp.f64 x)))
Compiler

Compiled 6 to 5 computations (16.7% saved)

simplify7.0ms (0.1%)

Algorithm
egg-herbie
Localize:

Found 3 expressions of interest:

NewMetricScoreProgram
cost-diff0
(exp.f64 x)
cost-diff0
(+.f64 #s(literal 1 binary64) (exp.f64 x))
cost-diff0
(sqrt.f64 (+.f64 #s(literal 1 binary64) (exp.f64 x)))
Rules
+-lowering-+.f64
+-lowering-+.f32
sqrt-lowering-sqrt.f64
exp-lowering-exp.f32
1-exp
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
0513
1813
0813
Stop Event
iter limit
saturated
Calls
Call 1
Inputs
(sqrt (+ 1 (exp x)))
(+ 1 (exp x))
1
(exp x)
x
Outputs
(sqrt (+ 1 (exp x)))
(sqrt.f64 (+.f64 #s(literal 1 binary64) (exp.f64 x)))
(+ 1 (exp x))
(+.f64 #s(literal 1 binary64) (exp.f64 x))
1
#s(literal 1 binary64)
(exp x)
(exp.f64 x)
x

localize20.0ms (0.3%)

Localize:

Found 3 expressions of interest:

NewMetricScoreProgram
accuracy100.0%
(sqrt.f64 (+.f64 #s(literal 1 binary64) (exp.f64 x)))
accuracy100.0%
(exp.f64 x)
accuracy100.0%
(+.f64 #s(literal 1 binary64) (exp.f64 x))
Results
13.0ms256×0valid
Compiler

Compiled 15 to 6 computations (60% saved)

Precisions
Click to see histograms. Total time spent on operations: 6.0ms
ival-exp: 2.0ms (33.8% of total)
ival-add: 2.0ms (33.8% of total)
ival-sqrt: 2.0ms (33.8% of total)
const: 0.0ms (0% of total)
backward-pass: 0.0ms (0% of total)

series5.0ms (0.1%)

Counts
3 → 36
Calls
Call 1
Inputs
#<alt (sqrt (+ 1 (exp x)))>
#<alt (+ 1 (exp x))>
#<alt (exp x)>
Outputs
#<alt (sqrt 2)>
#<alt (+ (sqrt 2) (* 1/2 (/ x (sqrt 2))))>
#<alt (+ (sqrt 2) (* x (+ (* 1/2 (/ (* x (- 1/2 (* 1/4 (/ 1 (pow (sqrt 2) 2))))) (sqrt 2))) (* 1/2 (/ 1 (sqrt 2))))))>
#<alt (+ (sqrt 2) (* x (+ (* x (+ (* 1/2 (/ (* x (- 1/6 (* 1/2 (/ (- 1/2 (* 1/4 (/ 1 (pow (sqrt 2) 2)))) (pow (sqrt 2) 2))))) (sqrt 2))) (* 1/2 (/ (- 1/2 (* 1/4 (/ 1 (pow (sqrt 2) 2)))) (sqrt 2))))) (* 1/2 (/ 1 (sqrt 2))))))>
#<alt (sqrt (+ 1 (exp x)))>
#<alt (sqrt (+ 1 (exp x)))>
#<alt (sqrt (+ 1 (exp x)))>
#<alt (sqrt (+ 1 (exp x)))>
#<alt (sqrt (+ 1 (exp x)))>
#<alt (sqrt (+ 1 (exp x)))>
#<alt (sqrt (+ 1 (exp x)))>
#<alt (sqrt (+ 1 (exp x)))>
#<alt 2>
#<alt (+ 2 x)>
#<alt (+ 2 (* x (+ 1 (* 1/2 x))))>
#<alt (+ 2 (* x (+ 1 (* x (+ 1/2 (* 1/6 x))))))>
#<alt (+ 1 (exp x))>
#<alt (+ 1 (exp x))>
#<alt (+ 1 (exp x))>
#<alt (+ 1 (exp x))>
#<alt (+ 1 (exp x))>
#<alt (+ 1 (exp x))>
#<alt (+ 1 (exp x))>
#<alt (+ 1 (exp x))>
#<alt 1>
#<alt (+ 1 x)>
#<alt (+ 1 (* x (+ 1 (* 1/2 x))))>
#<alt (+ 1 (* x (+ 1 (* x (+ 1/2 (* 1/6 x))))))>
#<alt (exp x)>
#<alt (exp x)>
#<alt (exp x)>
#<alt (exp x)>
#<alt (exp x)>
#<alt (exp x)>
#<alt (exp x)>
#<alt (exp x)>
Calls

9 calls:

TimeVariablePointExpression
4.0ms
x
@-inf
(sqrt (+ 1 (exp x)))
1.0ms
x
@0
(sqrt (+ 1 (exp x)))
0.0ms
x
@inf
(sqrt (+ 1 (exp x)))
0.0ms
x
@0
(+ 1 (exp x))
0.0ms
x
@0
(exp x)

rewrite335.0ms (4.6%)

Algorithm
batch-egg-rewrite
Rules
3504×/-lowering-/.f32
3504×/-lowering-/.f64
2980×*-lowering-*.f32
2980×*-lowering-*.f64
1782×+-lowering-+.f64
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
0511
12311
215311
3116811
0824511
Stop Event
iter limit
node limit
Counts
3 → 241
Calls
Call 1
Inputs
(sqrt (+ 1 (exp x)))
(+ 1 (exp x))
(exp x)
Outputs
(exp.f64 (*.f64 #s(literal 1/2 binary64) (log1p.f64 (exp.f64 x))))
(exp.f64 (*.f64 (log.f64 (pow.f64 (+.f64 #s(literal 1 binary64) (exp.f64 x)) #s(literal 1/4 binary64))) #s(literal 2 binary64)))
(exp.f64 (*.f64 (log.f64 (pow.f64 (+.f64 #s(literal 1 binary64) (exp.f64 x)) #s(literal 2 binary64))) #s(literal 1/4 binary64)))
(exp.f64 (*.f64 (*.f64 (log1p.f64 (exp.f64 x)) #s(literal 1/4 binary64)) #s(literal 2 binary64)))
(exp.f64 (+.f64 (*.f64 (log1p.f64 (exp.f64 x)) #s(literal 1/4 binary64)) (*.f64 (log1p.f64 (exp.f64 x)) #s(literal 1/4 binary64))))
(sqrt.f64 (+.f64 #s(literal 1 binary64) (exp.f64 x)))
(/.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (pow.f64 (+.f64 #s(literal 1 binary64) (exp.f64 x)) #s(literal 1/2 binary64))))
(/.f64 #s(literal 1 binary64) (sqrt.f64 (/.f64 (/.f64 #s(literal 1 binary64) (+.f64 #s(literal 1 binary64) (exp.f64 x))) #s(literal 1 binary64))))
(/.f64 #s(literal 1 binary64) (sqrt.f64 (/.f64 (expm1.f64 x) (expm1.f64 (*.f64 x #s(literal 2 binary64))))))
(/.f64 (hypot.f64 #s(literal 1 binary64) (exp.f64 (*.f64 x #s(literal 3/2 binary64)))) (sqrt.f64 (-.f64 (exp.f64 (*.f64 x #s(literal 2 binary64))) (expm1.f64 x))))
(/.f64 (sqrt.f64 (-.f64 #s(literal 1 binary64) (exp.f64 (*.f64 x #s(literal 2 binary64))))) (pow.f64 (-.f64 #s(literal 1 binary64) (exp.f64 x)) #s(literal 1/2 binary64)))
(/.f64 #s(literal -1 binary64) (neg.f64 (/.f64 #s(literal 1 binary64) (pow.f64 (+.f64 #s(literal 1 binary64) (exp.f64 x)) #s(literal 1/2 binary64)))))
(/.f64 (hypot.f64 #s(literal 1 binary64) (exp.f64 (*.f64 (*.f64 x #s(literal 3 binary64)) #s(literal 3/2 binary64)))) (sqrt.f64 (*.f64 (-.f64 (exp.f64 (*.f64 x #s(literal 2 binary64))) (expm1.f64 x)) (+.f64 #s(literal 1 binary64) (*.f64 (exp.f64 (*.f64 x #s(literal 3 binary64))) (expm1.f64 (*.f64 x #s(literal 3 binary64))))))))
(/.f64 (sqrt.f64 (-.f64 #s(literal 0 binary64) (+.f64 #s(literal 1 binary64) (exp.f64 (*.f64 x #s(literal 3 binary64)))))) (sqrt.f64 (-.f64 #s(literal 0 binary64) (-.f64 (exp.f64 (*.f64 x #s(literal 2 binary64))) (expm1.f64 x)))))
(/.f64 (sqrt.f64 (-.f64 #s(literal 0 binary64) (-.f64 #s(literal 1 binary64) (exp.f64 (*.f64 x #s(literal 2 binary64)))))) (pow.f64 (-.f64 #s(literal 0 binary64) (-.f64 #s(literal 1 binary64) (exp.f64 x))) #s(literal 1/2 binary64)))
(/.f64 (sqrt.f64 (expm1.f64 (*.f64 x #s(literal 2 binary64)))) (pow.f64 (expm1.f64 x) #s(literal 1/2 binary64)))
(/.f64 (sqrt.f64 (-.f64 #s(literal 1 binary64) (exp.f64 (*.f64 x #s(literal 6 binary64))))) (sqrt.f64 (*.f64 (-.f64 (exp.f64 (*.f64 x #s(literal 2 binary64))) (expm1.f64 x)) (-.f64 #s(literal 1 binary64) (exp.f64 (*.f64 x #s(literal 3 binary64)))))))
(/.f64 (sqrt.f64 (-.f64 #s(literal 1 binary64) (exp.f64 (*.f64 x #s(literal 6 binary64))))) (sqrt.f64 (*.f64 (-.f64 #s(literal 1 binary64) (exp.f64 x)) (+.f64 #s(literal 1 binary64) (+.f64 (exp.f64 (*.f64 x #s(literal 2 binary64))) (exp.f64 (*.f64 x #s(literal 4 binary64))))))))
(/.f64 (sqrt.f64 (-.f64 #s(literal 1 binary64) (exp.f64 (*.f64 x #s(literal 4 binary64))))) (sqrt.f64 (*.f64 (-.f64 #s(literal 1 binary64) (exp.f64 x)) (+.f64 #s(literal 1 binary64) (exp.f64 (*.f64 x #s(literal 2 binary64)))))))
(/.f64 (neg.f64 (hypot.f64 #s(literal 1 binary64) (exp.f64 (*.f64 x #s(literal 3/2 binary64))))) (neg.f64 (sqrt.f64 (-.f64 (exp.f64 (*.f64 x #s(literal 2 binary64))) (expm1.f64 x)))))
(/.f64 (neg.f64 (sqrt.f64 (-.f64 #s(literal 1 binary64) (exp.f64 (*.f64 x #s(literal 2 binary64)))))) (neg.f64 (pow.f64 (-.f64 #s(literal 1 binary64) (exp.f64 x)) #s(literal 1/2 binary64))))
(/.f64 (sqrt.f64 #s(literal -1 binary64)) (sqrt.f64 (neg.f64 (/.f64 #s(literal 1 binary64) (+.f64 #s(literal 1 binary64) (exp.f64 x))))))
(/.f64 (sqrt.f64 (-.f64 (*.f64 #s(literal 1 binary64) (-.f64 #s(literal 1 binary64) (exp.f64 x))) (*.f64 (-.f64 #s(literal 1 binary64) (exp.f64 x)) (exp.f64 (*.f64 x #s(literal 2 binary64)))))) (sqrt.f64 (pow.f64 (-.f64 #s(literal 1 binary64) (exp.f64 x)) #s(literal 2 binary64))))
(/.f64 (sqrt.f64 (*.f64 (+.f64 #s(literal 1 binary64) (exp.f64 (*.f64 x #s(literal 9 binary64)))) #s(literal 1 binary64))) (sqrt.f64 (*.f64 (+.f64 #s(literal 1 binary64) (*.f64 (exp.f64 (*.f64 x #s(literal 3 binary64))) (expm1.f64 (*.f64 x #s(literal 3 binary64))))) (-.f64 (exp.f64 (*.f64 x #s(literal 2 binary64))) (expm1.f64 x)))))
(/.f64 (sqrt.f64 (*.f64 (-.f64 #s(literal 1 binary64) (exp.f64 (*.f64 x #s(literal 6 binary64)))) #s(literal 1 binary64))) (sqrt.f64 (*.f64 (-.f64 #s(literal 1 binary64) (exp.f64 (*.f64 x #s(literal 3 binary64)))) (-.f64 (exp.f64 (*.f64 x #s(literal 2 binary64))) (expm1.f64 x)))))
(/.f64 (sqrt.f64 (*.f64 (-.f64 #s(literal 1 binary64) (exp.f64 (*.f64 x #s(literal 6 binary64)))) #s(literal 1 binary64))) (sqrt.f64 (*.f64 (+.f64 #s(literal 1 binary64) (+.f64 (exp.f64 (*.f64 x #s(literal 2 binary64))) (exp.f64 (*.f64 x #s(literal 4 binary64))))) (-.f64 #s(literal 1 binary64) (exp.f64 x)))))
(/.f64 (sqrt.f64 (*.f64 (-.f64 #s(literal 1 binary64) (exp.f64 (*.f64 x #s(literal 4 binary64)))) #s(literal 1 binary64))) (sqrt.f64 (*.f64 (+.f64 #s(literal 1 binary64) (exp.f64 (*.f64 x #s(literal 2 binary64)))) (-.f64 #s(literal 1 binary64) (exp.f64 x)))))
(/.f64 (sqrt.f64 (neg.f64 (-.f64 #s(literal 0 binary64) (+.f64 #s(literal 1 binary64) (exp.f64 (*.f64 x #s(literal 3 binary64))))))) (sqrt.f64 (neg.f64 (-.f64 #s(literal 0 binary64) (-.f64 (exp.f64 (*.f64 x #s(literal 2 binary64))) (expm1.f64 x))))))
(/.f64 (sqrt.f64 (neg.f64 (-.f64 #s(literal 0 binary64) (-.f64 #s(literal 1 binary64) (exp.f64 (*.f64 x #s(literal 2 binary64))))))) (sqrt.f64 (neg.f64 (-.f64 #s(literal 0 binary64) (-.f64 #s(literal 1 binary64) (exp.f64 x))))))
(/.f64 (sqrt.f64 (neg.f64 (expm1.f64 (*.f64 x #s(literal 2 binary64))))) (sqrt.f64 (neg.f64 (expm1.f64 x))))
(/.f64 (sqrt.f64 (-.f64 (pow.f64 (-.f64 #s(literal 1 binary64) (exp.f64 x)) #s(literal -3 binary64)) (/.f64 (exp.f64 (*.f64 x #s(literal 6 binary64))) (pow.f64 (-.f64 #s(literal 1 binary64) (exp.f64 x)) #s(literal 3 binary64))))) (sqrt.f64 (+.f64 (pow.f64 (-.f64 #s(literal 1 binary64) (exp.f64 x)) #s(literal -2 binary64)) (+.f64 (pow.f64 (/.f64 (exp.f64 (*.f64 x #s(literal 2 binary64))) (-.f64 #s(literal 1 binary64) (exp.f64 x))) #s(literal 2 binary64)) (*.f64 (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 1 binary64) (exp.f64 x))) (/.f64 (exp.f64 (*.f64 x #s(literal 2 binary64))) (-.f64 #s(literal 1 binary64) (exp.f64 x))))))))
(/.f64 (sqrt.f64 (-.f64 (pow.f64 (-.f64 #s(literal 1 binary64) (exp.f64 x)) #s(literal -2 binary64)) (pow.f64 (/.f64 (exp.f64 (*.f64 x #s(literal 2 binary64))) (-.f64 #s(literal 1 binary64) (exp.f64 x))) #s(literal 2 binary64)))) (sqrt.f64 (+.f64 (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 1 binary64) (exp.f64 x))) (/.f64 (exp.f64 (*.f64 x #s(literal 2 binary64))) (-.f64 #s(literal 1 binary64) (exp.f64 x))))))
(/.f64 (sqrt.f64 (*.f64 (+.f64 #s(literal 1 binary64) (exp.f64 (*.f64 x #s(literal 3 binary64)))) #s(literal 1 binary64))) (sqrt.f64 (-.f64 (exp.f64 (*.f64 x #s(literal 2 binary64))) (expm1.f64 x))))
(/.f64 (sqrt.f64 (*.f64 (-.f64 #s(literal 1 binary64) (exp.f64 (*.f64 x #s(literal 2 binary64)))) #s(literal 1 binary64))) (pow.f64 (-.f64 #s(literal 1 binary64) (exp.f64 x)) #s(literal 1/2 binary64)))
(/.f64 (sqrt.f64 (*.f64 (+.f64 #s(literal 1 binary64) (exp.f64 (*.f64 x #s(literal 9 binary64)))) (/.f64 #s(literal 1 binary64) (-.f64 (exp.f64 (*.f64 x #s(literal 2 binary64))) (expm1.f64 x))))) (sqrt.f64 (+.f64 #s(literal 1 binary64) (*.f64 (exp.f64 (*.f64 x #s(literal 3 binary64))) (expm1.f64 (*.f64 x #s(literal 3 binary64)))))))
(/.f64 (sqrt.f64 (*.f64 (-.f64 #s(literal 1 binary64) (exp.f64 (*.f64 x #s(literal 6 binary64)))) (/.f64 #s(literal 1 binary64) (-.f64 (exp.f64 (*.f64 x #s(literal 2 binary64))) (expm1.f64 x))))) (sqrt.f64 (-.f64 #s(literal 1 binary64) (exp.f64 (*.f64 x #s(literal 3 binary64))))))
(/.f64 (sqrt.f64 (*.f64 (-.f64 #s(literal 1 binary64) (exp.f64 (*.f64 x #s(literal 6 binary64)))) (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 1 binary64) (exp.f64 x))))) (sqrt.f64 (+.f64 #s(literal 1 binary64) (+.f64 (exp.f64 (*.f64 x #s(literal 2 binary64))) (exp.f64 (*.f64 x #s(literal 4 binary64)))))))
(/.f64 (sqrt.f64 (*.f64 (-.f64 #s(literal 1 binary64) (exp.f64 (*.f64 x #s(literal 4 binary64)))) (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 1 binary64) (exp.f64 x))))) (hypot.f64 #s(literal 1 binary64) (exp.f64 x)))
(/.f64 (neg.f64 (sqrt.f64 (-.f64 #s(literal 0 binary64) (+.f64 #s(literal 1 binary64) (exp.f64 (*.f64 x #s(literal 3 binary64))))))) (neg.f64 (sqrt.f64 (-.f64 #s(literal 0 binary64) (-.f64 (exp.f64 (*.f64 x #s(literal 2 binary64))) (expm1.f64 x))))))
(/.f64 (neg.f64 (sqrt.f64 (-.f64 #s(literal 0 binary64) (-.f64 #s(literal 1 binary64) (exp.f64 (*.f64 x #s(literal 2 binary64))))))) (neg.f64 (pow.f64 (-.f64 #s(literal 0 binary64) (-.f64 #s(literal 1 binary64) (exp.f64 x))) #s(literal 1/2 binary64))))
(/.f64 (neg.f64 (sqrt.f64 (expm1.f64 (*.f64 x #s(literal 2 binary64))))) (neg.f64 (pow.f64 (expm1.f64 x) #s(literal 1/2 binary64))))
(/.f64 (neg.f64 (neg.f64 (hypot.f64 #s(literal 1 binary64) (exp.f64 (*.f64 x #s(literal 3/2 binary64)))))) (neg.f64 (neg.f64 (sqrt.f64 (-.f64 (exp.f64 (*.f64 x #s(literal 2 binary64))) (expm1.f64 x))))))
(/.f64 (neg.f64 (neg.f64 (sqrt.f64 (-.f64 #s(literal 1 binary64) (exp.f64 (*.f64 x #s(literal 2 binary64))))))) (neg.f64 (neg.f64 (pow.f64 (-.f64 #s(literal 1 binary64) (exp.f64 x)) #s(literal 1/2 binary64)))))
(pow.f64 (+.f64 #s(literal 1 binary64) (exp.f64 x)) #s(literal 1/2 binary64))
(pow.f64 (/.f64 #s(literal 1 binary64) (+.f64 #s(literal 1 binary64) (exp.f64 x))) #s(literal -1/2 binary64))
(pow.f64 (pow.f64 (+.f64 #s(literal 1 binary64) (exp.f64 x)) #s(literal 1/4 binary64)) #s(literal 2 binary64))
(pow.f64 (pow.f64 (+.f64 #s(literal 1 binary64) (exp.f64 x)) #s(literal 2 binary64)) #s(literal 1/4 binary64))
(pow.f64 (/.f64 #s(literal 1 binary64) (pow.f64 (+.f64 #s(literal 1 binary64) (exp.f64 x)) #s(literal 1/2 binary64))) #s(literal -1 binary64))
(pow.f64 (exp.f64 #s(literal 1/2 binary64)) (log1p.f64 (exp.f64 x)))
(*.f64 #s(literal 1 binary64) (pow.f64 (+.f64 #s(literal 1 binary64) (exp.f64 x)) #s(literal 1/2 binary64)))
(*.f64 (pow.f64 (+.f64 #s(literal 1 binary64) (exp.f64 x)) #s(literal 1/2 binary64)) #s(literal 1 binary64))
(*.f64 (pow.f64 (+.f64 #s(literal 1 binary64) (exp.f64 x)) #s(literal 1/2 binary64)) (pow.f64 #s(literal 1 binary64) #s(literal 1/2 binary64)))
(*.f64 (hypot.f64 #s(literal 1 binary64) (exp.f64 (*.f64 x #s(literal 3/2 binary64)))) (pow.f64 (-.f64 (exp.f64 (*.f64 x #s(literal 2 binary64))) (expm1.f64 x)) #s(literal -1/2 binary64)))
(*.f64 (sqrt.f64 (-.f64 #s(literal 1 binary64) (exp.f64 (*.f64 x #s(literal 2 binary64))))) (pow.f64 (-.f64 #s(literal 1 binary64) (exp.f64 x)) #s(literal -1/2 binary64)))
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(*.f64 (/.f64 (-.f64 #s(literal 1 binary64) (exp.f64 (*.f64 x #s(literal 4 binary64)))) (/.f64 (-.f64 #s(literal 1 binary64) (exp.f64 (*.f64 x #s(literal 2 binary64)))) (-.f64 #s(literal 0 binary64) (+.f64 #s(literal 1 binary64) (exp.f64 (*.f64 x #s(literal 3 binary64))))))) (/.f64 (/.f64 #s(literal 1 binary64) (+.f64 #s(literal 1 binary64) (exp.f64 (*.f64 x #s(literal 2 binary64))))) (-.f64 #s(literal 0 binary64) (-.f64 (exp.f64 (*.f64 x #s(literal 2 binary64))) (expm1.f64 x)))))
(*.f64 (/.f64 (-.f64 #s(literal 1 binary64) (exp.f64 (*.f64 x #s(literal 4 binary64)))) (/.f64 (-.f64 #s(literal 1 binary64) (exp.f64 (*.f64 x #s(literal 2 binary64)))) (-.f64 #s(literal 0 binary64) (-.f64 #s(literal 1 binary64) (exp.f64 (*.f64 x #s(literal 2 binary64))))))) (/.f64 (/.f64 #s(literal 1 binary64) (+.f64 #s(literal 1 binary64) (exp.f64 (*.f64 x #s(literal 2 binary64))))) (-.f64 #s(literal 0 binary64) (-.f64 #s(literal 1 binary64) (exp.f64 x)))))
(*.f64 (/.f64 (-.f64 #s(literal 1 binary64) (exp.f64 (*.f64 x #s(literal 4 binary64)))) (/.f64 (-.f64 #s(literal 1 binary64) (exp.f64 (*.f64 x #s(literal 2 binary64)))) (expm1.f64 (*.f64 x #s(literal 2 binary64))))) (/.f64 (/.f64 #s(literal 1 binary64) (+.f64 #s(literal 1 binary64) (exp.f64 (*.f64 x #s(literal 2 binary64))))) (expm1.f64 x)))
(*.f64 (/.f64 (-.f64 #s(literal 1 binary64) (exp.f64 (*.f64 x #s(literal 2 binary64)))) (/.f64 (-.f64 #s(literal 1 binary64) (exp.f64 (*.f64 x #s(literal 2 binary64)))) (+.f64 #s(literal 1 binary64) (exp.f64 (*.f64 x #s(literal 3 binary64)))))) (/.f64 #s(literal 1 binary64) (-.f64 (exp.f64 (*.f64 x #s(literal 2 binary64))) (expm1.f64 x))))
(*.f64 (/.f64 (-.f64 #s(literal 1 binary64) (exp.f64 (*.f64 x #s(literal 2 binary64)))) (/.f64 (-.f64 #s(literal 1 binary64) (exp.f64 (*.f64 x #s(literal 2 binary64)))) (-.f64 #s(literal 1 binary64) (exp.f64 (*.f64 x #s(literal 2 binary64)))))) (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 1 binary64) (exp.f64 x))))
(*.f64 (/.f64 (-.f64 #s(literal 1 binary64) (exp.f64 (*.f64 x #s(literal 2 binary64)))) (/.f64 (-.f64 #s(literal 1 binary64) (exp.f64 (*.f64 x #s(literal 2 binary64)))) #s(literal 1 binary64))) (+.f64 #s(literal 1 binary64) (exp.f64 x)))
(*.f64 (/.f64 (-.f64 #s(literal 1 binary64) (exp.f64 (*.f64 x #s(literal 2 binary64)))) (/.f64 (-.f64 #s(literal 1 binary64) (exp.f64 (*.f64 x #s(literal 2 binary64)))) (-.f64 #s(literal 0 binary64) (+.f64 #s(literal 1 binary64) (exp.f64 (*.f64 x #s(literal 3 binary64))))))) (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 0 binary64) (-.f64 (exp.f64 (*.f64 x #s(literal 2 binary64))) (expm1.f64 x)))))
(*.f64 (/.f64 (-.f64 #s(literal 1 binary64) (exp.f64 (*.f64 x #s(literal 2 binary64)))) (/.f64 (-.f64 #s(literal 1 binary64) (exp.f64 (*.f64 x #s(literal 2 binary64)))) (-.f64 #s(literal 0 binary64) (-.f64 #s(literal 1 binary64) (exp.f64 (*.f64 x #s(literal 2 binary64))))))) (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 0 binary64) (-.f64 #s(literal 1 binary64) (exp.f64 x)))))
(*.f64 (/.f64 (-.f64 #s(literal 1 binary64) (exp.f64 (*.f64 x #s(literal 2 binary64)))) (/.f64 (-.f64 #s(literal 1 binary64) (exp.f64 (*.f64 x #s(literal 2 binary64)))) (expm1.f64 (*.f64 x #s(literal 2 binary64))))) (/.f64 #s(literal 1 binary64) (expm1.f64 x)))
(exp.f64 x)
(exp.f64 (*.f64 x #s(literal 1 binary64)))
(pow.f64 (exp.f64 x) #s(literal 1 binary64))
(*.f64 #s(literal 1 binary64) (exp.f64 x))
(*.f64 (exp.f64 x) #s(literal 1 binary64))

simplify212.0ms (2.9%)

Algorithm
egg-herbie
Rules
3346×*-lowering-*.f32
3346×*-lowering-*.f64
1870×+-lowering-+.f64
1870×+-lowering-+.f32
1432×fma-lowering-fma.f32
Iterations

Useful iterations: 4 (0.0ms)

IterNodesCost
052221
1162175
2539174
31189171
42839170
56888170
08224170
Stop Event
iter limit
node limit
Counts
36 → 36
Calls
Call 1
Inputs
(sqrt 2)
(+ (sqrt 2) (* 1/2 (/ x (sqrt 2))))
(+ (sqrt 2) (* x (+ (* 1/2 (/ (* x (- 1/2 (* 1/4 (/ 1 (pow (sqrt 2) 2))))) (sqrt 2))) (* 1/2 (/ 1 (sqrt 2))))))
(+ (sqrt 2) (* x (+ (* x (+ (* 1/2 (/ (* x (- 1/6 (* 1/2 (/ (- 1/2 (* 1/4 (/ 1 (pow (sqrt 2) 2)))) (pow (sqrt 2) 2))))) (sqrt 2))) (* 1/2 (/ (- 1/2 (* 1/4 (/ 1 (pow (sqrt 2) 2)))) (sqrt 2))))) (* 1/2 (/ 1 (sqrt 2))))))
(sqrt (+ 1 (exp x)))
(sqrt (+ 1 (exp x)))
(sqrt (+ 1 (exp x)))
(sqrt (+ 1 (exp x)))
(sqrt (+ 1 (exp x)))
(sqrt (+ 1 (exp x)))
(sqrt (+ 1 (exp x)))
(sqrt (+ 1 (exp x)))
2
(+ 2 x)
(+ 2 (* x (+ 1 (* 1/2 x))))
(+ 2 (* x (+ 1 (* x (+ 1/2 (* 1/6 x))))))
(+ 1 (exp x))
(+ 1 (exp x))
(+ 1 (exp x))
(+ 1 (exp x))
(+ 1 (exp x))
(+ 1 (exp x))
(+ 1 (exp x))
(+ 1 (exp x))
1
(+ 1 x)
(+ 1 (* x (+ 1 (* 1/2 x))))
(+ 1 (* x (+ 1 (* x (+ 1/2 (* 1/6 x))))))
(exp x)
(exp x)
(exp x)
(exp x)
(exp x)
(exp x)
(exp x)
(exp x)
Outputs
(sqrt 2)
(sqrt.f64 #s(literal 2 binary64))
(+ (sqrt 2) (* 1/2 (/ x (sqrt 2))))
(+.f64 (sqrt.f64 #s(literal 2 binary64)) (*.f64 x (/.f64 #s(literal 1/2 binary64) (sqrt.f64 #s(literal 2 binary64)))))
(+ (sqrt 2) (* x (+ (* 1/2 (/ (* x (- 1/2 (* 1/4 (/ 1 (pow (sqrt 2) 2))))) (sqrt 2))) (* 1/2 (/ 1 (sqrt 2))))))
(+.f64 (sqrt.f64 #s(literal 2 binary64)) (/.f64 (*.f64 x (+.f64 #s(literal 1/2 binary64) (*.f64 x #s(literal 3/16 binary64)))) (sqrt.f64 #s(literal 2 binary64))))
(+ (sqrt 2) (* x (+ (* x (+ (* 1/2 (/ (* x (- 1/6 (* 1/2 (/ (- 1/2 (* 1/4 (/ 1 (pow (sqrt 2) 2)))) (pow (sqrt 2) 2))))) (sqrt 2))) (* 1/2 (/ (- 1/2 (* 1/4 (/ 1 (pow (sqrt 2) 2)))) (sqrt 2))))) (* 1/2 (/ 1 (sqrt 2))))))
(+.f64 (sqrt.f64 #s(literal 2 binary64)) (*.f64 (/.f64 x (sqrt.f64 #s(literal 2 binary64))) (+.f64 (+.f64 #s(literal 1/2 binary64) (*.f64 x #s(literal 3/16 binary64))) (*.f64 x (*.f64 x #s(literal 7/192 binary64))))))
(sqrt (+ 1 (exp x)))
(sqrt.f64 (+.f64 #s(literal 1 binary64) (exp.f64 x)))
(sqrt (+ 1 (exp x)))
(sqrt.f64 (+.f64 #s(literal 1 binary64) (exp.f64 x)))
(sqrt (+ 1 (exp x)))
(sqrt.f64 (+.f64 #s(literal 1 binary64) (exp.f64 x)))
(sqrt (+ 1 (exp x)))
(sqrt.f64 (+.f64 #s(literal 1 binary64) (exp.f64 x)))
(sqrt (+ 1 (exp x)))
(sqrt.f64 (+.f64 #s(literal 1 binary64) (exp.f64 x)))
(sqrt (+ 1 (exp x)))
(sqrt.f64 (+.f64 #s(literal 1 binary64) (exp.f64 x)))
(sqrt (+ 1 (exp x)))
(sqrt.f64 (+.f64 #s(literal 1 binary64) (exp.f64 x)))
(sqrt (+ 1 (exp x)))
(sqrt.f64 (+.f64 #s(literal 1 binary64) (exp.f64 x)))
2
#s(literal 2 binary64)
(+ 2 x)
(+.f64 #s(literal 2 binary64) x)
(+ 2 (* x (+ 1 (* 1/2 x))))
(+.f64 #s(literal 2 binary64) (*.f64 x (+.f64 #s(literal 1 binary64) (*.f64 #s(literal 1/2 binary64) x))))
(+ 2 (* x (+ 1 (* x (+ 1/2 (* 1/6 x))))))
(+.f64 #s(literal 2 binary64) (*.f64 x (+.f64 #s(literal 1 binary64) (*.f64 x (+.f64 #s(literal 1/2 binary64) (*.f64 x #s(literal 1/6 binary64)))))))
(+ 1 (exp x))
(+.f64 #s(literal 1 binary64) (exp.f64 x))
(+ 1 (exp x))
(+.f64 #s(literal 1 binary64) (exp.f64 x))
(+ 1 (exp x))
(+.f64 #s(literal 1 binary64) (exp.f64 x))
(+ 1 (exp x))
(+.f64 #s(literal 1 binary64) (exp.f64 x))
(+ 1 (exp x))
(+.f64 #s(literal 1 binary64) (exp.f64 x))
(+ 1 (exp x))
(+.f64 #s(literal 1 binary64) (exp.f64 x))
(+ 1 (exp x))
(+.f64 #s(literal 1 binary64) (exp.f64 x))
(+ 1 (exp x))
(+.f64 #s(literal 1 binary64) (exp.f64 x))
1
#s(literal 1 binary64)
(+ 1 x)
(+.f64 x #s(literal 1 binary64))
(+ 1 (* x (+ 1 (* 1/2 x))))
(+.f64 #s(literal 1 binary64) (*.f64 x (+.f64 #s(literal 1 binary64) (*.f64 #s(literal 1/2 binary64) x))))
(+ 1 (* x (+ 1 (* x (+ 1/2 (* 1/6 x))))))
(+.f64 #s(literal 1 binary64) (*.f64 x (+.f64 #s(literal 1 binary64) (*.f64 x (+.f64 #s(literal 1/2 binary64) (*.f64 x #s(literal 1/6 binary64)))))))
(exp x)
(exp.f64 x)
(exp x)
(exp.f64 x)
(exp x)
(exp.f64 x)
(exp x)
(exp.f64 x)
(exp x)
(exp.f64 x)
(exp x)
(exp.f64 x)
(exp x)
(exp.f64 x)
(exp x)
(exp.f64 x)

eval267.0ms (3.7%)

Compiler

Compiled 6138 to 918 computations (85% saved)

prune32.0ms (0.4%)

Pruning

5 alts after pruning (4 fresh and 1 done)

PrunedKeptTotal
New2734277
Fresh000
Picked011
Done000
Total2735278
Accuracy
100.0%
Counts
278 → 5
Alt Table
Click to see full alt table
StatusAccuracyProgram
63.9%
(sqrt.f64 (+.f64 #s(literal 2 binary64) (*.f64 x (+.f64 #s(literal 1 binary64) (*.f64 x (+.f64 #s(literal 1/2 binary64) (*.f64 x #s(literal 1/6 binary64))))))))
65.6%
(sqrt.f64 (+.f64 #s(literal 2 binary64) (*.f64 x (+.f64 #s(literal 1 binary64) (*.f64 #s(literal 1/2 binary64) x)))))
63.5%
(sqrt.f64 (+.f64 #s(literal 2 binary64) x))
100.0%
(sqrt.f64 (+.f64 #s(literal 1 binary64) (exp.f64 x)))
70.2%
(sqrt.f64 #s(literal 2 binary64))
Compiler

Compiled 40 to 33 computations (17.5% saved)

simplify32.0ms (0.4%)

Algorithm
egg-herbie
Localize:

Found 11 expressions of interest:

NewMetricScoreProgram
cost-diff0
(+.f64 #s(literal 1 binary64) (*.f64 x (+.f64 #s(literal 1/2 binary64) (*.f64 x #s(literal 1/6 binary64)))))
cost-diff0
(*.f64 x (+.f64 #s(literal 1 binary64) (*.f64 x (+.f64 #s(literal 1/2 binary64) (*.f64 x #s(literal 1/6 binary64))))))
cost-diff0
(+.f64 #s(literal 2 binary64) (*.f64 x (+.f64 #s(literal 1 binary64) (*.f64 x (+.f64 #s(literal 1/2 binary64) (*.f64 x #s(literal 1/6 binary64)))))))
cost-diff0
(sqrt.f64 (+.f64 #s(literal 2 binary64) (*.f64 x (+.f64 #s(literal 1 binary64) (*.f64 x (+.f64 #s(literal 1/2 binary64) (*.f64 x #s(literal 1/6 binary64))))))))
cost-diff0
(+.f64 #s(literal 1 binary64) (*.f64 #s(literal 1/2 binary64) x))
cost-diff0
(*.f64 x (+.f64 #s(literal 1 binary64) (*.f64 #s(literal 1/2 binary64) x)))
cost-diff0
(+.f64 #s(literal 2 binary64) (*.f64 x (+.f64 #s(literal 1 binary64) (*.f64 #s(literal 1/2 binary64) x))))
cost-diff0
(sqrt.f64 (+.f64 #s(literal 2 binary64) (*.f64 x (+.f64 #s(literal 1 binary64) (*.f64 #s(literal 1/2 binary64) x)))))
cost-diff0
(+.f64 #s(literal 2 binary64) x)
cost-diff0
(sqrt.f64 (+.f64 #s(literal 2 binary64) x))
cost-diff0
(sqrt.f64 #s(literal 2 binary64))
Rules
500×fma-define
400×fma-lowering-fma.f32
400×fma-lowering-fma.f64
146×sum3-define
134×*-lowering-*.f32
Iterations

Useful iterations: 1 (0.0ms)

IterNodesCost
020117
14899
212199
326099
444399
556199
658499
058499
Stop Event
iter limit
saturated
Calls
Call 1
Inputs
(sqrt 2)
2
(sqrt (+ 2 x))
(+ 2 x)
2
x
(sqrt (+ 2 (* x (+ 1 (* 1/2 x)))))
(+ 2 (* x (+ 1 (* 1/2 x))))
2
(* x (+ 1 (* 1/2 x)))
x
(+ 1 (* 1/2 x))
1
(* 1/2 x)
1/2
(sqrt (+ 2 (* x (+ 1 (* x (+ 1/2 (* x 1/6)))))))
(+ 2 (* x (+ 1 (* x (+ 1/2 (* x 1/6))))))
2
(* x (+ 1 (* x (+ 1/2 (* x 1/6)))))
x
(+ 1 (* x (+ 1/2 (* x 1/6))))
1
(* x (+ 1/2 (* x 1/6)))
(+ 1/2 (* x 1/6))
1/2
(* x 1/6)
1/6
Outputs
(sqrt 2)
(sqrt.f64 #s(literal 2 binary64))
2
#s(literal 2 binary64)
(sqrt (+ 2 x))
(sqrt.f64 (+.f64 #s(literal 2 binary64) x))
(+ 2 x)
(+.f64 #s(literal 2 binary64) x)
2
#s(literal 2 binary64)
x
(sqrt (+ 2 (* x (+ 1 (* 1/2 x)))))
(sqrt.f64 (+.f64 #s(literal 2 binary64) (*.f64 x (+.f64 #s(literal 1 binary64) (*.f64 x #s(literal 1/2 binary64))))))
(+ 2 (* x (+ 1 (* 1/2 x))))
(+.f64 #s(literal 2 binary64) (*.f64 x (+.f64 #s(literal 1 binary64) (*.f64 x #s(literal 1/2 binary64)))))
2
#s(literal 2 binary64)
(* x (+ 1 (* 1/2 x)))
(*.f64 x (+.f64 #s(literal 1 binary64) (*.f64 x #s(literal 1/2 binary64))))
x
(+ 1 (* 1/2 x))
(+.f64 #s(literal 1 binary64) (*.f64 x #s(literal 1/2 binary64)))
1
#s(literal 1 binary64)
(* 1/2 x)
(*.f64 x #s(literal 1/2 binary64))
1/2
#s(literal 1/2 binary64)
(sqrt (+ 2 (* x (+ 1 (* x (+ 1/2 (* x 1/6)))))))
(sqrt.f64 (+.f64 #s(literal 2 binary64) (*.f64 x (+.f64 #s(literal 1 binary64) (*.f64 x (+.f64 #s(literal 1/2 binary64) (*.f64 x #s(literal 1/6 binary64))))))))
(+ 2 (* x (+ 1 (* x (+ 1/2 (* x 1/6))))))
(+.f64 #s(literal 2 binary64) (*.f64 x (+.f64 #s(literal 1 binary64) (*.f64 x (+.f64 #s(literal 1/2 binary64) (*.f64 x #s(literal 1/6 binary64)))))))
2
#s(literal 2 binary64)
(* x (+ 1 (* x (+ 1/2 (* x 1/6)))))
(*.f64 x (+.f64 #s(literal 1 binary64) (*.f64 x (+.f64 #s(literal 1/2 binary64) (*.f64 x #s(literal 1/6 binary64))))))
x
(+ 1 (* x (+ 1/2 (* x 1/6))))
(+.f64 #s(literal 1 binary64) (*.f64 x (+.f64 #s(literal 1/2 binary64) (*.f64 x #s(literal 1/6 binary64)))))
1
#s(literal 1 binary64)
(* x (+ 1/2 (* x 1/6)))
(*.f64 x (+.f64 #s(literal 1/2 binary64) (*.f64 x #s(literal 1/6 binary64))))
(+ 1/2 (* x 1/6))
(+.f64 #s(literal 1/2 binary64) (*.f64 x #s(literal 1/6 binary64)))
1/2
#s(literal 1/2 binary64)
(* x 1/6)
(*.f64 x #s(literal 1/6 binary64))
1/6
#s(literal 1/6 binary64)

localize91.0ms (1.3%)

Localize:

Found 11 expressions of interest:

NewMetricScoreProgram
accuracy100.0%
(sqrt.f64 (+.f64 #s(literal 2 binary64) (*.f64 x (+.f64 #s(literal 1 binary64) (*.f64 x (+.f64 #s(literal 1/2 binary64) (*.f64 x #s(literal 1/6 binary64))))))))
accuracy100.0%
(*.f64 x (+.f64 #s(literal 1/2 binary64) (*.f64 x #s(literal 1/6 binary64))))
accuracy100.0%
(*.f64 x (+.f64 #s(literal 1 binary64) (*.f64 x (+.f64 #s(literal 1/2 binary64) (*.f64 x #s(literal 1/6 binary64))))))
accuracy99.7%
(*.f64 x #s(literal 1/6 binary64))
accuracy100.0%
(+.f64 #s(literal 1 binary64) (*.f64 #s(literal 1/2 binary64) x))
accuracy100.0%
(*.f64 x (+.f64 #s(literal 1 binary64) (*.f64 #s(literal 1/2 binary64) x)))
accuracy100.0%
(*.f64 #s(literal 1/2 binary64) x)
accuracy100.0%
(sqrt.f64 (+.f64 #s(literal 2 binary64) (*.f64 x (+.f64 #s(literal 1 binary64) (*.f64 #s(literal 1/2 binary64) x)))))
accuracy100.0%
(+.f64 #s(literal 2 binary64) x)
accuracy100.0%
(sqrt.f64 (+.f64 #s(literal 2 binary64) x))
accuracy100.0%
(sqrt.f64 #s(literal 2 binary64))
Results
42.0ms165×0valid
21.0ms91×0invalid
Compiler

Compiled 119 to 21 computations (82.4% saved)

Precisions
Click to see histograms. Total time spent on operations: 40.0ms
ival-add: 11.0ms (27.3% of total)
ival-sqrt: 11.0ms (27.3% of total)
ival-mult: 9.0ms (22.3% of total)
...c/correct-round.rkt:119:19: 9.0ms (22.3% of total)
const: 1.0ms (2.5% of total)
backward-pass: 0.0ms (0% of total)

series12.0ms (0.2%)

Counts
14 → 156
Calls
Call 1
Inputs
#<alt (sqrt 2)>
#<alt (sqrt (+ 2 x))>
#<alt (+ 2 x)>
#<alt (sqrt (+ 2 (* x (+ 1 (* 1/2 x)))))>
#<alt (+ 2 (* x (+ 1 (* 1/2 x))))>
#<alt (* x (+ 1 (* 1/2 x)))>
#<alt (+ 1 (* 1/2 x))>
#<alt (sqrt (+ 2 (* x (+ 1 (* x (+ 1/2 (* x 1/6)))))))>
#<alt (+ 2 (* x (+ 1 (* x (+ 1/2 (* x 1/6))))))>
#<alt (* x (+ 1 (* x (+ 1/2 (* x 1/6)))))>
#<alt (+ 1 (* x (+ 1/2 (* x 1/6))))>
#<alt (* 1/2 x)>
#<alt (* x 1/6)>
#<alt (* x (+ 1/2 (* x 1/6)))>
Outputs
#<alt (sqrt 2)>
#<alt (+ (sqrt 2) (* 1/2 (/ x (sqrt 2))))>
#<alt (+ (sqrt 2) (* x (+ (* -1/8 (/ x (pow (sqrt 2) 3))) (* 1/2 (/ 1 (sqrt 2))))))>
#<alt (+ (sqrt 2) (* x (+ (* x (- (* 1/16 (/ x (pow (sqrt 2) 5))) (* 1/8 (/ 1 (pow (sqrt 2) 3))))) (* 1/2 (/ 1 (sqrt 2))))))>
#<alt (sqrt x)>
#<alt (* x (+ (sqrt (/ 1 x)) (sqrt (/ 1 (pow x 3)))))>
#<alt (* x (+ (sqrt (/ 1 x)) (+ (sqrt (/ 1 (pow x 3))) (* -1/2 (sqrt (/ 1 (pow x 5)))))))>
#<alt (* x (+ (sqrt (/ 1 x)) (+ (sqrt (/ 1 (pow x 3))) (+ (* -1/2 (sqrt (/ 1 (pow x 5)))) (* 1/2 (sqrt (/ 1 (pow x 7))))))))>
#<alt (* -1 (* (sqrt x) (pow (sqrt -1) 2)))>
#<alt (* -1 (* x (+ (sqrt (/ 1 (pow x 3))) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)))))>
#<alt (* -1 (* x (+ (sqrt (/ 1 (pow x 3))) (+ (* -1/2 (* (sqrt (/ 1 (pow x 5))) (/ 1 (pow (sqrt -1) 2)))) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))))))>
#<alt (* -1 (* x (+ (sqrt (/ 1 (pow x 3))) (+ (* -1/2 (* (sqrt (/ 1 (pow x 5))) (/ 1 (pow (sqrt -1) 2)))) (+ (* 1/2 (* (sqrt (/ 1 (pow x 7))) (/ 1 (pow (sqrt -1) 4)))) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)))))))>
#<alt 2>
#<alt (+ 2 x)>
#<alt (+ 2 x)>
#<alt (+ 2 x)>
#<alt x>
#<alt (* x (+ 1 (* 2 (/ 1 x))))>
#<alt (* x (+ 1 (* 2 (/ 1 x))))>
#<alt (* x (+ 1 (* 2 (/ 1 x))))>
#<alt x>
#<alt (* x (+ 1 (* 2 (/ 1 x))))>
#<alt (* x (+ 1 (* 2 (/ 1 x))))>
#<alt (* x (+ 1 (* 2 (/ 1 x))))>
#<alt (sqrt 2)>
#<alt (+ (sqrt 2) (* 1/2 (/ x (sqrt 2))))>
#<alt (+ (sqrt 2) (* x (+ (* 1/2 (/ (* x (- 1/2 (* 1/4 (/ 1 (pow (sqrt 2) 2))))) (sqrt 2))) (* 1/2 (/ 1 (sqrt 2))))))>
#<alt (+ (sqrt 2) (* x (+ (* x (+ (* -1/4 (/ (* x (- 1/2 (* 1/4 (/ 1 (pow (sqrt 2) 2))))) (pow (sqrt 2) 3))) (* 1/2 (/ (- 1/2 (* 1/4 (/ 1 (pow (sqrt 2) 2)))) (sqrt 2))))) (* 1/2 (/ 1 (sqrt 2))))))>
#<alt (* x (sqrt 1/2))>
#<alt (* x (+ (sqrt 1/2) (* 1/2 (/ 1 (* x (sqrt 1/2))))))>
#<alt (* x (+ (sqrt 1/2) (+ (* 1/2 (/ (- 2 (* 1/4 (/ 1 (pow (sqrt 1/2) 2)))) (* (pow x 2) (sqrt 1/2)))) (/ 1/2 (* x (sqrt 1/2))))))>
#<alt (* x (+ (sqrt 1/2) (+ (* -1/4 (/ (- 2 (* 1/4 (/ 1 (pow (sqrt 1/2) 2)))) (* (pow x 3) (pow (sqrt 1/2) 3)))) (+ (* 1/2 (/ (- 2 (* 1/4 (/ 1 (pow (sqrt 1/2) 2)))) (* (pow x 2) (sqrt 1/2)))) (/ 1/2 (* x (sqrt 1/2)))))))>
#<alt (* -1 (* x (sqrt 1/2)))>
#<alt (* -1 (* x (+ (sqrt 1/2) (* 1/2 (/ 1 (* x (sqrt 1/2)))))))>
#<alt (* -1 (* x (+ (sqrt 1/2) (* -1 (/ (- (* -1/2 (/ (- 2 (* 1/4 (/ 1 (pow (sqrt 1/2) 2)))) (* x (sqrt 1/2)))) (* 1/2 (/ 1 (sqrt 1/2)))) x)))))>
#<alt (* -1 (* x (+ (sqrt 1/2) (* -1 (/ (- (* -1 (/ (+ (* -1/4 (/ (- 2 (* 1/4 (/ 1 (pow (sqrt 1/2) 2)))) (* x (pow (sqrt 1/2) 3)))) (* 1/2 (/ (- 2 (* 1/4 (/ 1 (pow (sqrt 1/2) 2)))) (sqrt 1/2)))) x)) (* 1/2 (/ 1 (sqrt 1/2)))) x)))))>
#<alt 2>
#<alt (+ 2 x)>
#<alt (+ 2 (* x (+ 1 (* 1/2 x))))>
#<alt (+ 2 (* x (+ 1 (* 1/2 x))))>
#<alt (* 1/2 (pow x 2))>
#<alt (* (pow x 2) (+ 1/2 (/ 1 x)))>
#<alt (* (pow x 2) (+ 1/2 (+ (/ 1 x) (/ 2 (pow x 2)))))>
#<alt (* (pow x 2) (+ 1/2 (+ (/ 1 x) (/ 2 (pow x 2)))))>
#<alt (* 1/2 (pow x 2))>
#<alt (* (pow x 2) (+ 1/2 (/ 1 x)))>
#<alt (* (pow x 2) (+ 1/2 (+ (/ 1 x) (/ 2 (pow x 2)))))>
#<alt (* (pow x 2) (+ 1/2 (+ (/ 1 x) (/ 2 (pow x 2)))))>
#<alt x>
#<alt (* x (+ 1 (* 1/2 x)))>
#<alt (* x (+ 1 (* 1/2 x)))>
#<alt (* x (+ 1 (* 1/2 x)))>
#<alt (* 1/2 (pow x 2))>
#<alt (* (pow x 2) (+ 1/2 (/ 1 x)))>
#<alt (* (pow x 2) (+ 1/2 (/ 1 x)))>
#<alt (* (pow x 2) (+ 1/2 (/ 1 x)))>
#<alt (* 1/2 (pow x 2))>
#<alt (* (pow x 2) (+ 1/2 (/ 1 x)))>
#<alt (* (pow x 2) (+ 1/2 (/ 1 x)))>
#<alt (* (pow x 2) (+ 1/2 (/ 1 x)))>
#<alt 1>
#<alt (+ 1 (* 1/2 x))>
#<alt (+ 1 (* 1/2 x))>
#<alt (+ 1 (* 1/2 x))>
#<alt (* 1/2 x)>
#<alt (* x (+ 1/2 (/ 1 x)))>
#<alt (* x (+ 1/2 (/ 1 x)))>
#<alt (* x (+ 1/2 (/ 1 x)))>
#<alt (* 1/2 x)>
#<alt (* x (+ 1/2 (/ 1 x)))>
#<alt (* x (+ 1/2 (/ 1 x)))>
#<alt (* x (+ 1/2 (/ 1 x)))>
#<alt (sqrt 2)>
#<alt (+ (sqrt 2) (* 1/2 (/ x (sqrt 2))))>
#<alt (+ (sqrt 2) (* x (+ (* 1/2 (/ (* x (- 1/2 (* 1/4 (/ 1 (pow (sqrt 2) 2))))) (sqrt 2))) (* 1/2 (/ 1 (sqrt 2))))))>
#<alt (+ (sqrt 2) (* x (+ (* x (+ (* 1/2 (/ (* x (- 1/6 (* 1/2 (/ (- 1/2 (* 1/4 (/ 1 (pow (sqrt 2) 2)))) (pow (sqrt 2) 2))))) (sqrt 2))) (* 1/2 (/ (- 1/2 (* 1/4 (/ 1 (pow (sqrt 2) 2)))) (sqrt 2))))) (* 1/2 (/ 1 (sqrt 2))))))>
#<alt (* (sqrt (pow x 3)) (sqrt 1/6))>
#<alt (* (pow x 2) (+ (* 1/4 (* (sqrt (/ 1 (pow x 3))) (/ 1 (sqrt 1/6)))) (* (sqrt (/ 1 x)) (sqrt 1/6))))>
#<alt (* (pow x 2) (+ (* 1/4 (* (sqrt (/ 1 (pow x 3))) (/ 1 (sqrt 1/6)))) (+ (* 1/2 (* (sqrt (/ 1 (pow x 5))) (/ 1 (sqrt 1/6)))) (* (sqrt (/ 1 x)) (sqrt 1/6)))))>
#<alt (* (pow x 2) (+ (* 1/4 (* (sqrt (/ 1 (pow x 3))) (/ 1 (sqrt 1/6)))) (+ (* 1/2 (* (sqrt (/ 1 (pow x 5))) (/ 1 (sqrt 1/6)))) (+ (* 1/2 (* (sqrt (/ 1 (pow x 7))) (/ (- 2 (* 1/16 (/ x (pow (sqrt 1/6) 2)))) (sqrt 1/6)))) (* (sqrt (/ 1 x)) (sqrt 1/6))))))>
#<alt (* (sqrt (pow x 3)) (* (sqrt -1) (sqrt -1/6)))>
#<alt (* (pow x 2) (+ (* 1/4 (* (sqrt (/ 1 (pow x 3))) (/ (sqrt -1) (sqrt -1/6)))) (* (sqrt (/ 1 x)) (* (sqrt -1) (sqrt -1/6)))))>
#<alt (* (pow x 2) (+ (* 1/4 (* (sqrt (/ 1 (pow x 3))) (/ (sqrt -1) (sqrt -1/6)))) (+ (* 1/2 (* (sqrt (/ 1 (pow x 5))) (/ (sqrt -1) (sqrt -1/6)))) (* (sqrt (/ 1 x)) (* (sqrt -1) (sqrt -1/6))))))>
#<alt (* (pow x 2) (+ (* -1 (/ (+ (* -1/2 (* (sqrt x) (/ (sqrt -1) (sqrt -1/6)))) (* -1/2 (* (sqrt (/ 1 x)) (/ (* (sqrt -1) (- 2 (* -1/16 (/ x (pow (sqrt -1/6) 2))))) (sqrt -1/6))))) (pow x 3))) (+ (* 1/4 (* (sqrt (/ 1 (pow x 3))) (/ (sqrt -1) (sqrt -1/6)))) (* (sqrt (/ 1 x)) (* (sqrt -1) (sqrt -1/6))))))>
#<alt 2>
#<alt (+ 2 x)>
#<alt (+ 2 (* x (+ 1 (* 1/2 x))))>
#<alt (+ 2 (* x (+ 1 (* x (+ 1/2 (* 1/6 x))))))>
#<alt (* 1/6 (pow x 3))>
#<alt (* (pow x 3) (+ 1/6 (* 1/2 (/ 1 x))))>
#<alt (* (pow x 3) (+ 1/6 (+ (* 1/2 (/ 1 x)) (/ 1 (pow x 2)))))>
#<alt (* (pow x 3) (+ 1/6 (+ (* 1/2 (/ 1 x)) (+ (/ 1 (pow x 2)) (* 2 (/ 1 (pow x 3)))))))>
#<alt (* 1/6 (pow x 3))>
#<alt (* (pow x 3) (+ 1/6 (* 1/2 (/ 1 x))))>
#<alt (* -1 (* (pow x 3) (- (* -1 (/ (+ 1/2 (/ 1 x)) x)) 1/6)))>
#<alt (* -1 (* (pow x 3) (- (* -1 (/ (+ 1/2 (+ (/ 1 x) (/ 2 (pow x 2)))) x)) 1/6)))>
#<alt x>
#<alt (* x (+ 1 (* 1/2 x)))>
#<alt (* x (+ 1 (* x (+ 1/2 (* 1/6 x)))))>
#<alt (* x (+ 1 (* x (+ 1/2 (* 1/6 x)))))>
#<alt (* 1/6 (pow x 3))>
#<alt (* (pow x 3) (+ 1/6 (* 1/2 (/ 1 x))))>
#<alt (* (pow x 3) (+ 1/6 (+ (* 1/2 (/ 1 x)) (/ 1 (pow x 2)))))>
#<alt (* (pow x 3) (+ 1/6 (+ (* 1/2 (/ 1 x)) (/ 1 (pow x 2)))))>
#<alt (* 1/6 (pow x 3))>
#<alt (* (pow x 3) (+ 1/6 (* 1/2 (/ 1 x))))>
#<alt (* -1 (* (pow x 3) (- (* -1 (/ (+ 1/2 (/ 1 x)) x)) 1/6)))>
#<alt (* -1 (* (pow x 3) (- (* -1 (/ (+ 1/2 (/ 1 x)) x)) 1/6)))>
#<alt 1>
#<alt (+ 1 (* 1/2 x))>
#<alt (+ 1 (* x (+ 1/2 (* 1/6 x))))>
#<alt (+ 1 (* x (+ 1/2 (* 1/6 x))))>
#<alt (* 1/6 (pow x 2))>
#<alt (* (pow x 2) (+ 1/6 (* 1/2 (/ 1 x))))>
#<alt (* (pow x 2) (+ 1/6 (+ (* 1/2 (/ 1 x)) (/ 1 (pow x 2)))))>
#<alt (* (pow x 2) (+ 1/6 (+ (* 1/2 (/ 1 x)) (/ 1 (pow x 2)))))>
#<alt (* 1/6 (pow x 2))>
#<alt (* (pow x 2) (+ 1/6 (* 1/2 (/ 1 x))))>
#<alt (* (pow x 2) (+ 1/6 (+ (* 1/2 (/ 1 x)) (/ 1 (pow x 2)))))>
#<alt (* (pow x 2) (+ 1/6 (+ (* 1/2 (/ 1 x)) (/ 1 (pow x 2)))))>
#<alt (* 1/2 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 (* 1/6 x)>
#<alt (* 1/6 x)>
#<alt (* 1/6 x)>
#<alt (* 1/6 x)>
#<alt (* 1/6 x)>
#<alt (* 1/6 x)>
#<alt (* 1/6 x)>
#<alt (* 1/6 x)>
#<alt (* 1/6 x)>
#<alt (* 1/6 x)>
#<alt (* 1/6 x)>
#<alt (* 1/6 x)>
#<alt (* 1/2 x)>
#<alt (* x (+ 1/2 (* 1/6 x)))>
#<alt (* x (+ 1/2 (* 1/6 x)))>
#<alt (* x (+ 1/2 (* 1/6 x)))>
#<alt (* 1/6 (pow x 2))>
#<alt (* (pow x 2) (+ 1/6 (* 1/2 (/ 1 x))))>
#<alt (* (pow x 2) (+ 1/6 (* 1/2 (/ 1 x))))>
#<alt (* (pow x 2) (+ 1/6 (* 1/2 (/ 1 x))))>
#<alt (* 1/6 (pow x 2))>
#<alt (* (pow x 2) (+ 1/6 (* 1/2 (/ 1 x))))>
#<alt (* (pow x 2) (+ 1/6 (* 1/2 (/ 1 x))))>
#<alt (* (pow x 2) (+ 1/6 (* 1/2 (/ 1 x))))>
Calls

39 calls:

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

rewrite331.0ms (4.5%)

Algorithm
batch-egg-rewrite
Rules
3910×/-lowering-/.f32
3910×/-lowering-/.f64
3676×*-lowering-*.f32
3676×*-lowering-*.f64
1854×+-lowering-+.f64
Iterations

Useful iterations: 1 (0.0ms)

IterNodesCost
020100
112383
2115983
0829883
Stop Event
iter limit
node limit
Counts
14 → 424
Calls
Call 1
Inputs
(sqrt 2)
(sqrt (+ 2 x))
(+ 2 x)
(sqrt (+ 2 (* x (+ 1 (* 1/2 x)))))
(+ 2 (* x (+ 1 (* 1/2 x))))
(* x (+ 1 (* 1/2 x)))
(+ 1 (* 1/2 x))
(sqrt (+ 2 (* x (+ 1 (* x (+ 1/2 (* x 1/6)))))))
(+ 2 (* x (+ 1 (* x (+ 1/2 (* x 1/6))))))
(* x (+ 1 (* x (+ 1/2 (* x 1/6)))))
(+ 1 (* x (+ 1/2 (* x 1/6))))
(* 1/2 x)
(* x 1/6)
(* x (+ 1/2 (* x 1/6)))
Outputs
(exp.f64 (*.f64 (log.f64 #s(literal 2 binary64)) #s(literal 1/2 binary64)))
(sqrt.f64 #s(literal 2 binary64))
(pow.f64 #s(literal 2 binary64) #s(literal 1/2 binary64))
(pow.f64 #s(literal 4 binary64) #s(literal 1/4 binary64))
(pow.f64 (pow.f64 #s(literal 2 binary64) #s(literal 1/4 binary64)) #s(literal 2 binary64))
(pow.f64 (exp.f64 (log.f64 #s(literal 2 binary64))) #s(literal 1/2 binary64))
(*.f64 (pow.f64 #s(literal 2 binary64) #s(literal 1/4 binary64)) (pow.f64 #s(literal 2 binary64) #s(literal 1/4 binary64)))
(exp.f64 (*.f64 (log.f64 (+.f64 #s(literal 2 binary64) x)) #s(literal 1/2 binary64)))
(sqrt.f64 (+.f64 #s(literal 2 binary64) x))
(/.f64 #s(literal 1 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) (+.f64 #s(literal 2 binary64) x))))
(/.f64 #s(literal 1 binary64) (/.f64 (sqrt.f64 (+.f64 #s(literal 4 binary64) (*.f64 x (+.f64 x #s(literal -2 binary64))))) (sqrt.f64 (+.f64 #s(literal 8 binary64) (*.f64 x (*.f64 x x))))))
(/.f64 #s(literal 1 binary64) (/.f64 (pow.f64 (-.f64 #s(literal 2 binary64) x) #s(literal 1/2 binary64)) (pow.f64 (-.f64 #s(literal 4 binary64) (*.f64 x x)) #s(literal 1/2 binary64))))
(/.f64 (sqrt.f64 (+.f64 #s(literal 8 binary64) (*.f64 x (*.f64 x x)))) (sqrt.f64 (+.f64 #s(literal 4 binary64) (*.f64 x (+.f64 x #s(literal -2 binary64))))))
(/.f64 (sqrt.f64 (+.f64 #s(literal 8 binary64) (*.f64 x (*.f64 x x)))) (sqrt.f64 (+.f64 (*.f64 x x) (-.f64 #s(literal 4 binary64) (*.f64 #s(literal 2 binary64) x)))))
(/.f64 (pow.f64 (-.f64 #s(literal 4 binary64) (*.f64 x x)) #s(literal 1/2 binary64)) (pow.f64 (-.f64 #s(literal 2 binary64) x) #s(literal 1/2 binary64)))
(/.f64 (sqrt.f64 (-.f64 #s(literal 0 binary64) (+.f64 #s(literal 8 binary64) (*.f64 x (*.f64 x x))))) (sqrt.f64 (-.f64 #s(literal 0 binary64) (+.f64 #s(literal 4 binary64) (*.f64 x (+.f64 x #s(literal -2 binary64)))))))
(/.f64 (sqrt.f64 (-.f64 #s(literal 0 binary64) (-.f64 #s(literal 4 binary64) (*.f64 x x)))) (sqrt.f64 (-.f64 #s(literal 0 binary64) (-.f64 #s(literal 2 binary64) x))))
(/.f64 (sqrt.f64 (+.f64 (*.f64 x x) #s(literal -4 binary64))) (sqrt.f64 (+.f64 x #s(literal -2 binary64))))
(/.f64 (neg.f64 (sqrt.f64 (+.f64 #s(literal 8 binary64) (*.f64 x (*.f64 x x))))) (neg.f64 (sqrt.f64 (+.f64 #s(literal 4 binary64) (*.f64 x (+.f64 x #s(literal -2 binary64)))))))
(/.f64 (neg.f64 (pow.f64 (-.f64 #s(literal 4 binary64) (*.f64 x x)) #s(literal 1/2 binary64))) (neg.f64 (pow.f64 (-.f64 #s(literal 2 binary64) x) #s(literal 1/2 binary64))))
(pow.f64 (+.f64 #s(literal 2 binary64) x) #s(literal 1/2 binary64))
(pow.f64 (pow.f64 (+.f64 #s(literal 2 binary64) x) #s(literal 1/4 binary64)) #s(literal 2 binary64))
(pow.f64 (*.f64 (+.f64 #s(literal 2 binary64) x) (+.f64 #s(literal 2 binary64) x)) #s(literal 1/4 binary64))
(pow.f64 (exp.f64 (log.f64 (+.f64 #s(literal 2 binary64) x))) #s(literal 1/2 binary64))
(*.f64 (sqrt.f64 (+.f64 #s(literal 8 binary64) (*.f64 x (*.f64 x x)))) (pow.f64 (/.f64 #s(literal 1 binary64) (+.f64 #s(literal 4 binary64) (*.f64 x (+.f64 x #s(literal -2 binary64))))) #s(literal 1/2 binary64)))
(*.f64 (sqrt.f64 (+.f64 #s(literal 8 binary64) (*.f64 x (*.f64 x x)))) (sqrt.f64 (/.f64 #s(literal 1 binary64) (+.f64 #s(literal 4 binary64) (*.f64 x (+.f64 x #s(literal -2 binary64)))))))
(*.f64 (sqrt.f64 (+.f64 #s(literal 8 binary64) (*.f64 x (*.f64 x x)))) (/.f64 #s(literal 1 binary64) (sqrt.f64 (+.f64 #s(literal 4 binary64) (*.f64 x (+.f64 x #s(literal -2 binary64)))))))
(*.f64 (pow.f64 (-.f64 #s(literal 4 binary64) (*.f64 x x)) #s(literal 1/2 binary64)) (pow.f64 (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 2 binary64) x)) #s(literal 1/2 binary64)))
(*.f64 (pow.f64 (-.f64 #s(literal 4 binary64) (*.f64 x x)) #s(literal 1/2 binary64)) (sqrt.f64 (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 2 binary64) x))))
(*.f64 (pow.f64 (-.f64 #s(literal 4 binary64) (*.f64 x x)) #s(literal 1/2 binary64)) (/.f64 #s(literal 1 binary64) (pow.f64 (-.f64 #s(literal 2 binary64) x) #s(literal 1/2 binary64))))
(*.f64 (pow.f64 (+.f64 #s(literal 2 binary64) x) #s(literal 1/4 binary64)) (pow.f64 (+.f64 #s(literal 2 binary64) x) #s(literal 1/4 binary64)))
(+.f64 #s(literal 2 binary64) x)
(+.f64 x #s(literal 2 binary64))
(+.f64 (/.f64 #s(literal 4 binary64) (-.f64 #s(literal 2 binary64) x)) (neg.f64 (/.f64 (*.f64 x x) (-.f64 #s(literal 2 binary64) x))))
(-.f64 (/.f64 #s(literal 4 binary64) (-.f64 #s(literal 2 binary64) x)) (/.f64 (*.f64 x x) (-.f64 #s(literal 2 binary64) x)))
(-.f64 (/.f64 (*.f64 x x) (+.f64 x #s(literal -2 binary64))) (/.f64 #s(literal 4 binary64) (+.f64 x #s(literal -2 binary64))))
(fma.f64 x #s(literal 1 binary64) #s(literal 2 binary64))
(fma.f64 #s(literal 1 binary64) x #s(literal 2 binary64))
(/.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (+.f64 #s(literal 2 binary64) x)))
(/.f64 #s(literal 1 binary64) (/.f64 (/.f64 #s(literal 1 binary64) (+.f64 #s(literal 2 binary64) x)) #s(literal 1 binary64)))
(/.f64 #s(literal 1 binary64) (/.f64 (+.f64 (*.f64 x x) (-.f64 #s(literal 4 binary64) (*.f64 #s(literal 2 binary64) x))) (+.f64 #s(literal 8 binary64) (*.f64 x (*.f64 x x)))))
(/.f64 #s(literal 1 binary64) (/.f64 (+.f64 x #s(literal -2 binary64)) (+.f64 (*.f64 x x) #s(literal -4 binary64))))
(/.f64 (+.f64 #s(literal 8 binary64) (*.f64 x (*.f64 x x))) (+.f64 #s(literal 4 binary64) (*.f64 x (+.f64 x #s(literal -2 binary64)))))
(/.f64 (+.f64 #s(literal 8 binary64) (*.f64 x (*.f64 x x))) (+.f64 (*.f64 x x) (-.f64 #s(literal 4 binary64) (*.f64 #s(literal 2 binary64) x))))
(/.f64 (-.f64 #s(literal 4 binary64) (*.f64 x x)) (-.f64 #s(literal 2 binary64) x))
(/.f64 (-.f64 #s(literal 0 binary64) (+.f64 #s(literal 8 binary64) (*.f64 x (*.f64 x x)))) (-.f64 #s(literal 0 binary64) (+.f64 #s(literal 4 binary64) (*.f64 x (+.f64 x #s(literal -2 binary64))))))
(/.f64 (-.f64 #s(literal 0 binary64) (+.f64 #s(literal 8 binary64) (*.f64 x (*.f64 x x)))) (neg.f64 (+.f64 (*.f64 x x) (-.f64 #s(literal 4 binary64) (*.f64 #s(literal 2 binary64) x)))))
(/.f64 (-.f64 #s(literal 0 binary64) (-.f64 #s(literal 4 binary64) (*.f64 x x))) (-.f64 #s(literal 0 binary64) (-.f64 #s(literal 2 binary64) x)))
(/.f64 (+.f64 (*.f64 x x) #s(literal -4 binary64)) (+.f64 x #s(literal -2 binary64)))
(/.f64 #s(literal -1 binary64) (neg.f64 (/.f64 #s(literal 1 binary64) (+.f64 #s(literal 2 binary64) x))))
(/.f64 (-.f64 (*.f64 #s(literal 4 binary64) (-.f64 #s(literal 2 binary64) x)) (*.f64 (-.f64 #s(literal 2 binary64) x) (*.f64 x x))) (*.f64 (-.f64 #s(literal 2 binary64) x) (-.f64 #s(literal 2 binary64) x)))
(/.f64 (*.f64 (+.f64 #s(literal 512 binary64) (*.f64 (*.f64 x (*.f64 x x)) (*.f64 (*.f64 x (*.f64 x x)) (*.f64 x (*.f64 x x))))) #s(literal 1 binary64)) (*.f64 (+.f64 #s(literal 64 binary64) (-.f64 (*.f64 (*.f64 x (*.f64 x x)) (*.f64 x (*.f64 x x))) (*.f64 #s(literal 8 binary64) (*.f64 x (*.f64 x x))))) (+.f64 #s(literal 4 binary64) (*.f64 x (+.f64 x #s(literal -2 binary64))))))
(/.f64 (*.f64 (-.f64 #s(literal 64 binary64) (*.f64 (*.f64 x (*.f64 x x)) (*.f64 x (*.f64 x x)))) #s(literal 1 binary64)) (*.f64 (-.f64 #s(literal 8 binary64) (*.f64 x (*.f64 x x))) (+.f64 #s(literal 4 binary64) (*.f64 x (+.f64 x #s(literal -2 binary64))))))
(/.f64 (*.f64 (-.f64 #s(literal 64 binary64) (*.f64 (*.f64 x (*.f64 x x)) (*.f64 x (*.f64 x x)))) #s(literal 1 binary64)) (*.f64 (+.f64 #s(literal 16 binary64) (+.f64 (*.f64 (*.f64 x x) (*.f64 x x)) (*.f64 #s(literal 4 binary64) (*.f64 x x)))) (-.f64 #s(literal 2 binary64) x)))
(/.f64 (*.f64 (-.f64 #s(literal 16 binary64) (*.f64 (*.f64 x x) (*.f64 x x))) #s(literal 1 binary64)) (*.f64 (+.f64 #s(literal 4 binary64) (*.f64 x x)) (-.f64 #s(literal 2 binary64) x)))
(/.f64 (neg.f64 (-.f64 #s(literal 0 binary64) (+.f64 #s(literal 8 binary64) (*.f64 x (*.f64 x x))))) (neg.f64 (-.f64 #s(literal 0 binary64) (+.f64 #s(literal 4 binary64) (*.f64 x (+.f64 x #s(literal -2 binary64)))))))
(/.f64 (neg.f64 (-.f64 #s(literal 0 binary64) (-.f64 #s(literal 4 binary64) (*.f64 x x)))) (neg.f64 (-.f64 #s(literal 0 binary64) (-.f64 #s(literal 2 binary64) x))))
(/.f64 (neg.f64 (+.f64 (*.f64 x x) #s(literal -4 binary64))) (neg.f64 (+.f64 x #s(literal -2 binary64))))
(/.f64 (-.f64 (pow.f64 (/.f64 #s(literal 4 binary64) (-.f64 #s(literal 2 binary64) x)) #s(literal 3 binary64)) (pow.f64 (/.f64 (*.f64 x x) (-.f64 #s(literal 2 binary64) x)) #s(literal 3 binary64))) (+.f64 (*.f64 (/.f64 #s(literal 4 binary64) (-.f64 #s(literal 2 binary64) x)) (/.f64 #s(literal 4 binary64) (-.f64 #s(literal 2 binary64) x))) (+.f64 (*.f64 (/.f64 (*.f64 x x) (-.f64 #s(literal 2 binary64) x)) (/.f64 (*.f64 x x) (-.f64 #s(literal 2 binary64) x))) (*.f64 (/.f64 #s(literal 4 binary64) (-.f64 #s(literal 2 binary64) x)) (/.f64 (*.f64 x x) (-.f64 #s(literal 2 binary64) x))))))
(/.f64 (-.f64 (*.f64 (/.f64 #s(literal 4 binary64) (-.f64 #s(literal 2 binary64) x)) (/.f64 #s(literal 4 binary64) (-.f64 #s(literal 2 binary64) x))) (*.f64 (/.f64 (*.f64 x x) (-.f64 #s(literal 2 binary64) x)) (/.f64 (*.f64 x x) (-.f64 #s(literal 2 binary64) x)))) (+.f64 (/.f64 #s(literal 4 binary64) (-.f64 #s(literal 2 binary64) x)) (/.f64 (*.f64 x x) (-.f64 #s(literal 2 binary64) x))))
(pow.f64 (/.f64 #s(literal 1 binary64) (+.f64 #s(literal 2 binary64) x)) #s(literal -1 binary64))
(*.f64 #s(literal 1 binary64) (+.f64 #s(literal 2 binary64) x))
(*.f64 (+.f64 #s(literal 8 binary64) (*.f64 x (*.f64 x x))) (/.f64 #s(literal 1 binary64) (+.f64 #s(literal 4 binary64) (*.f64 x (+.f64 x #s(literal -2 binary64))))))
(*.f64 (+.f64 #s(literal 8 binary64) (*.f64 x (*.f64 x x))) (/.f64 #s(literal 1 binary64) (+.f64 (*.f64 x x) (-.f64 #s(literal 4 binary64) (*.f64 #s(literal 2 binary64) x)))))
(*.f64 (-.f64 #s(literal 4 binary64) (*.f64 x x)) (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 2 binary64) x)))
(*.f64 (-.f64 #s(literal 0 binary64) (+.f64 #s(literal 8 binary64) (*.f64 x (*.f64 x x)))) (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 0 binary64) (+.f64 #s(literal 4 binary64) (*.f64 x (+.f64 x #s(literal -2 binary64)))))))
(*.f64 (-.f64 #s(literal 0 binary64) (-.f64 #s(literal 4 binary64) (*.f64 x x))) (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 0 binary64) (-.f64 #s(literal 2 binary64) x))))
(*.f64 (+.f64 (*.f64 x x) #s(literal -4 binary64)) (/.f64 #s(literal 1 binary64) (+.f64 x #s(literal -2 binary64))))
(exp.f64 (*.f64 (log.f64 (+.f64 #s(literal 2 binary64) (*.f64 x (+.f64 #s(literal 1 binary64) (*.f64 x #s(literal 1/2 binary64)))))) #s(literal 1/2 binary64)))
(sqrt.f64 (+.f64 #s(literal 2 binary64) (*.f64 x (+.f64 #s(literal 1 binary64) (*.f64 x #s(literal 1/2 binary64))))))
(/.f64 #s(literal 1 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) (+.f64 #s(literal 2 binary64) (*.f64 x (+.f64 #s(literal 1 binary64) (*.f64 x #s(literal 1/2 binary64))))))))
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(/.f64 (-.f64 (*.f64 (+.f64 #s(literal 1 binary64) (*.f64 x #s(literal 1/2 binary64))) (+.f64 #s(literal 1 binary64) (*.f64 x #s(literal 1/2 binary64)))) (*.f64 (*.f64 #s(literal 1/6 binary64) (*.f64 x x)) (*.f64 #s(literal 1/6 binary64) (*.f64 x x)))) (-.f64 (+.f64 #s(literal 1 binary64) (*.f64 x #s(literal 1/2 binary64))) (*.f64 #s(literal 1/6 binary64) (*.f64 x x))))
(/.f64 (-.f64 (*.f64 (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 1 binary64) (*.f64 x (+.f64 #s(literal 1/2 binary64) (*.f64 x #s(literal 1/6 binary64)))))) (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 1 binary64) (*.f64 x (+.f64 #s(literal 1/2 binary64) (*.f64 x #s(literal 1/6 binary64))))))) (*.f64 (/.f64 (*.f64 x (*.f64 (+.f64 #s(literal 1/2 binary64) (*.f64 x #s(literal 1/6 binary64))) (*.f64 x (+.f64 #s(literal 1/2 binary64) (*.f64 x #s(literal 1/6 binary64)))))) (-.f64 #s(literal 1 binary64) (*.f64 x (+.f64 #s(literal 1/2 binary64) (*.f64 x #s(literal 1/6 binary64)))))) (/.f64 (*.f64 x (*.f64 (+.f64 #s(literal 1/2 binary64) (*.f64 x #s(literal 1/6 binary64))) (*.f64 x (+.f64 #s(literal 1/2 binary64) (*.f64 x #s(literal 1/6 binary64)))))) (-.f64 #s(literal 1 binary64) (*.f64 x (+.f64 #s(literal 1/2 binary64) (*.f64 x #s(literal 1/6 binary64)))))))) (+.f64 (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 1 binary64) (*.f64 x (+.f64 #s(literal 1/2 binary64) (*.f64 x #s(literal 1/6 binary64)))))) (/.f64 (*.f64 x (*.f64 (+.f64 #s(literal 1/2 binary64) (*.f64 x #s(literal 1/6 binary64))) (*.f64 x (+.f64 #s(literal 1/2 binary64) (*.f64 x #s(literal 1/6 binary64)))))) (-.f64 #s(literal 1 binary64) (*.f64 x (+.f64 #s(literal 1/2 binary64) (*.f64 x #s(literal 1/6 binary64))))))))
(pow.f64 (/.f64 #s(literal 1 binary64) (+.f64 #s(literal 1 binary64) (*.f64 x (+.f64 #s(literal 1/2 binary64) (*.f64 x #s(literal 1/6 binary64)))))) #s(literal -1 binary64))
(*.f64 #s(literal 1 binary64) (+.f64 #s(literal 1 binary64) (*.f64 x (+.f64 #s(literal 1/2 binary64) (*.f64 x #s(literal 1/6 binary64))))))
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(*.f64 (-.f64 #s(literal 0 binary64) (+.f64 #s(literal 1 binary64) (*.f64 (*.f64 x (*.f64 x x)) (*.f64 (+.f64 #s(literal 1/2 binary64) (*.f64 x #s(literal 1/6 binary64))) (*.f64 (+.f64 #s(literal 1/2 binary64) (*.f64 x #s(literal 1/6 binary64))) (+.f64 #s(literal 1/2 binary64) (*.f64 x #s(literal 1/6 binary64)))))))) (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 0 binary64) (+.f64 #s(literal 1 binary64) (*.f64 (*.f64 x (+.f64 #s(literal 1/2 binary64) (*.f64 x #s(literal 1/6 binary64)))) (+.f64 (*.f64 x (+.f64 #s(literal 1/2 binary64) (*.f64 x #s(literal 1/6 binary64)))) #s(literal -1 binary64)))))))
(*.f64 (-.f64 #s(literal 0 binary64) (-.f64 #s(literal 1 binary64) (*.f64 x (*.f64 (+.f64 #s(literal 1/2 binary64) (*.f64 x #s(literal 1/6 binary64))) (*.f64 x (+.f64 #s(literal 1/2 binary64) (*.f64 x #s(literal 1/6 binary64)))))))) (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 0 binary64) (-.f64 #s(literal 1 binary64) (*.f64 x (+.f64 #s(literal 1/2 binary64) (*.f64 x #s(literal 1/6 binary64))))))))
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(*.f64 x #s(literal 1/2 binary64))
(*.f64 #s(literal 1 binary64) (*.f64 x #s(literal 1/2 binary64)))
(*.f64 #s(literal 1/2 binary64) x)
(*.f64 (*.f64 x #s(literal 1/2 binary64)) #s(literal 1 binary64))
(*.f64 x #s(literal 1/6 binary64))
(*.f64 #s(literal 1/6 binary64) x)
(+.f64 (*.f64 x #s(literal 1/2 binary64)) (*.f64 #s(literal 1/6 binary64) (*.f64 x x)))
(+.f64 (*.f64 #s(literal 1/6 binary64) (*.f64 x x)) (*.f64 x #s(literal 1/2 binary64)))
(-.f64 (/.f64 (*.f64 #s(literal 1/4 binary64) (*.f64 x x)) (-.f64 (*.f64 x #s(literal 1/2 binary64)) (*.f64 #s(literal 1/6 binary64) (*.f64 x x)))) (/.f64 (*.f64 (*.f64 #s(literal 1/6 binary64) (*.f64 x x)) (*.f64 #s(literal 1/6 binary64) (*.f64 x x))) (-.f64 (*.f64 x #s(literal 1/2 binary64)) (*.f64 #s(literal 1/6 binary64) (*.f64 x x)))))
(fma.f64 x #s(literal 1/2 binary64) (*.f64 #s(literal 1/6 binary64) (*.f64 x x)))
(fma.f64 x (*.f64 x #s(literal 1/6 binary64)) (*.f64 x #s(literal 1/2 binary64)))
(fma.f64 #s(literal 1 binary64) (*.f64 x #s(literal 1/2 binary64)) (*.f64 #s(literal 1/6 binary64) (*.f64 x x)))
(fma.f64 #s(literal 1/2 binary64) x (*.f64 #s(literal 1/6 binary64) (*.f64 x x)))
(fma.f64 (*.f64 x #s(literal 1/2 binary64)) #s(literal 1 binary64) (*.f64 #s(literal 1/6 binary64) (*.f64 x x)))
(fma.f64 #s(literal 1/6 binary64) (*.f64 x x) (*.f64 x #s(literal 1/2 binary64)))
(fma.f64 (*.f64 x #s(literal 1/6 binary64)) x (*.f64 x #s(literal 1/2 binary64)))
(fma.f64 (*.f64 x x) #s(literal 1/6 binary64) (*.f64 x #s(literal 1/2 binary64)))
(/.f64 x (/.f64 #s(literal 1 binary64) (+.f64 #s(literal 1/2 binary64) (*.f64 x #s(literal 1/6 binary64)))))
(/.f64 #s(literal 1 binary64) (/.f64 (+.f64 (*.f64 #s(literal 1/4 binary64) (*.f64 x x)) (-.f64 (*.f64 (*.f64 #s(literal 1/6 binary64) (*.f64 x x)) (*.f64 #s(literal 1/6 binary64) (*.f64 x x))) (*.f64 (*.f64 x #s(literal 1/2 binary64)) (*.f64 #s(literal 1/6 binary64) (*.f64 x x))))) (+.f64 (*.f64 #s(literal 1/8 binary64) (*.f64 x (*.f64 x x))) (*.f64 (*.f64 (*.f64 x (*.f64 x x)) #s(literal 1/216 binary64)) (*.f64 x (*.f64 x x))))))
(/.f64 #s(literal 1 binary64) (/.f64 (-.f64 (*.f64 x #s(literal 1/2 binary64)) (*.f64 #s(literal 1/6 binary64) (*.f64 x x))) (-.f64 (*.f64 #s(literal 1/4 binary64) (*.f64 x x)) (*.f64 (*.f64 #s(literal 1/6 binary64) (*.f64 x x)) (*.f64 #s(literal 1/6 binary64) (*.f64 x x))))))
(/.f64 #s(literal 1 binary64) (/.f64 (+.f64 #s(literal 1/4 binary64) (*.f64 (*.f64 x #s(literal 1/6 binary64)) (+.f64 (*.f64 x #s(literal 1/6 binary64)) #s(literal -1/2 binary64)))) (*.f64 x (+.f64 #s(literal 1/8 binary64) (*.f64 (*.f64 x (*.f64 x x)) #s(literal 1/216 binary64))))))
(/.f64 #s(literal 1 binary64) (/.f64 (-.f64 #s(literal 1/2 binary64) (*.f64 x #s(literal 1/6 binary64))) (*.f64 x (-.f64 #s(literal 1/4 binary64) (*.f64 (*.f64 x x) #s(literal 1/36 binary64))))))
(/.f64 #s(literal 1 binary64) (/.f64 (+.f64 #s(literal 1/4 binary64) (*.f64 (*.f64 x #s(literal 1/6 binary64)) (+.f64 (*.f64 x #s(literal 1/6 binary64)) #s(literal -1/2 binary64)))) (*.f64 (+.f64 #s(literal 1/8 binary64) (*.f64 (*.f64 x (*.f64 x x)) #s(literal 1/216 binary64))) x)))
(/.f64 #s(literal 1 binary64) (/.f64 (-.f64 #s(literal 1/2 binary64) (*.f64 x #s(literal 1/6 binary64))) (*.f64 (-.f64 #s(literal 1/4 binary64) (*.f64 (*.f64 x x) #s(literal 1/36 binary64))) x)))
(/.f64 (+.f64 (*.f64 #s(literal 1/8 binary64) (*.f64 x (*.f64 x x))) (*.f64 (*.f64 (*.f64 x (*.f64 x x)) #s(literal 1/216 binary64)) (*.f64 x (*.f64 x x)))) (+.f64 (*.f64 #s(literal 1/4 binary64) (*.f64 x x)) (-.f64 (*.f64 (*.f64 #s(literal 1/6 binary64) (*.f64 x x)) (*.f64 #s(literal 1/6 binary64) (*.f64 x x))) (*.f64 (*.f64 x #s(literal 1/2 binary64)) (*.f64 #s(literal 1/6 binary64) (*.f64 x x))))))
(/.f64 (-.f64 (*.f64 #s(literal 1/4 binary64) (*.f64 x x)) (*.f64 (*.f64 #s(literal 1/6 binary64) (*.f64 x x)) (*.f64 #s(literal 1/6 binary64) (*.f64 x x)))) (-.f64 (*.f64 x #s(literal 1/2 binary64)) (*.f64 #s(literal 1/6 binary64) (*.f64 x x))))
(/.f64 (*.f64 x (+.f64 #s(literal 1/8 binary64) (*.f64 (*.f64 x (*.f64 x x)) #s(literal 1/216 binary64)))) (+.f64 #s(literal 1/4 binary64) (*.f64 (*.f64 x #s(literal 1/6 binary64)) (+.f64 (*.f64 x #s(literal 1/6 binary64)) #s(literal -1/2 binary64)))))
(/.f64 (*.f64 x (-.f64 #s(literal 1/4 binary64) (*.f64 (*.f64 x x) #s(literal 1/36 binary64)))) (-.f64 #s(literal 1/2 binary64) (*.f64 x #s(literal 1/6 binary64))))
(/.f64 (*.f64 (+.f64 #s(literal 1/8 binary64) (*.f64 (*.f64 x (*.f64 x x)) #s(literal 1/216 binary64))) x) (+.f64 #s(literal 1/4 binary64) (*.f64 (*.f64 x #s(literal 1/6 binary64)) (+.f64 (*.f64 x #s(literal 1/6 binary64)) #s(literal -1/2 binary64)))))
(/.f64 (*.f64 (-.f64 #s(literal 1/4 binary64) (*.f64 (*.f64 x x) #s(literal 1/36 binary64))) x) (-.f64 #s(literal 1/2 binary64) (*.f64 x #s(literal 1/6 binary64))))
(/.f64 (neg.f64 (+.f64 (*.f64 #s(literal 1/8 binary64) (*.f64 x (*.f64 x x))) (*.f64 (*.f64 (*.f64 x (*.f64 x x)) #s(literal 1/216 binary64)) (*.f64 x (*.f64 x x))))) (neg.f64 (+.f64 (*.f64 #s(literal 1/4 binary64) (*.f64 x x)) (-.f64 (*.f64 (*.f64 #s(literal 1/6 binary64) (*.f64 x x)) (*.f64 #s(literal 1/6 binary64) (*.f64 x x))) (*.f64 (*.f64 x #s(literal 1/2 binary64)) (*.f64 #s(literal 1/6 binary64) (*.f64 x x)))))))
(/.f64 (neg.f64 (-.f64 (*.f64 #s(literal 1/4 binary64) (*.f64 x x)) (*.f64 (*.f64 #s(literal 1/6 binary64) (*.f64 x x)) (*.f64 #s(literal 1/6 binary64) (*.f64 x x))))) (neg.f64 (-.f64 (*.f64 x #s(literal 1/2 binary64)) (*.f64 #s(literal 1/6 binary64) (*.f64 x x)))))
(/.f64 (neg.f64 (*.f64 x (+.f64 #s(literal 1/8 binary64) (*.f64 (*.f64 x (*.f64 x x)) #s(literal 1/216 binary64))))) (-.f64 #s(literal 0 binary64) (+.f64 #s(literal 1/4 binary64) (*.f64 (*.f64 x #s(literal 1/6 binary64)) (+.f64 (*.f64 x #s(literal 1/6 binary64)) #s(literal -1/2 binary64))))))
(/.f64 (neg.f64 (*.f64 x (-.f64 #s(literal 1/4 binary64) (*.f64 (*.f64 x x) #s(literal 1/36 binary64))))) (-.f64 #s(literal 0 binary64) (-.f64 #s(literal 1/2 binary64) (*.f64 x #s(literal 1/6 binary64)))))
(/.f64 (neg.f64 (*.f64 (+.f64 #s(literal 1/8 binary64) (*.f64 (*.f64 x (*.f64 x x)) #s(literal 1/216 binary64))) x)) (-.f64 #s(literal 0 binary64) (+.f64 #s(literal 1/4 binary64) (*.f64 (*.f64 x #s(literal 1/6 binary64)) (+.f64 (*.f64 x #s(literal 1/6 binary64)) #s(literal -1/2 binary64))))))
(/.f64 (neg.f64 (*.f64 (-.f64 #s(literal 1/4 binary64) (*.f64 (*.f64 x x) #s(literal 1/36 binary64))) x)) (-.f64 #s(literal 0 binary64) (-.f64 #s(literal 1/2 binary64) (*.f64 x #s(literal 1/6 binary64)))))
(/.f64 (+.f64 (*.f64 (*.f64 (*.f64 x (*.f64 x x)) #s(literal 1/216 binary64)) (*.f64 x (*.f64 x x))) (*.f64 #s(literal 1/8 binary64) (*.f64 x (*.f64 x x)))) (+.f64 (*.f64 (*.f64 #s(literal 1/6 binary64) (*.f64 x x)) (*.f64 #s(literal 1/6 binary64) (*.f64 x x))) (-.f64 (*.f64 #s(literal 1/4 binary64) (*.f64 x x)) (*.f64 (*.f64 #s(literal 1/6 binary64) (*.f64 x x)) (*.f64 x #s(literal 1/2 binary64))))))
(/.f64 (-.f64 (*.f64 (*.f64 #s(literal 1/6 binary64) (*.f64 x x)) (*.f64 #s(literal 1/6 binary64) (*.f64 x x))) (*.f64 #s(literal 1/4 binary64) (*.f64 x x))) (-.f64 (*.f64 #s(literal 1/6 binary64) (*.f64 x x)) (*.f64 x #s(literal 1/2 binary64))))
(*.f64 x (+.f64 #s(literal 1/2 binary64) (*.f64 x #s(literal 1/6 binary64))))
(*.f64 #s(literal 1 binary64) (*.f64 x (+.f64 #s(literal 1/2 binary64) (*.f64 x #s(literal 1/6 binary64)))))
(*.f64 (+.f64 #s(literal 1/2 binary64) (*.f64 x #s(literal 1/6 binary64))) x)
(*.f64 (*.f64 x (+.f64 #s(literal 1/2 binary64) (*.f64 x #s(literal 1/6 binary64)))) #s(literal 1 binary64))
(*.f64 (+.f64 (*.f64 #s(literal 1/8 binary64) (*.f64 x (*.f64 x x))) (*.f64 (*.f64 (*.f64 x (*.f64 x x)) #s(literal 1/216 binary64)) (*.f64 x (*.f64 x x)))) (/.f64 #s(literal 1 binary64) (+.f64 (*.f64 #s(literal 1/4 binary64) (*.f64 x x)) (-.f64 (*.f64 (*.f64 #s(literal 1/6 binary64) (*.f64 x x)) (*.f64 #s(literal 1/6 binary64) (*.f64 x x))) (*.f64 (*.f64 x #s(literal 1/2 binary64)) (*.f64 #s(literal 1/6 binary64) (*.f64 x x)))))))
(*.f64 (-.f64 (*.f64 #s(literal 1/4 binary64) (*.f64 x x)) (*.f64 (*.f64 #s(literal 1/6 binary64) (*.f64 x x)) (*.f64 #s(literal 1/6 binary64) (*.f64 x x)))) (/.f64 #s(literal 1 binary64) (-.f64 (*.f64 x #s(literal 1/2 binary64)) (*.f64 #s(literal 1/6 binary64) (*.f64 x x)))))
(*.f64 (*.f64 x (+.f64 #s(literal 1/8 binary64) (*.f64 (*.f64 x (*.f64 x x)) #s(literal 1/216 binary64)))) (/.f64 #s(literal 1 binary64) (+.f64 #s(literal 1/4 binary64) (*.f64 (*.f64 x #s(literal 1/6 binary64)) (+.f64 (*.f64 x #s(literal 1/6 binary64)) #s(literal -1/2 binary64))))))
(*.f64 (*.f64 x (-.f64 #s(literal 1/4 binary64) (*.f64 (*.f64 x x) #s(literal 1/36 binary64)))) (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 1/2 binary64) (*.f64 x #s(literal 1/6 binary64)))))
(*.f64 (*.f64 (+.f64 #s(literal 1/8 binary64) (*.f64 (*.f64 x (*.f64 x x)) #s(literal 1/216 binary64))) x) (/.f64 #s(literal 1 binary64) (+.f64 #s(literal 1/4 binary64) (*.f64 (*.f64 x #s(literal 1/6 binary64)) (+.f64 (*.f64 x #s(literal 1/6 binary64)) #s(literal -1/2 binary64))))))
(*.f64 (*.f64 (-.f64 #s(literal 1/4 binary64) (*.f64 (*.f64 x x) #s(literal 1/36 binary64))) x) (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 1/2 binary64) (*.f64 x #s(literal 1/6 binary64)))))

simplify256.0ms (3.5%)

Algorithm
egg-herbie
Rules
5062×*-lowering-*.f32
5062×*-lowering-*.f64
3334×+-lowering-+.f64
3334×+-lowering-+.f32
2396×/-lowering-/.f32
Iterations

Useful iterations: 2 (0.0ms)

IterNodesCost
02701553
19181282
234081236
087021236
Stop Event
iter limit
node limit
Counts
156 → 156
Calls
Call 1
Inputs
(sqrt 2)
(+ (sqrt 2) (* 1/2 (/ x (sqrt 2))))
(+ (sqrt 2) (* x (+ (* -1/8 (/ x (pow (sqrt 2) 3))) (* 1/2 (/ 1 (sqrt 2))))))
(+ (sqrt 2) (* x (+ (* x (- (* 1/16 (/ x (pow (sqrt 2) 5))) (* 1/8 (/ 1 (pow (sqrt 2) 3))))) (* 1/2 (/ 1 (sqrt 2))))))
(sqrt x)
(* x (+ (sqrt (/ 1 x)) (sqrt (/ 1 (pow x 3)))))
(* x (+ (sqrt (/ 1 x)) (+ (sqrt (/ 1 (pow x 3))) (* -1/2 (sqrt (/ 1 (pow x 5)))))))
(* x (+ (sqrt (/ 1 x)) (+ (sqrt (/ 1 (pow x 3))) (+ (* -1/2 (sqrt (/ 1 (pow x 5)))) (* 1/2 (sqrt (/ 1 (pow x 7))))))))
(* -1 (* (sqrt x) (pow (sqrt -1) 2)))
(* -1 (* x (+ (sqrt (/ 1 (pow x 3))) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)))))
(* -1 (* x (+ (sqrt (/ 1 (pow x 3))) (+ (* -1/2 (* (sqrt (/ 1 (pow x 5))) (/ 1 (pow (sqrt -1) 2)))) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))))))
(* -1 (* x (+ (sqrt (/ 1 (pow x 3))) (+ (* -1/2 (* (sqrt (/ 1 (pow x 5))) (/ 1 (pow (sqrt -1) 2)))) (+ (* 1/2 (* (sqrt (/ 1 (pow x 7))) (/ 1 (pow (sqrt -1) 4)))) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)))))))
2
(+ 2 x)
(+ 2 x)
(+ 2 x)
x
(* x (+ 1 (* 2 (/ 1 x))))
(* x (+ 1 (* 2 (/ 1 x))))
(* x (+ 1 (* 2 (/ 1 x))))
x
(* x (+ 1 (* 2 (/ 1 x))))
(* x (+ 1 (* 2 (/ 1 x))))
(* x (+ 1 (* 2 (/ 1 x))))
(sqrt 2)
(+ (sqrt 2) (* 1/2 (/ x (sqrt 2))))
(+ (sqrt 2) (* x (+ (* 1/2 (/ (* x (- 1/2 (* 1/4 (/ 1 (pow (sqrt 2) 2))))) (sqrt 2))) (* 1/2 (/ 1 (sqrt 2))))))
(+ (sqrt 2) (* x (+ (* x (+ (* -1/4 (/ (* x (- 1/2 (* 1/4 (/ 1 (pow (sqrt 2) 2))))) (pow (sqrt 2) 3))) (* 1/2 (/ (- 1/2 (* 1/4 (/ 1 (pow (sqrt 2) 2)))) (sqrt 2))))) (* 1/2 (/ 1 (sqrt 2))))))
(* x (sqrt 1/2))
(* x (+ (sqrt 1/2) (* 1/2 (/ 1 (* x (sqrt 1/2))))))
(* x (+ (sqrt 1/2) (+ (* 1/2 (/ (- 2 (* 1/4 (/ 1 (pow (sqrt 1/2) 2)))) (* (pow x 2) (sqrt 1/2)))) (/ 1/2 (* x (sqrt 1/2))))))
(* x (+ (sqrt 1/2) (+ (* -1/4 (/ (- 2 (* 1/4 (/ 1 (pow (sqrt 1/2) 2)))) (* (pow x 3) (pow (sqrt 1/2) 3)))) (+ (* 1/2 (/ (- 2 (* 1/4 (/ 1 (pow (sqrt 1/2) 2)))) (* (pow x 2) (sqrt 1/2)))) (/ 1/2 (* x (sqrt 1/2)))))))
(* -1 (* x (sqrt 1/2)))
(* -1 (* x (+ (sqrt 1/2) (* 1/2 (/ 1 (* x (sqrt 1/2)))))))
(* -1 (* x (+ (sqrt 1/2) (* -1 (/ (- (* -1/2 (/ (- 2 (* 1/4 (/ 1 (pow (sqrt 1/2) 2)))) (* x (sqrt 1/2)))) (* 1/2 (/ 1 (sqrt 1/2)))) x)))))
(* -1 (* x (+ (sqrt 1/2) (* -1 (/ (- (* -1 (/ (+ (* -1/4 (/ (- 2 (* 1/4 (/ 1 (pow (sqrt 1/2) 2)))) (* x (pow (sqrt 1/2) 3)))) (* 1/2 (/ (- 2 (* 1/4 (/ 1 (pow (sqrt 1/2) 2)))) (sqrt 1/2)))) x)) (* 1/2 (/ 1 (sqrt 1/2)))) x)))))
2
(+ 2 x)
(+ 2 (* x (+ 1 (* 1/2 x))))
(+ 2 (* x (+ 1 (* 1/2 x))))
(* 1/2 (pow x 2))
(* (pow x 2) (+ 1/2 (/ 1 x)))
(* (pow x 2) (+ 1/2 (+ (/ 1 x) (/ 2 (pow x 2)))))
(* (pow x 2) (+ 1/2 (+ (/ 1 x) (/ 2 (pow x 2)))))
(* 1/2 (pow x 2))
(* (pow x 2) (+ 1/2 (/ 1 x)))
(* (pow x 2) (+ 1/2 (+ (/ 1 x) (/ 2 (pow x 2)))))
(* (pow x 2) (+ 1/2 (+ (/ 1 x) (/ 2 (pow x 2)))))
x
(* x (+ 1 (* 1/2 x)))
(* x (+ 1 (* 1/2 x)))
(* x (+ 1 (* 1/2 x)))
(* 1/2 (pow x 2))
(* (pow x 2) (+ 1/2 (/ 1 x)))
(* (pow x 2) (+ 1/2 (/ 1 x)))
(* (pow x 2) (+ 1/2 (/ 1 x)))
(* 1/2 (pow x 2))
(* (pow x 2) (+ 1/2 (/ 1 x)))
(* (pow x 2) (+ 1/2 (/ 1 x)))
(* (pow x 2) (+ 1/2 (/ 1 x)))
1
(+ 1 (* 1/2 x))
(+ 1 (* 1/2 x))
(+ 1 (* 1/2 x))
(* 1/2 x)
(* x (+ 1/2 (/ 1 x)))
(* x (+ 1/2 (/ 1 x)))
(* x (+ 1/2 (/ 1 x)))
(* 1/2 x)
(* x (+ 1/2 (/ 1 x)))
(* x (+ 1/2 (/ 1 x)))
(* x (+ 1/2 (/ 1 x)))
(sqrt 2)
(+ (sqrt 2) (* 1/2 (/ x (sqrt 2))))
(+ (sqrt 2) (* x (+ (* 1/2 (/ (* x (- 1/2 (* 1/4 (/ 1 (pow (sqrt 2) 2))))) (sqrt 2))) (* 1/2 (/ 1 (sqrt 2))))))
(+ (sqrt 2) (* x (+ (* x (+ (* 1/2 (/ (* x (- 1/6 (* 1/2 (/ (- 1/2 (* 1/4 (/ 1 (pow (sqrt 2) 2)))) (pow (sqrt 2) 2))))) (sqrt 2))) (* 1/2 (/ (- 1/2 (* 1/4 (/ 1 (pow (sqrt 2) 2)))) (sqrt 2))))) (* 1/2 (/ 1 (sqrt 2))))))
(* (sqrt (pow x 3)) (sqrt 1/6))
(* (pow x 2) (+ (* 1/4 (* (sqrt (/ 1 (pow x 3))) (/ 1 (sqrt 1/6)))) (* (sqrt (/ 1 x)) (sqrt 1/6))))
(* (pow x 2) (+ (* 1/4 (* (sqrt (/ 1 (pow x 3))) (/ 1 (sqrt 1/6)))) (+ (* 1/2 (* (sqrt (/ 1 (pow x 5))) (/ 1 (sqrt 1/6)))) (* (sqrt (/ 1 x)) (sqrt 1/6)))))
(* (pow x 2) (+ (* 1/4 (* (sqrt (/ 1 (pow x 3))) (/ 1 (sqrt 1/6)))) (+ (* 1/2 (* (sqrt (/ 1 (pow x 5))) (/ 1 (sqrt 1/6)))) (+ (* 1/2 (* (sqrt (/ 1 (pow x 7))) (/ (- 2 (* 1/16 (/ x (pow (sqrt 1/6) 2)))) (sqrt 1/6)))) (* (sqrt (/ 1 x)) (sqrt 1/6))))))
(* (sqrt (pow x 3)) (* (sqrt -1) (sqrt -1/6)))
(* (pow x 2) (+ (* 1/4 (* (sqrt (/ 1 (pow x 3))) (/ (sqrt -1) (sqrt -1/6)))) (* (sqrt (/ 1 x)) (* (sqrt -1) (sqrt -1/6)))))
(* (pow x 2) (+ (* 1/4 (* (sqrt (/ 1 (pow x 3))) (/ (sqrt -1) (sqrt -1/6)))) (+ (* 1/2 (* (sqrt (/ 1 (pow x 5))) (/ (sqrt -1) (sqrt -1/6)))) (* (sqrt (/ 1 x)) (* (sqrt -1) (sqrt -1/6))))))
(* (pow x 2) (+ (* -1 (/ (+ (* -1/2 (* (sqrt x) (/ (sqrt -1) (sqrt -1/6)))) (* -1/2 (* (sqrt (/ 1 x)) (/ (* (sqrt -1) (- 2 (* -1/16 (/ x (pow (sqrt -1/6) 2))))) (sqrt -1/6))))) (pow x 3))) (+ (* 1/4 (* (sqrt (/ 1 (pow x 3))) (/ (sqrt -1) (sqrt -1/6)))) (* (sqrt (/ 1 x)) (* (sqrt -1) (sqrt -1/6))))))
2
(+ 2 x)
(+ 2 (* x (+ 1 (* 1/2 x))))
(+ 2 (* x (+ 1 (* x (+ 1/2 (* 1/6 x))))))
(* 1/6 (pow x 3))
(* (pow x 3) (+ 1/6 (* 1/2 (/ 1 x))))
(* (pow x 3) (+ 1/6 (+ (* 1/2 (/ 1 x)) (/ 1 (pow x 2)))))
(* (pow x 3) (+ 1/6 (+ (* 1/2 (/ 1 x)) (+ (/ 1 (pow x 2)) (* 2 (/ 1 (pow x 3)))))))
(* 1/6 (pow x 3))
(* (pow x 3) (+ 1/6 (* 1/2 (/ 1 x))))
(* -1 (* (pow x 3) (- (* -1 (/ (+ 1/2 (/ 1 x)) x)) 1/6)))
(* -1 (* (pow x 3) (- (* -1 (/ (+ 1/2 (+ (/ 1 x) (/ 2 (pow x 2)))) x)) 1/6)))
x
(* x (+ 1 (* 1/2 x)))
(* x (+ 1 (* x (+ 1/2 (* 1/6 x)))))
(* x (+ 1 (* x (+ 1/2 (* 1/6 x)))))
(* 1/6 (pow x 3))
(* (pow x 3) (+ 1/6 (* 1/2 (/ 1 x))))
(* (pow x 3) (+ 1/6 (+ (* 1/2 (/ 1 x)) (/ 1 (pow x 2)))))
(* (pow x 3) (+ 1/6 (+ (* 1/2 (/ 1 x)) (/ 1 (pow x 2)))))
(* 1/6 (pow x 3))
(* (pow x 3) (+ 1/6 (* 1/2 (/ 1 x))))
(* -1 (* (pow x 3) (- (* -1 (/ (+ 1/2 (/ 1 x)) x)) 1/6)))
(* -1 (* (pow x 3) (- (* -1 (/ (+ 1/2 (/ 1 x)) x)) 1/6)))
1
(+ 1 (* 1/2 x))
(+ 1 (* x (+ 1/2 (* 1/6 x))))
(+ 1 (* x (+ 1/2 (* 1/6 x))))
(* 1/6 (pow x 2))
(* (pow x 2) (+ 1/6 (* 1/2 (/ 1 x))))
(* (pow x 2) (+ 1/6 (+ (* 1/2 (/ 1 x)) (/ 1 (pow x 2)))))
(* (pow x 2) (+ 1/6 (+ (* 1/2 (/ 1 x)) (/ 1 (pow x 2)))))
(* 1/6 (pow x 2))
(* (pow x 2) (+ 1/6 (* 1/2 (/ 1 x))))
(* (pow x 2) (+ 1/6 (+ (* 1/2 (/ 1 x)) (/ 1 (pow x 2)))))
(* (pow x 2) (+ 1/6 (+ (* 1/2 (/ 1 x)) (/ 1 (pow x 2)))))
(* 1/2 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)
(* 1/6 x)
(* 1/6 x)
(* 1/6 x)
(* 1/6 x)
(* 1/6 x)
(* 1/6 x)
(* 1/6 x)
(* 1/6 x)
(* 1/6 x)
(* 1/6 x)
(* 1/6 x)
(* 1/6 x)
(* 1/2 x)
(* x (+ 1/2 (* 1/6 x)))
(* x (+ 1/2 (* 1/6 x)))
(* x (+ 1/2 (* 1/6 x)))
(* 1/6 (pow x 2))
(* (pow x 2) (+ 1/6 (* 1/2 (/ 1 x))))
(* (pow x 2) (+ 1/6 (* 1/2 (/ 1 x))))
(* (pow x 2) (+ 1/6 (* 1/2 (/ 1 x))))
(* 1/6 (pow x 2))
(* (pow x 2) (+ 1/6 (* 1/2 (/ 1 x))))
(* (pow x 2) (+ 1/6 (* 1/2 (/ 1 x))))
(* (pow x 2) (+ 1/6 (* 1/2 (/ 1 x))))
Outputs
(sqrt 2)
(sqrt.f64 #s(literal 2 binary64))
(+ (sqrt 2) (* 1/2 (/ x (sqrt 2))))
(+.f64 (sqrt.f64 #s(literal 2 binary64)) (/.f64 x (*.f64 #s(literal 2 binary64) (sqrt.f64 #s(literal 2 binary64)))))
(+ (sqrt 2) (* x (+ (* -1/8 (/ x (pow (sqrt 2) 3))) (* 1/2 (/ 1 (sqrt 2))))))
(+.f64 (sqrt.f64 #s(literal 2 binary64)) (*.f64 x (+.f64 (*.f64 x (/.f64 #s(literal -1/16 binary64) (sqrt.f64 #s(literal 2 binary64)))) (/.f64 #s(literal 1/2 binary64) (sqrt.f64 #s(literal 2 binary64))))))
(+ (sqrt 2) (* x (+ (* x (- (* 1/16 (/ x (pow (sqrt 2) 5))) (* 1/8 (/ 1 (pow (sqrt 2) 3))))) (* 1/2 (/ 1 (sqrt 2))))))
(+.f64 (sqrt.f64 #s(literal 2 binary64)) (*.f64 x (+.f64 (/.f64 #s(literal 1/2 binary64) (sqrt.f64 #s(literal 2 binary64))) (*.f64 x (+.f64 (/.f64 (*.f64 x #s(literal 1/16 binary64)) (pow.f64 (sqrt.f64 #s(literal 2 binary64)) #s(literal 5 binary64))) (/.f64 #s(literal -1/16 binary64) (sqrt.f64 #s(literal 2 binary64))))))))
(sqrt x)
(sqrt.f64 x)
(* x (+ (sqrt (/ 1 x)) (sqrt (/ 1 (pow x 3)))))
(*.f64 x (+.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) (sqrt.f64 (/.f64 #s(literal 1 binary64) (*.f64 x (*.f64 x x))))))
(* x (+ (sqrt (/ 1 x)) (+ (sqrt (/ 1 (pow x 3))) (* -1/2 (sqrt (/ 1 (pow x 5)))))))
(*.f64 x (+.f64 (+.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) (sqrt.f64 (/.f64 #s(literal 1 binary64) (*.f64 x (*.f64 x x))))) (*.f64 #s(literal -1/2 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 5 binary64)))))))
(* x (+ (sqrt (/ 1 x)) (+ (sqrt (/ 1 (pow x 3))) (+ (* -1/2 (sqrt (/ 1 (pow x 5)))) (* 1/2 (sqrt (/ 1 (pow x 7))))))))
(*.f64 x (+.f64 (+.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) (sqrt.f64 (/.f64 #s(literal 1 binary64) (*.f64 x (*.f64 x x))))) (+.f64 (*.f64 #s(literal -1/2 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 5 binary64))))) (*.f64 #s(literal 1/2 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 7 binary64))))))))
(* -1 (* (sqrt x) (pow (sqrt -1) 2)))
(sqrt.f64 x)
(* -1 (* x (+ (sqrt (/ 1 (pow x 3))) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)))))
(-.f64 #s(literal 0 binary64) (*.f64 x (+.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (*.f64 x (*.f64 x x)))) (neg.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x))))))
(* -1 (* x (+ (sqrt (/ 1 (pow x 3))) (+ (* -1/2 (* (sqrt (/ 1 (pow x 5))) (/ 1 (pow (sqrt -1) 2)))) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))))))
(*.f64 (+.f64 (+.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (*.f64 x (*.f64 x x)))) (neg.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)))) (*.f64 #s(literal 1/2 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 5 binary64)))))) (-.f64 #s(literal 0 binary64) x))
(* -1 (* x (+ (sqrt (/ 1 (pow x 3))) (+ (* -1/2 (* (sqrt (/ 1 (pow x 5))) (/ 1 (pow (sqrt -1) 2)))) (+ (* 1/2 (* (sqrt (/ 1 (pow x 7))) (/ 1 (pow (sqrt -1) 4)))) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)))))))
(*.f64 (+.f64 (+.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (*.f64 x (*.f64 x x)))) (neg.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)))) (*.f64 #s(literal 1/2 binary64) (+.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 5 binary64)))) (/.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 7 binary64)))) (pow.f64 (sqrt.f64 #s(literal -1 binary64)) #s(literal 4 binary64)))))) (-.f64 #s(literal 0 binary64) x))
2
#s(literal 2 binary64)
(+ 2 x)
(+.f64 #s(literal 2 binary64) x)
(+ 2 x)
(+.f64 #s(literal 2 binary64) x)
(+ 2 x)
(+.f64 #s(literal 2 binary64) x)
x
(* x (+ 1 (* 2 (/ 1 x))))
(+.f64 #s(literal 2 binary64) x)
(* x (+ 1 (* 2 (/ 1 x))))
(+.f64 #s(literal 2 binary64) x)
(* x (+ 1 (* 2 (/ 1 x))))
(+.f64 #s(literal 2 binary64) x)
x
(* x (+ 1 (* 2 (/ 1 x))))
(+.f64 #s(literal 2 binary64) x)
(* x (+ 1 (* 2 (/ 1 x))))
(+.f64 #s(literal 2 binary64) x)
(* x (+ 1 (* 2 (/ 1 x))))
(+.f64 #s(literal 2 binary64) x)
(sqrt 2)
(sqrt.f64 #s(literal 2 binary64))
(+ (sqrt 2) (* 1/2 (/ x (sqrt 2))))
(+.f64 (sqrt.f64 #s(literal 2 binary64)) (/.f64 x (*.f64 #s(literal 2 binary64) (sqrt.f64 #s(literal 2 binary64)))))
(+ (sqrt 2) (* x (+ (* 1/2 (/ (* x (- 1/2 (* 1/4 (/ 1 (pow (sqrt 2) 2))))) (sqrt 2))) (* 1/2 (/ 1 (sqrt 2))))))
(+.f64 (sqrt.f64 #s(literal 2 binary64)) (*.f64 x (+.f64 (/.f64 #s(literal 1/2 binary64) (sqrt.f64 #s(literal 2 binary64))) (*.f64 x (/.f64 #s(literal 3/16 binary64) (sqrt.f64 #s(literal 2 binary64)))))))
(+ (sqrt 2) (* x (+ (* x (+ (* -1/4 (/ (* x (- 1/2 (* 1/4 (/ 1 (pow (sqrt 2) 2))))) (pow (sqrt 2) 3))) (* 1/2 (/ (- 1/2 (* 1/4 (/ 1 (pow (sqrt 2) 2)))) (sqrt 2))))) (* 1/2 (/ 1 (sqrt 2))))))
(+.f64 (sqrt.f64 #s(literal 2 binary64)) (*.f64 x (+.f64 (/.f64 #s(literal 1/2 binary64) (sqrt.f64 #s(literal 2 binary64))) (*.f64 x (*.f64 (+.f64 (*.f64 #s(literal -1/4 binary64) x) #s(literal 1 binary64)) (/.f64 #s(literal 3/16 binary64) (sqrt.f64 #s(literal 2 binary64))))))))
(* x (sqrt 1/2))
(*.f64 x (sqrt.f64 #s(literal 1/2 binary64)))
(* x (+ (sqrt 1/2) (* 1/2 (/ 1 (* x (sqrt 1/2))))))
(+.f64 (*.f64 x (sqrt.f64 #s(literal 1/2 binary64))) (/.f64 #s(literal 1/2 binary64) (sqrt.f64 #s(literal 1/2 binary64))))
(* x (+ (sqrt 1/2) (+ (* 1/2 (/ (- 2 (* 1/4 (/ 1 (pow (sqrt 1/2) 2)))) (* (pow x 2) (sqrt 1/2)))) (/ 1/2 (* x (sqrt 1/2))))))
(+.f64 (/.f64 #s(literal 1/2 binary64) (sqrt.f64 #s(literal 1/2 binary64))) (*.f64 x (+.f64 (sqrt.f64 #s(literal 1/2 binary64)) (/.f64 (/.f64 #s(literal 3/4 binary64) (sqrt.f64 #s(literal 1/2 binary64))) (*.f64 x x)))))
(* x (+ (sqrt 1/2) (+ (* -1/4 (/ (- 2 (* 1/4 (/ 1 (pow (sqrt 1/2) 2)))) (* (pow x 3) (pow (sqrt 1/2) 3)))) (+ (* 1/2 (/ (- 2 (* 1/4 (/ 1 (pow (sqrt 1/2) 2)))) (* (pow x 2) (sqrt 1/2)))) (/ 1/2 (* x (sqrt 1/2)))))))
(+.f64 (*.f64 x (+.f64 (+.f64 (sqrt.f64 #s(literal 1/2 binary64)) (/.f64 (/.f64 (/.f64 #s(literal -3/4 binary64) (sqrt.f64 #s(literal 1/2 binary64))) x) (*.f64 x x))) (/.f64 (/.f64 #s(literal 3/4 binary64) (sqrt.f64 #s(literal 1/2 binary64))) (*.f64 x x)))) (/.f64 #s(literal 1/2 binary64) (sqrt.f64 #s(literal 1/2 binary64))))
(* -1 (* x (sqrt 1/2)))
(*.f64 x (-.f64 #s(literal 0 binary64) (sqrt.f64 #s(literal 1/2 binary64))))
(* -1 (* x (+ (sqrt 1/2) (* 1/2 (/ 1 (* x (sqrt 1/2)))))))
(-.f64 (/.f64 #s(literal -1/2 binary64) (sqrt.f64 #s(literal 1/2 binary64))) (*.f64 x (sqrt.f64 #s(literal 1/2 binary64))))
(* -1 (* x (+ (sqrt 1/2) (* -1 (/ (- (* -1/2 (/ (- 2 (* 1/4 (/ 1 (pow (sqrt 1/2) 2)))) (* x (sqrt 1/2)))) (* 1/2 (/ 1 (sqrt 1/2)))) x)))))
(*.f64 (-.f64 (sqrt.f64 #s(literal 1/2 binary64)) (/.f64 (+.f64 (/.f64 (/.f64 #s(literal -3/4 binary64) (sqrt.f64 #s(literal 1/2 binary64))) x) (/.f64 #s(literal -1/2 binary64) (sqrt.f64 #s(literal 1/2 binary64)))) x)) (-.f64 #s(literal 0 binary64) x))
(* -1 (* x (+ (sqrt 1/2) (* -1 (/ (- (* -1 (/ (+ (* -1/4 (/ (- 2 (* 1/4 (/ 1 (pow (sqrt 1/2) 2)))) (* x (pow (sqrt 1/2) 3)))) (* 1/2 (/ (- 2 (* 1/4 (/ 1 (pow (sqrt 1/2) 2)))) (sqrt 1/2)))) x)) (* 1/2 (/ 1 (sqrt 1/2)))) x)))))
(*.f64 x (+.f64 (/.f64 (-.f64 (/.f64 #s(literal -1/2 binary64) (sqrt.f64 #s(literal 1/2 binary64))) (/.f64 (+.f64 (/.f64 (/.f64 #s(literal -3/4 binary64) (sqrt.f64 #s(literal 1/2 binary64))) x) (/.f64 #s(literal 3/4 binary64) (sqrt.f64 #s(literal 1/2 binary64)))) x)) x) (-.f64 #s(literal 0 binary64) (sqrt.f64 #s(literal 1/2 binary64)))))
2
#s(literal 2 binary64)
(+ 2 x)
(+.f64 #s(literal 2 binary64) x)
(+ 2 (* x (+ 1 (* 1/2 x))))
(+.f64 #s(literal 2 binary64) (*.f64 x (+.f64 #s(literal 1 binary64) (*.f64 #s(literal 1/2 binary64) x))))
(+ 2 (* x (+ 1 (* 1/2 x))))
(+.f64 #s(literal 2 binary64) (*.f64 x (+.f64 #s(literal 1 binary64) (*.f64 #s(literal 1/2 binary64) x))))
(* 1/2 (pow x 2))
(*.f64 #s(literal 1/2 binary64) (*.f64 x x))
(* (pow x 2) (+ 1/2 (/ 1 x)))
(*.f64 x (+.f64 #s(literal 1 binary64) (*.f64 #s(literal 1/2 binary64) x)))
(* (pow x 2) (+ 1/2 (+ (/ 1 x) (/ 2 (pow x 2)))))
(*.f64 x (+.f64 #s(literal 1 binary64) (*.f64 x (+.f64 (/.f64 #s(literal 2 binary64) (*.f64 x x)) #s(literal 1/2 binary64)))))
(* (pow x 2) (+ 1/2 (+ (/ 1 x) (/ 2 (pow x 2)))))
(*.f64 x (+.f64 #s(literal 1 binary64) (*.f64 x (+.f64 (/.f64 #s(literal 2 binary64) (*.f64 x x)) #s(literal 1/2 binary64)))))
(* 1/2 (pow x 2))
(*.f64 #s(literal 1/2 binary64) (*.f64 x x))
(* (pow x 2) (+ 1/2 (/ 1 x)))
(*.f64 x (+.f64 #s(literal 1 binary64) (*.f64 #s(literal 1/2 binary64) x)))
(* (pow x 2) (+ 1/2 (+ (/ 1 x) (/ 2 (pow x 2)))))
(*.f64 x (+.f64 #s(literal 1 binary64) (*.f64 x (+.f64 (/.f64 #s(literal 2 binary64) (*.f64 x x)) #s(literal 1/2 binary64)))))
(* (pow x 2) (+ 1/2 (+ (/ 1 x) (/ 2 (pow x 2)))))
(*.f64 x (+.f64 #s(literal 1 binary64) (*.f64 x (+.f64 (/.f64 #s(literal 2 binary64) (*.f64 x x)) #s(literal 1/2 binary64)))))
x
(* x (+ 1 (* 1/2 x)))
(*.f64 x (+.f64 #s(literal 1 binary64) (*.f64 #s(literal 1/2 binary64) x)))
(* x (+ 1 (* 1/2 x)))
(*.f64 x (+.f64 #s(literal 1 binary64) (*.f64 #s(literal 1/2 binary64) x)))
(* x (+ 1 (* 1/2 x)))
(*.f64 x (+.f64 #s(literal 1 binary64) (*.f64 #s(literal 1/2 binary64) x)))
(* 1/2 (pow x 2))
(*.f64 #s(literal 1/2 binary64) (*.f64 x x))
(* (pow x 2) (+ 1/2 (/ 1 x)))
(*.f64 x (+.f64 #s(literal 1 binary64) (*.f64 #s(literal 1/2 binary64) x)))
(* (pow x 2) (+ 1/2 (/ 1 x)))
(*.f64 x (+.f64 #s(literal 1 binary64) (*.f64 #s(literal 1/2 binary64) x)))
(* (pow x 2) (+ 1/2 (/ 1 x)))
(*.f64 x (+.f64 #s(literal 1 binary64) (*.f64 #s(literal 1/2 binary64) x)))
(* 1/2 (pow x 2))
(*.f64 #s(literal 1/2 binary64) (*.f64 x x))
(* (pow x 2) (+ 1/2 (/ 1 x)))
(*.f64 x (+.f64 #s(literal 1 binary64) (*.f64 #s(literal 1/2 binary64) x)))
(* (pow x 2) (+ 1/2 (/ 1 x)))
(*.f64 x (+.f64 #s(literal 1 binary64) (*.f64 #s(literal 1/2 binary64) x)))
(* (pow x 2) (+ 1/2 (/ 1 x)))
(*.f64 x (+.f64 #s(literal 1 binary64) (*.f64 #s(literal 1/2 binary64) x)))
1
#s(literal 1 binary64)
(+ 1 (* 1/2 x))
(+.f64 #s(literal 1 binary64) (*.f64 #s(literal 1/2 binary64) x))
(+ 1 (* 1/2 x))
(+.f64 #s(literal 1 binary64) (*.f64 #s(literal 1/2 binary64) x))
(+ 1 (* 1/2 x))
(+.f64 #s(literal 1 binary64) (*.f64 #s(literal 1/2 binary64) x))
(* 1/2 x)
(*.f64 #s(literal 1/2 binary64) x)
(* x (+ 1/2 (/ 1 x)))
(+.f64 #s(literal 1 binary64) (*.f64 #s(literal 1/2 binary64) x))
(* x (+ 1/2 (/ 1 x)))
(+.f64 #s(literal 1 binary64) (*.f64 #s(literal 1/2 binary64) x))
(* x (+ 1/2 (/ 1 x)))
(+.f64 #s(literal 1 binary64) (*.f64 #s(literal 1/2 binary64) x))
(* 1/2 x)
(*.f64 #s(literal 1/2 binary64) x)
(* x (+ 1/2 (/ 1 x)))
(+.f64 #s(literal 1 binary64) (*.f64 #s(literal 1/2 binary64) x))
(* x (+ 1/2 (/ 1 x)))
(+.f64 #s(literal 1 binary64) (*.f64 #s(literal 1/2 binary64) x))
(* x (+ 1/2 (/ 1 x)))
(+.f64 #s(literal 1 binary64) (*.f64 #s(literal 1/2 binary64) x))
(sqrt 2)
(sqrt.f64 #s(literal 2 binary64))
(+ (sqrt 2) (* 1/2 (/ x (sqrt 2))))
(+.f64 (sqrt.f64 #s(literal 2 binary64)) (/.f64 x (*.f64 #s(literal 2 binary64) (sqrt.f64 #s(literal 2 binary64)))))
(+ (sqrt 2) (* x (+ (* 1/2 (/ (* x (- 1/2 (* 1/4 (/ 1 (pow (sqrt 2) 2))))) (sqrt 2))) (* 1/2 (/ 1 (sqrt 2))))))
(+.f64 (sqrt.f64 #s(literal 2 binary64)) (*.f64 x (+.f64 (/.f64 #s(literal 1/2 binary64) (sqrt.f64 #s(literal 2 binary64))) (*.f64 x (/.f64 #s(literal 3/16 binary64) (sqrt.f64 #s(literal 2 binary64)))))))
(+ (sqrt 2) (* x (+ (* x (+ (* 1/2 (/ (* x (- 1/6 (* 1/2 (/ (- 1/2 (* 1/4 (/ 1 (pow (sqrt 2) 2)))) (pow (sqrt 2) 2))))) (sqrt 2))) (* 1/2 (/ (- 1/2 (* 1/4 (/ 1 (pow (sqrt 2) 2)))) (sqrt 2))))) (* 1/2 (/ 1 (sqrt 2))))))
(+.f64 (sqrt.f64 #s(literal 2 binary64)) (*.f64 x (+.f64 (/.f64 #s(literal 1/2 binary64) (sqrt.f64 #s(literal 2 binary64))) (*.f64 x (+.f64 (/.f64 #s(literal 3/16 binary64) (sqrt.f64 #s(literal 2 binary64))) (/.f64 (*.f64 #s(literal 7/192 binary64) x) (sqrt.f64 #s(literal 2 binary64))))))))
(* (sqrt (pow x 3)) (sqrt 1/6))
(*.f64 (sqrt.f64 (*.f64 x (*.f64 x x))) (sqrt.f64 #s(literal 1/6 binary64)))
(* (pow x 2) (+ (* 1/4 (* (sqrt (/ 1 (pow x 3))) (/ 1 (sqrt 1/6)))) (* (sqrt (/ 1 x)) (sqrt 1/6))))
(*.f64 x (*.f64 x (+.f64 (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (*.f64 x (*.f64 x x)))) (/.f64 #s(literal 1/4 binary64) (sqrt.f64 #s(literal 1/6 binary64)))) (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) (sqrt.f64 #s(literal 1/6 binary64))))))
(* (pow x 2) (+ (* 1/4 (* (sqrt (/ 1 (pow x 3))) (/ 1 (sqrt 1/6)))) (+ (* 1/2 (* (sqrt (/ 1 (pow x 5))) (/ 1 (sqrt 1/6)))) (* (sqrt (/ 1 x)) (sqrt 1/6)))))
(*.f64 (*.f64 x x) (+.f64 (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) (sqrt.f64 #s(literal 1/6 binary64))) (*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 #s(literal 1/6 binary64))) (+.f64 (*.f64 #s(literal 1/2 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 5 binary64))))) (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (*.f64 x (*.f64 x x)))) #s(literal 1/4 binary64))))))
(* (pow x 2) (+ (* 1/4 (* (sqrt (/ 1 (pow x 3))) (/ 1 (sqrt 1/6)))) (+ (* 1/2 (* (sqrt (/ 1 (pow x 5))) (/ 1 (sqrt 1/6)))) (+ (* 1/2 (* (sqrt (/ 1 (pow x 7))) (/ (- 2 (* 1/16 (/ x (pow (sqrt 1/6) 2)))) (sqrt 1/6)))) (* (sqrt (/ 1 x)) (sqrt 1/6))))))
(*.f64 x (*.f64 x (+.f64 (+.f64 (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) (sqrt.f64 #s(literal 1/6 binary64))) (*.f64 #s(literal 1/2 binary64) (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 7 binary64)))) (/.f64 (+.f64 #s(literal 2 binary64) (/.f64 (*.f64 x #s(literal 1/16 binary64)) #s(literal -1/6 binary64))) (sqrt.f64 #s(literal 1/6 binary64)))))) (*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 #s(literal 1/6 binary64))) (+.f64 (*.f64 #s(literal 1/2 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 5 binary64))))) (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (*.f64 x (*.f64 x x)))) #s(literal 1/4 binary64)))))))
(* (sqrt (pow x 3)) (* (sqrt -1) (sqrt -1/6)))
(*.f64 (sqrt.f64 #s(literal -1 binary64)) (*.f64 (sqrt.f64 #s(literal -1/6 binary64)) (sqrt.f64 (*.f64 x (*.f64 x x)))))
(* (pow x 2) (+ (* 1/4 (* (sqrt (/ 1 (pow x 3))) (/ (sqrt -1) (sqrt -1/6)))) (* (sqrt (/ 1 x)) (* (sqrt -1) (sqrt -1/6)))))
(*.f64 (*.f64 x x) (+.f64 (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (*.f64 x (*.f64 x x)))) (/.f64 (*.f64 (sqrt.f64 #s(literal -1 binary64)) #s(literal 1/4 binary64)) (sqrt.f64 #s(literal -1/6 binary64)))) (*.f64 (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) (sqrt.f64 #s(literal -1/6 binary64))) (sqrt.f64 #s(literal -1 binary64)))))
(* (pow x 2) (+ (* 1/4 (* (sqrt (/ 1 (pow x 3))) (/ (sqrt -1) (sqrt -1/6)))) (+ (* 1/2 (* (sqrt (/ 1 (pow x 5))) (/ (sqrt -1) (sqrt -1/6)))) (* (sqrt (/ 1 x)) (* (sqrt -1) (sqrt -1/6))))))
(*.f64 (*.f64 x x) (+.f64 (*.f64 (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) (sqrt.f64 #s(literal -1/6 binary64))) (sqrt.f64 #s(literal -1 binary64))) (*.f64 (/.f64 (sqrt.f64 #s(literal -1 binary64)) (sqrt.f64 #s(literal -1/6 binary64))) (+.f64 (*.f64 #s(literal 1/2 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 5 binary64))))) (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (*.f64 x (*.f64 x x)))) #s(literal 1/4 binary64))))))
(* (pow x 2) (+ (* -1 (/ (+ (* -1/2 (* (sqrt x) (/ (sqrt -1) (sqrt -1/6)))) (* -1/2 (* (sqrt (/ 1 x)) (/ (* (sqrt -1) (- 2 (* -1/16 (/ x (pow (sqrt -1/6) 2))))) (sqrt -1/6))))) (pow x 3))) (+ (* 1/4 (* (sqrt (/ 1 (pow x 3))) (/ (sqrt -1) (sqrt -1/6)))) (* (sqrt (/ 1 x)) (* (sqrt -1) (sqrt -1/6))))))
(+.f64 (*.f64 (*.f64 x x) (+.f64 (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (*.f64 x (*.f64 x x)))) (/.f64 (*.f64 (sqrt.f64 #s(literal -1 binary64)) #s(literal 1/4 binary64)) (sqrt.f64 #s(literal -1/6 binary64)))) (*.f64 (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) (sqrt.f64 #s(literal -1/6 binary64))) (sqrt.f64 #s(literal -1 binary64))))) (*.f64 #s(literal 1 binary64) (/.f64 (*.f64 #s(literal 1/2 binary64) (+.f64 (/.f64 (*.f64 (sqrt.f64 x) (sqrt.f64 #s(literal -1 binary64))) (sqrt.f64 #s(literal -1/6 binary64))) (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) (/.f64 (*.f64 (sqrt.f64 #s(literal -1 binary64)) (+.f64 #s(literal 2 binary64) (/.f64 (*.f64 x #s(literal 1/16 binary64)) #s(literal -1/6 binary64)))) (sqrt.f64 #s(literal -1/6 binary64)))))) x)))
2
#s(literal 2 binary64)
(+ 2 x)
(+.f64 #s(literal 2 binary64) x)
(+ 2 (* x (+ 1 (* 1/2 x))))
(+.f64 #s(literal 2 binary64) (*.f64 x (+.f64 #s(literal 1 binary64) (*.f64 #s(literal 1/2 binary64) x))))
(+ 2 (* x (+ 1 (* x (+ 1/2 (* 1/6 x))))))
(+.f64 #s(literal 2 binary64) (*.f64 x (+.f64 #s(literal 1 binary64) (*.f64 x (+.f64 #s(literal 1/2 binary64) (*.f64 x #s(literal 1/6 binary64)))))))
(* 1/6 (pow x 3))
(*.f64 (*.f64 x (*.f64 x x)) #s(literal 1/6 binary64))
(* (pow x 3) (+ 1/6 (* 1/2 (/ 1 x))))
(*.f64 x (*.f64 x (+.f64 #s(literal 1/2 binary64) (*.f64 x #s(literal 1/6 binary64)))))
(* (pow x 3) (+ 1/6 (+ (* 1/2 (/ 1 x)) (/ 1 (pow x 2)))))
(*.f64 x (+.f64 #s(literal 1 binary64) (*.f64 x (+.f64 #s(literal 1/2 binary64) (*.f64 x #s(literal 1/6 binary64))))))
(* (pow x 3) (+ 1/6 (+ (* 1/2 (/ 1 x)) (+ (/ 1 (pow x 2)) (* 2 (/ 1 (pow x 3)))))))
(*.f64 x (+.f64 (+.f64 #s(literal 1 binary64) (*.f64 #s(literal 1/2 binary64) x)) (*.f64 (*.f64 x x) (+.f64 (/.f64 #s(literal 2 binary64) (*.f64 x (*.f64 x x))) #s(literal 1/6 binary64)))))
(* 1/6 (pow x 3))
(*.f64 (*.f64 x (*.f64 x x)) #s(literal 1/6 binary64))
(* (pow x 3) (+ 1/6 (* 1/2 (/ 1 x))))
(*.f64 x (*.f64 x (+.f64 #s(literal 1/2 binary64) (*.f64 x #s(literal 1/6 binary64)))))
(* -1 (* (pow x 3) (- (* -1 (/ (+ 1/2 (/ 1 x)) x)) 1/6)))
(*.f64 (*.f64 x (*.f64 x x)) (-.f64 #s(literal 0 binary64) (-.f64 #s(literal -1/6 binary64) (/.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 #s(literal 1 binary64) x)) x))))
(* -1 (* (pow x 3) (- (* -1 (/ (+ 1/2 (+ (/ 1 x) (/ 2 (pow x 2)))) x)) 1/6)))
(*.f64 (*.f64 x (*.f64 x x)) (-.f64 #s(literal 0 binary64) (-.f64 #s(literal -1/6 binary64) (/.f64 (+.f64 (/.f64 #s(literal 1 binary64) x) (+.f64 #s(literal 1/2 binary64) (/.f64 #s(literal 2 binary64) (*.f64 x x)))) x))))
x
(* x (+ 1 (* 1/2 x)))
(*.f64 x (+.f64 #s(literal 1 binary64) (*.f64 #s(literal 1/2 binary64) x)))
(* x (+ 1 (* x (+ 1/2 (* 1/6 x)))))
(*.f64 x (+.f64 #s(literal 1 binary64) (*.f64 x (+.f64 #s(literal 1/2 binary64) (*.f64 x #s(literal 1/6 binary64))))))
(* x (+ 1 (* x (+ 1/2 (* 1/6 x)))))
(*.f64 x (+.f64 #s(literal 1 binary64) (*.f64 x (+.f64 #s(literal 1/2 binary64) (*.f64 x #s(literal 1/6 binary64))))))
(* 1/6 (pow x 3))
(*.f64 (*.f64 x (*.f64 x x)) #s(literal 1/6 binary64))
(* (pow x 3) (+ 1/6 (* 1/2 (/ 1 x))))
(*.f64 x (*.f64 x (+.f64 #s(literal 1/2 binary64) (*.f64 x #s(literal 1/6 binary64)))))
(* (pow x 3) (+ 1/6 (+ (* 1/2 (/ 1 x)) (/ 1 (pow x 2)))))
(*.f64 x (+.f64 #s(literal 1 binary64) (*.f64 x (+.f64 #s(literal 1/2 binary64) (*.f64 x #s(literal 1/6 binary64))))))
(* (pow x 3) (+ 1/6 (+ (* 1/2 (/ 1 x)) (/ 1 (pow x 2)))))
(*.f64 x (+.f64 #s(literal 1 binary64) (*.f64 x (+.f64 #s(literal 1/2 binary64) (*.f64 x #s(literal 1/6 binary64))))))
(* 1/6 (pow x 3))
(*.f64 (*.f64 x (*.f64 x x)) #s(literal 1/6 binary64))
(* (pow x 3) (+ 1/6 (* 1/2 (/ 1 x))))
(*.f64 x (*.f64 x (+.f64 #s(literal 1/2 binary64) (*.f64 x #s(literal 1/6 binary64)))))
(* -1 (* (pow x 3) (- (* -1 (/ (+ 1/2 (/ 1 x)) x)) 1/6)))
(*.f64 (*.f64 x (*.f64 x x)) (-.f64 #s(literal 0 binary64) (-.f64 #s(literal -1/6 binary64) (/.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 #s(literal 1 binary64) x)) x))))
(* -1 (* (pow x 3) (- (* -1 (/ (+ 1/2 (/ 1 x)) x)) 1/6)))
(*.f64 (*.f64 x (*.f64 x x)) (-.f64 #s(literal 0 binary64) (-.f64 #s(literal -1/6 binary64) (/.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 #s(literal 1 binary64) x)) x))))
1
#s(literal 1 binary64)
(+ 1 (* 1/2 x))
(+.f64 #s(literal 1 binary64) (*.f64 #s(literal 1/2 binary64) x))
(+ 1 (* x (+ 1/2 (* 1/6 x))))
(+.f64 #s(literal 1 binary64) (*.f64 x (+.f64 #s(literal 1/2 binary64) (*.f64 x #s(literal 1/6 binary64)))))
(+ 1 (* x (+ 1/2 (* 1/6 x))))
(+.f64 #s(literal 1 binary64) (*.f64 x (+.f64 #s(literal 1/2 binary64) (*.f64 x #s(literal 1/6 binary64)))))
(* 1/6 (pow x 2))
(*.f64 (*.f64 x x) #s(literal 1/6 binary64))
(* (pow x 2) (+ 1/6 (* 1/2 (/ 1 x))))
(*.f64 x (+.f64 #s(literal 1/2 binary64) (*.f64 x #s(literal 1/6 binary64))))
(* (pow x 2) (+ 1/6 (+ (* 1/2 (/ 1 x)) (/ 1 (pow x 2)))))
(+.f64 #s(literal 1 binary64) (*.f64 x (+.f64 #s(literal 1/2 binary64) (*.f64 x #s(literal 1/6 binary64)))))
(* (pow x 2) (+ 1/6 (+ (* 1/2 (/ 1 x)) (/ 1 (pow x 2)))))
(+.f64 #s(literal 1 binary64) (*.f64 x (+.f64 #s(literal 1/2 binary64) (*.f64 x #s(literal 1/6 binary64)))))
(* 1/6 (pow x 2))
(*.f64 (*.f64 x x) #s(literal 1/6 binary64))
(* (pow x 2) (+ 1/6 (* 1/2 (/ 1 x))))
(*.f64 x (+.f64 #s(literal 1/2 binary64) (*.f64 x #s(literal 1/6 binary64))))
(* (pow x 2) (+ 1/6 (+ (* 1/2 (/ 1 x)) (/ 1 (pow x 2)))))
(+.f64 #s(literal 1 binary64) (*.f64 x (+.f64 #s(literal 1/2 binary64) (*.f64 x #s(literal 1/6 binary64)))))
(* (pow x 2) (+ 1/6 (+ (* 1/2 (/ 1 x)) (/ 1 (pow x 2)))))
(+.f64 #s(literal 1 binary64) (*.f64 x (+.f64 #s(literal 1/2 binary64) (*.f64 x #s(literal 1/6 binary64)))))
(* 1/2 x)
(*.f64 #s(literal 1/2 binary64) x)
(* 1/2 x)
(*.f64 #s(literal 1/2 binary64) x)
(* 1/2 x)
(*.f64 #s(literal 1/2 binary64) x)
(* 1/2 x)
(*.f64 #s(literal 1/2 binary64) x)
(* 1/2 x)
(*.f64 #s(literal 1/2 binary64) x)
(* 1/2 x)
(*.f64 #s(literal 1/2 binary64) x)
(* 1/2 x)
(*.f64 #s(literal 1/2 binary64) x)
(* 1/2 x)
(*.f64 #s(literal 1/2 binary64) x)
(* 1/2 x)
(*.f64 #s(literal 1/2 binary64) x)
(* 1/2 x)
(*.f64 #s(literal 1/2 binary64) x)
(* 1/2 x)
(*.f64 #s(literal 1/2 binary64) x)
(* 1/2 x)
(*.f64 #s(literal 1/2 binary64) x)
(* 1/6 x)
(*.f64 x #s(literal 1/6 binary64))
(* 1/6 x)
(*.f64 x #s(literal 1/6 binary64))
(* 1/6 x)
(*.f64 x #s(literal 1/6 binary64))
(* 1/6 x)
(*.f64 x #s(literal 1/6 binary64))
(* 1/6 x)
(*.f64 x #s(literal 1/6 binary64))
(* 1/6 x)
(*.f64 x #s(literal 1/6 binary64))
(* 1/6 x)
(*.f64 x #s(literal 1/6 binary64))
(* 1/6 x)
(*.f64 x #s(literal 1/6 binary64))
(* 1/6 x)
(*.f64 x #s(literal 1/6 binary64))
(* 1/6 x)
(*.f64 x #s(literal 1/6 binary64))
(* 1/6 x)
(*.f64 x #s(literal 1/6 binary64))
(* 1/6 x)
(*.f64 x #s(literal 1/6 binary64))
(* 1/2 x)
(*.f64 #s(literal 1/2 binary64) x)
(* x (+ 1/2 (* 1/6 x)))
(*.f64 x (+.f64 #s(literal 1/2 binary64) (*.f64 x #s(literal 1/6 binary64))))
(* x (+ 1/2 (* 1/6 x)))
(*.f64 x (+.f64 #s(literal 1/2 binary64) (*.f64 x #s(literal 1/6 binary64))))
(* x (+ 1/2 (* 1/6 x)))
(*.f64 x (+.f64 #s(literal 1/2 binary64) (*.f64 x #s(literal 1/6 binary64))))
(* 1/6 (pow x 2))
(*.f64 (*.f64 x x) #s(literal 1/6 binary64))
(* (pow x 2) (+ 1/6 (* 1/2 (/ 1 x))))
(*.f64 x (+.f64 #s(literal 1/2 binary64) (*.f64 x #s(literal 1/6 binary64))))
(* (pow x 2) (+ 1/6 (* 1/2 (/ 1 x))))
(*.f64 x (+.f64 #s(literal 1/2 binary64) (*.f64 x #s(literal 1/6 binary64))))
(* (pow x 2) (+ 1/6 (* 1/2 (/ 1 x))))
(*.f64 x (+.f64 #s(literal 1/2 binary64) (*.f64 x #s(literal 1/6 binary64))))
(* 1/6 (pow x 2))
(*.f64 (*.f64 x x) #s(literal 1/6 binary64))
(* (pow x 2) (+ 1/6 (* 1/2 (/ 1 x))))
(*.f64 x (+.f64 #s(literal 1/2 binary64) (*.f64 x #s(literal 1/6 binary64))))
(* (pow x 2) (+ 1/6 (* 1/2 (/ 1 x))))
(*.f64 x (+.f64 #s(literal 1/2 binary64) (*.f64 x #s(literal 1/6 binary64))))
(* (pow x 2) (+ 1/6 (* 1/2 (/ 1 x))))
(*.f64 x (+.f64 #s(literal 1/2 binary64) (*.f64 x #s(literal 1/6 binary64))))

eval75.0ms (1%)

Compiler

Compiled 16511 to 2007 computations (87.8% saved)

prune76.0ms (1%)

Pruning

11 alts after pruning (6 fresh and 5 done)

PrunedKeptTotal
New5746580
Fresh000
Picked044
Done011
Total57411585
Accuracy
100.0%
Counts
585 → 11
Alt Table
Click to see full alt table
StatusAccuracyProgram
63.1%
(/.f64 #s(literal 1 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) (+.f64 #s(literal 2 binary64) (*.f64 x (+.f64 #s(literal 1 binary64) (*.f64 x (+.f64 #s(literal 1/2 binary64) (*.f64 x #s(literal 1/6 binary64))))))))))
2.9%
(*.f64 x (sqrt.f64 #s(literal 1/2 binary64)))
63.9%
(sqrt.f64 (+.f64 #s(literal 2 binary64) (*.f64 x (+.f64 #s(literal 1 binary64) (*.f64 x (+.f64 #s(literal 1/2 binary64) (*.f64 x #s(literal 1/6 binary64))))))))
65.6%
(sqrt.f64 (+.f64 #s(literal 2 binary64) (*.f64 x (+.f64 #s(literal 1 binary64) (*.f64 #s(literal 1/2 binary64) x)))))
63.5%
(sqrt.f64 (+.f64 #s(literal 2 binary64) x))
100.0%
(sqrt.f64 (+.f64 #s(literal 1 binary64) (exp.f64 x)))
2.2%
(sqrt.f64 (*.f64 (*.f64 x (*.f64 x x)) #s(literal 1/6 binary64)))
2.3%
(sqrt.f64 (*.f64 x (+.f64 #s(literal 1 binary64) (*.f64 x (+.f64 #s(literal 1/2 binary64) (*.f64 x #s(literal 1/6 binary64)))))))
3.3%
(sqrt.f64 (*.f64 x (*.f64 x (+.f64 #s(literal 1/2 binary64) (*.f64 x #s(literal 1/6 binary64))))))
2.3%
(sqrt.f64 x)
70.2%
(sqrt.f64 #s(literal 2 binary64))
Compiler

Compiled 160 to 121 computations (24.4% saved)

simplify24.0ms (0.3%)

Algorithm
egg-herbie
Localize:

Found 15 expressions of interest:

NewMetricScoreProgram
cost-diff0
(+.f64 #s(literal 1/2 binary64) (*.f64 x #s(literal 1/6 binary64)))
cost-diff0
(*.f64 x (+.f64 #s(literal 1/2 binary64) (*.f64 x #s(literal 1/6 binary64))))
cost-diff0
(*.f64 x (*.f64 x (+.f64 #s(literal 1/2 binary64) (*.f64 x #s(literal 1/6 binary64)))))
cost-diff0
(sqrt.f64 (*.f64 x (*.f64 x (+.f64 #s(literal 1/2 binary64) (*.f64 x #s(literal 1/6 binary64))))))
cost-diff0
(*.f64 x x)
cost-diff0
(*.f64 x (*.f64 x x))
cost-diff0
(*.f64 (*.f64 x (*.f64 x x)) #s(literal 1/6 binary64))
cost-diff0
(sqrt.f64 (*.f64 (*.f64 x (*.f64 x x)) #s(literal 1/6 binary64)))
cost-diff0
(sqrt.f64 #s(literal 1/2 binary64))
cost-diff0
(*.f64 x (sqrt.f64 #s(literal 1/2 binary64)))
cost-diff0
(sqrt.f64 x)
cost-diff0
(+.f64 #s(literal 2 binary64) (*.f64 x (+.f64 #s(literal 1 binary64) (*.f64 x (+.f64 #s(literal 1/2 binary64) (*.f64 x #s(literal 1/6 binary64)))))))
cost-diff0
(/.f64 #s(literal 1 binary64) (+.f64 #s(literal 2 binary64) (*.f64 x (+.f64 #s(literal 1 binary64) (*.f64 x (+.f64 #s(literal 1/2 binary64) (*.f64 x #s(literal 1/6 binary64))))))))
cost-diff0
(sqrt.f64 (/.f64 #s(literal 1 binary64) (+.f64 #s(literal 2 binary64) (*.f64 x (+.f64 #s(literal 1 binary64) (*.f64 x (+.f64 #s(literal 1/2 binary64) (*.f64 x #s(literal 1/6 binary64)))))))))
cost-diff0
(/.f64 #s(literal 1 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) (+.f64 #s(literal 2 binary64) (*.f64 x (+.f64 #s(literal 1 binary64) (*.f64 x (+.f64 #s(literal 1/2 binary64) (*.f64 x #s(literal 1/6 binary64))))))))))
Rules
532×fma-define
400×fma-lowering-fma.f32
400×fma-lowering-fma.f64
160×sum3-define
146×*-lowering-*.f32
Iterations

Useful iterations: 1 (0.0ms)

IterNodesCost
023164
154142
2121142
3287142
4517142
5667142
6671142
0671142
Stop Event
iter limit
saturated
Calls
Call 1
Inputs
(/ 1 (sqrt (/ 1 (+ 2 (* x (+ 1 (* x (+ 1/2 (* x 1/6)))))))))
1
(sqrt (/ 1 (+ 2 (* x (+ 1 (* x (+ 1/2 (* x 1/6))))))))
(/ 1 (+ 2 (* x (+ 1 (* x (+ 1/2 (* x 1/6)))))))
(+ 2 (* x (+ 1 (* x (+ 1/2 (* x 1/6))))))
2
(* x (+ 1 (* x (+ 1/2 (* x 1/6)))))
x
(+ 1 (* x (+ 1/2 (* x 1/6))))
(* x (+ 1/2 (* x 1/6)))
(+ 1/2 (* x 1/6))
1/2
(* x 1/6)
1/6
(sqrt x)
x
(* x (sqrt 1/2))
x
(sqrt 1/2)
1/2
(sqrt (* (* x (* x x)) 1/6))
(* (* x (* x x)) 1/6)
(* x (* x x))
x
(* x x)
1/6
(sqrt (* x (* x (+ 1/2 (* x 1/6)))))
(* x (* x (+ 1/2 (* x 1/6))))
x
(* x (+ 1/2 (* x 1/6)))
(+ 1/2 (* x 1/6))
1/2
(* x 1/6)
1/6
Outputs
(/ 1 (sqrt (/ 1 (+ 2 (* x (+ 1 (* x (+ 1/2 (* x 1/6)))))))))
(/.f64 #s(literal 1 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) (+.f64 #s(literal 2 binary64) (*.f64 x (+.f64 #s(literal 1 binary64) (*.f64 x (+.f64 #s(literal 1/2 binary64) (*.f64 x #s(literal 1/6 binary64))))))))))
1
#s(literal 1 binary64)
(sqrt (/ 1 (+ 2 (* x (+ 1 (* x (+ 1/2 (* x 1/6))))))))
(sqrt.f64 (/.f64 #s(literal 1 binary64) (+.f64 #s(literal 2 binary64) (*.f64 x (+.f64 #s(literal 1 binary64) (*.f64 x (+.f64 #s(literal 1/2 binary64) (*.f64 x #s(literal 1/6 binary64)))))))))
(/ 1 (+ 2 (* x (+ 1 (* x (+ 1/2 (* x 1/6)))))))
(/.f64 #s(literal 1 binary64) (+.f64 #s(literal 2 binary64) (*.f64 x (+.f64 #s(literal 1 binary64) (*.f64 x (+.f64 #s(literal 1/2 binary64) (*.f64 x #s(literal 1/6 binary64))))))))
(+ 2 (* x (+ 1 (* x (+ 1/2 (* x 1/6))))))
(+.f64 #s(literal 2 binary64) (*.f64 x (+.f64 #s(literal 1 binary64) (*.f64 x (+.f64 #s(literal 1/2 binary64) (*.f64 x #s(literal 1/6 binary64)))))))
2
#s(literal 2 binary64)
(* x (+ 1 (* x (+ 1/2 (* x 1/6)))))
(*.f64 x (+.f64 #s(literal 1 binary64) (*.f64 x (+.f64 #s(literal 1/2 binary64) (*.f64 x #s(literal 1/6 binary64))))))
x
(+ 1 (* x (+ 1/2 (* x 1/6))))
(+.f64 #s(literal 1 binary64) (*.f64 x (+.f64 #s(literal 1/2 binary64) (*.f64 x #s(literal 1/6 binary64)))))
(* x (+ 1/2 (* x 1/6)))
(*.f64 x (+.f64 #s(literal 1/2 binary64) (*.f64 x #s(literal 1/6 binary64))))
(+ 1/2 (* x 1/6))
(+.f64 #s(literal 1/2 binary64) (*.f64 x #s(literal 1/6 binary64)))
1/2
#s(literal 1/2 binary64)
(* x 1/6)
(*.f64 x #s(literal 1/6 binary64))
1/6
#s(literal 1/6 binary64)
(sqrt x)
(sqrt.f64 x)
x
(* x (sqrt 1/2))
(*.f64 x (sqrt.f64 #s(literal 1/2 binary64)))
x
(sqrt 1/2)
(sqrt.f64 #s(literal 1/2 binary64))
1/2
#s(literal 1/2 binary64)
(sqrt (* (* x (* x x)) 1/6))
(sqrt.f64 (*.f64 #s(literal 1/6 binary64) (*.f64 x (*.f64 x x))))
(* (* x (* x x)) 1/6)
(*.f64 #s(literal 1/6 binary64) (*.f64 x (*.f64 x x)))
(* x (* x x))
(*.f64 x (*.f64 x x))
x
(* x x)
(*.f64 x x)
1/6
#s(literal 1/6 binary64)
(sqrt (* x (* x (+ 1/2 (* x 1/6)))))
(sqrt.f64 (*.f64 x (*.f64 x (+.f64 #s(literal 1/2 binary64) (*.f64 x #s(literal 1/6 binary64))))))
(* x (* x (+ 1/2 (* x 1/6))))
(*.f64 x (*.f64 x (+.f64 #s(literal 1/2 binary64) (*.f64 x #s(literal 1/6 binary64)))))
x
(* x (+ 1/2 (* x 1/6)))
(*.f64 x (+.f64 #s(literal 1/2 binary64) (*.f64 x #s(literal 1/6 binary64))))
(+ 1/2 (* x 1/6))
(+.f64 #s(literal 1/2 binary64) (*.f64 x #s(literal 1/6 binary64)))
1/2
#s(literal 1/2 binary64)
(* x 1/6)
(*.f64 x #s(literal 1/6 binary64))
1/6
#s(literal 1/6 binary64)

localize104.0ms (1.4%)

Localize:

Found 15 expressions of interest:

NewMetricScoreProgram
accuracy100.0%
(*.f64 x (+.f64 #s(literal 1/2 binary64) (*.f64 x #s(literal 1/6 binary64))))
accuracy100.0%
(*.f64 x (*.f64 x (+.f64 #s(literal 1/2 binary64) (*.f64 x #s(literal 1/6 binary64)))))
accuracy99.9%
(*.f64 x #s(literal 1/6 binary64))
accuracy86.2%
(sqrt.f64 (*.f64 x (*.f64 x (+.f64 #s(literal 1/2 binary64) (*.f64 x #s(literal 1/6 binary64))))))
accuracy100.0%
(*.f64 x x)
accuracy100.0%
(*.f64 x (*.f64 x x))
accuracy99.9%
(*.f64 (*.f64 x (*.f64 x x)) #s(literal 1/6 binary64))
accuracy90.6%
(sqrt.f64 (*.f64 (*.f64 x (*.f64 x x)) #s(literal 1/6 binary64)))
accuracy100.0%
(sqrt.f64 #s(literal 1/2 binary64))
accuracy99.8%
(*.f64 x (sqrt.f64 #s(literal 1/2 binary64)))
accuracy100.0%
(sqrt.f64 x)
accuracy100.0%
(/.f64 #s(literal 1 binary64) (+.f64 #s(literal 2 binary64) (*.f64 x (+.f64 #s(literal 1 binary64) (*.f64 x (+.f64 #s(literal 1/2 binary64) (*.f64 x #s(literal 1/6 binary64))))))))
accuracy100.0%
(*.f64 x (+.f64 #s(literal 1 binary64) (*.f64 x (+.f64 #s(literal 1/2 binary64) (*.f64 x #s(literal 1/6 binary64))))))
accuracy99.9%
(*.f64 x #s(literal 1/6 binary64))
accuracy99.5%
(/.f64 #s(literal 1 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) (+.f64 #s(literal 2 binary64) (*.f64 x (+.f64 #s(literal 1 binary64) (*.f64 x (+.f64 #s(literal 1/2 binary64) (*.f64 x #s(literal 1/6 binary64))))))))))
Results
46.0ms175×0invalid
20.0ms81×0valid
Compiler

Compiled 177 to 24 computations (86.4% saved)

Precisions
Click to see histograms. Total time spent on operations: 36.0ms
ival-mult: 16.0ms (44.2% of total)
ival-sqrt: 8.0ms (22.1% of total)
ival-add: 4.0ms (11.1% of total)
...c/correct-round.rkt:119:19: 4.0ms (11.1% of total)
ival-div: 3.0ms (8.3% of total)
const: 1.0ms (2.8% of total)
backward-pass: 0.0ms (0% of total)

series17.0ms (0.2%)

Counts
17 → 192
Calls
Call 1
Inputs
#<alt (/ 1 (sqrt (/ 1 (+ 2 (* x (+ 1 (* x (+ 1/2 (* x 1/6)))))))))>
#<alt (sqrt (/ 1 (+ 2 (* x (+ 1 (* x (+ 1/2 (* x 1/6))))))))>
#<alt (/ 1 (+ 2 (* x (+ 1 (* x (+ 1/2 (* x 1/6)))))))>
#<alt (+ 2 (* x (+ 1 (* x (+ 1/2 (* x 1/6))))))>
#<alt (sqrt x)>
#<alt (* x (sqrt 1/2))>
#<alt (sqrt 1/2)>
#<alt (sqrt (* (* x (* x x)) 1/6))>
#<alt (* (* x (* x x)) 1/6)>
#<alt (* x (* x x))>
#<alt (* x x)>
#<alt (sqrt (* x (* x (+ 1/2 (* x 1/6)))))>
#<alt (* x (* x (+ 1/2 (* x 1/6))))>
#<alt (* x (+ 1/2 (* x 1/6)))>
#<alt (+ 1/2 (* x 1/6))>
#<alt (* x 1/6)>
#<alt (* x (+ 1 (* x (+ 1/2 (* x 1/6)))))>
Outputs
#<alt (sqrt 2)>
#<alt (+ (sqrt 2) (* 1/2 (/ x (sqrt 2))))>
#<alt (+ (sqrt 2) (* x (+ (* 1/2 (/ (* x (- 1/2 (* 1/4 (/ 1 (pow (sqrt 2) 2))))) (sqrt 2))) (* 1/2 (/ 1 (sqrt 2))))))>
#<alt (+ (sqrt 2) (* x (+ (* x (+ (* 1/2 (/ (* x (- 1/6 (* 1/2 (/ (- 1/2 (* 1/4 (/ 1 (pow (sqrt 2) 2)))) (pow (sqrt 2) 2))))) (sqrt 2))) (* 1/2 (/ (- 1/2 (* 1/4 (/ 1 (pow (sqrt 2) 2)))) (sqrt 2))))) (* 1/2 (/ 1 (sqrt 2))))))>
#<alt (* (sqrt (pow x 3)) (sqrt 1/6))>
#<alt (* (pow x 2) (+ (* 1/4 (* (sqrt (/ 1 (pow x 3))) (/ 1 (sqrt 1/6)))) (* (sqrt (/ 1 x)) (sqrt 1/6))))>
#<alt (* (pow x 2) (+ (* 1/4 (* (sqrt (/ 1 (pow x 3))) (/ 1 (sqrt 1/6)))) (+ (* 1/2 (* (sqrt (/ 1 (pow x 5))) (/ 1 (sqrt 1/6)))) (* (sqrt (/ 1 x)) (sqrt 1/6)))))>
#<alt (* (pow x 2) (+ (* 1/4 (* (sqrt (/ 1 (pow x 3))) (/ 1 (sqrt 1/6)))) (+ (* 1/2 (* (sqrt (/ 1 (pow x 5))) (/ 1 (sqrt 1/6)))) (+ (* 1/2 (* (sqrt (/ 1 (pow x 7))) (/ (- 2 (* 1/16 (/ x (pow (sqrt 1/6) 2)))) (sqrt 1/6)))) (* (sqrt (/ 1 x)) (sqrt 1/6))))))>
#<alt (* (sqrt (pow x 3)) (* (sqrt -1) (sqrt -1/6)))>
#<alt (* (pow x 2) (+ (* 1/4 (* (sqrt (/ 1 (pow x 3))) (/ (sqrt -1) (sqrt -1/6)))) (* (sqrt (/ 1 x)) (* (sqrt -1) (sqrt -1/6)))))>
#<alt (* (pow x 2) (+ (* 1/4 (* (sqrt (/ 1 (pow x 3))) (/ (sqrt -1) (sqrt -1/6)))) (+ (* 1/2 (* (sqrt (/ 1 (pow x 5))) (/ (sqrt -1) (sqrt -1/6)))) (* (sqrt (/ 1 x)) (* (sqrt -1) (sqrt -1/6))))))>
#<alt (* (pow x 2) (+ (* -1 (/ (+ (* -1/2 (* (sqrt x) (/ (sqrt -1) (sqrt -1/6)))) (* -1/2 (* (sqrt (/ 1 x)) (/ (* (sqrt -1) (- 2 (* -1/16 (/ x (pow (sqrt -1/6) 2))))) (sqrt -1/6))))) (pow x 3))) (+ (* 1/4 (* (sqrt (/ 1 (pow x 3))) (/ (sqrt -1) (sqrt -1/6)))) (* (sqrt (/ 1 x)) (* (sqrt -1) (sqrt -1/6))))))>
#<alt (sqrt 1/2)>
#<alt (+ (sqrt 1/2) (* -1/8 (/ x (sqrt 1/2))))>
#<alt (+ (sqrt 1/2) (* x (- (* -1/128 (/ x (pow (sqrt 1/2) 3))) (* 1/8 (/ 1 (sqrt 1/2))))))>
#<alt (+ (sqrt 1/2) (* x (- (* x (- (* 1/2 (/ (* x (- 1/48 (* 1/512 (/ 1 (pow (sqrt 1/2) 4))))) (sqrt 1/2))) (* 1/128 (/ 1 (pow (sqrt 1/2) 3))))) (* 1/8 (/ 1 (sqrt 1/2))))))>
#<alt (* (sqrt (/ 1 (pow x 3))) (sqrt 6))>
#<alt (/ (+ (* -9 (* (sqrt (/ 1 (pow x 3))) (/ 1 (sqrt 6)))) (* (sqrt (/ 1 x)) (sqrt 6))) x)>
#<alt (/ (+ (* -9 (* (sqrt (/ 1 (pow x 3))) (/ 1 (sqrt 6)))) (+ (* 9 (* (sqrt (/ 1 (pow x 5))) (/ 1 (sqrt 6)))) (* (sqrt (/ 1 x)) (sqrt 6)))) x)>
#<alt (/ (+ (* -9 (* (sqrt (/ 1 (pow x 3))) (/ 1 (sqrt 6)))) (+ (* -1/2 (* (sqrt (/ 1 (pow x 7))) (/ (+ 18 (* 81 (/ x (pow (sqrt 6) 2)))) (sqrt 6)))) (+ (* 9 (* (sqrt (/ 1 (pow x 5))) (/ 1 (sqrt 6)))) (* (sqrt (/ 1 x)) (sqrt 6))))) x)>
#<alt (* -1 (* (sqrt (/ 1 (pow x 3))) (* (sqrt -6) (sqrt -1))))>
#<alt (* -1 (/ (+ (* -9 (* (sqrt (/ 1 (pow x 3))) (/ (sqrt -1) (sqrt -6)))) (* (sqrt (/ 1 x)) (* (sqrt -6) (sqrt -1)))) x))>
#<alt (* -1 (/ (+ (* -9 (* (sqrt (/ 1 (pow x 3))) (/ (sqrt -1) (sqrt -6)))) (+ (* 9 (* (sqrt (/ 1 (pow x 5))) (/ (sqrt -1) (sqrt -6)))) (* (sqrt (/ 1 x)) (* (sqrt -6) (sqrt -1))))) x))>
#<alt (* -1 (/ (+ (* -9 (* (sqrt (/ 1 (pow x 3))) (/ (sqrt -1) (sqrt -6)))) (+ (* -1 (/ (+ (* -9 (* (sqrt x) (/ (sqrt -1) (sqrt -6)))) (* 1/2 (* (sqrt (/ 1 x)) (/ (* (sqrt -1) (+ 18 (* -81 (/ x (pow (sqrt -6) 2))))) (sqrt -6))))) (pow x 3))) (* (sqrt (/ 1 x)) (* (sqrt -6) (sqrt -1))))) x))>
#<alt 1/2>
#<alt (+ 1/2 (* -1/4 x))>
#<alt (+ 1/2 (* x (- (* 1/48 (pow x 2)) 1/4)))>
#<alt (+ 1/2 (* x (- (* (pow x 2) (+ 1/48 (* 1/96 x))) 1/4)))>
#<alt (/ 6 (pow x 3))>
#<alt (/ (- 6 (* 18 (/ 1 x))) (pow x 3))>
#<alt (/ (- (+ 6 (/ 18 (pow x 2))) (* 18 (/ 1 x))) (pow x 3))>
#<alt (/ (- (+ 6 (/ 18 (pow x 2))) (+ (* 18 (/ 1 x)) (* 18 (/ 1 (pow x 3))))) (pow x 3))>
#<alt (/ 6 (pow x 3))>
#<alt (* -1 (/ (- (* 18 (/ 1 x)) 6) (pow x 3)))>
#<alt (* -1 (/ (- (* -1 (/ (- (* 18 (/ 1 x)) 18) x)) 6) (pow x 3)))>
#<alt (* -1 (/ (- (* -1 (/ (- (* -1 (/ (- (* 18 (/ 1 x)) 18) x)) 18) x)) 6) (pow x 3)))>
#<alt 2>
#<alt (+ 2 x)>
#<alt (+ 2 (* x (+ 1 (* 1/2 x))))>
#<alt (+ 2 (* x (+ 1 (* x (+ 1/2 (* 1/6 x))))))>
#<alt (* 1/6 (pow x 3))>
#<alt (* (pow x 3) (+ 1/6 (* 1/2 (/ 1 x))))>
#<alt (* (pow x 3) (+ 1/6 (+ (* 1/2 (/ 1 x)) (/ 1 (pow x 2)))))>
#<alt (* (pow x 3) (+ 1/6 (+ (* 1/2 (/ 1 x)) (+ (/ 1 (pow x 2)) (* 2 (/ 1 (pow x 3)))))))>
#<alt (* 1/6 (pow x 3))>
#<alt (* (pow x 3) (+ 1/6 (* 1/2 (/ 1 x))))>
#<alt (* -1 (* (pow x 3) (- (* -1 (/ (+ 1/2 (/ 1 x)) x)) 1/6)))>
#<alt (* -1 (* (pow x 3) (- (* -1 (/ (+ 1/2 (+ (/ 1 x) (/ 2 (pow x 2)))) x)) 1/6)))>
#<alt (sqrt x)>
#<alt (sqrt x)>
#<alt (sqrt x)>
#<alt (sqrt x)>
#<alt (sqrt x)>
#<alt (sqrt x)>
#<alt (sqrt x)>
#<alt (sqrt x)>
#<alt (* -1 (* (sqrt x) (pow (sqrt -1) 2)))>
#<alt (* -1 (* (sqrt x) (pow (sqrt -1) 2)))>
#<alt (* -1 (* (sqrt x) (pow (sqrt -1) 2)))>
#<alt (* -1 (* (sqrt x) (pow (sqrt -1) 2)))>
#<alt (* x (sqrt 1/2))>
#<alt (* x (sqrt 1/2))>
#<alt (* x (sqrt 1/2))>
#<alt (* x (sqrt 1/2))>
#<alt (* x (sqrt 1/2))>
#<alt (* x (sqrt 1/2))>
#<alt (* x (sqrt 1/2))>
#<alt (* x (sqrt 1/2))>
#<alt (* x (sqrt 1/2))>
#<alt (* x (sqrt 1/2))>
#<alt (* x (sqrt 1/2))>
#<alt (* x (sqrt 1/2))>
#<alt (* (sqrt (pow x 3)) (sqrt 1/6))>
#<alt (* (sqrt (pow x 3)) (sqrt 1/6))>
#<alt (* (sqrt (pow x 3)) (sqrt 1/6))>
#<alt (* (sqrt (pow x 3)) (sqrt 1/6))>
#<alt (* (sqrt (pow x 3)) (sqrt 1/6))>
#<alt (* (sqrt (pow x 3)) (sqrt 1/6))>
#<alt (* (sqrt (pow x 3)) (sqrt 1/6))>
#<alt (* (sqrt (pow x 3)) (sqrt 1/6))>
#<alt (* (sqrt (pow x 3)) (* (sqrt -1) (sqrt -1/6)))>
#<alt (* (sqrt (pow x 3)) (* (sqrt -1) (sqrt -1/6)))>
#<alt (* (sqrt (pow x 3)) (* (sqrt -1) (sqrt -1/6)))>
#<alt (* (sqrt (pow x 3)) (* (sqrt -1) (sqrt -1/6)))>
#<alt (* 1/6 (pow x 3))>
#<alt (* 1/6 (pow x 3))>
#<alt (* 1/6 (pow x 3))>
#<alt (* 1/6 (pow x 3))>
#<alt (* 1/6 (pow x 3))>
#<alt (* 1/6 (pow x 3))>
#<alt (* 1/6 (pow x 3))>
#<alt (* 1/6 (pow x 3))>
#<alt (* 1/6 (pow x 3))>
#<alt (* 1/6 (pow x 3))>
#<alt (* 1/6 (pow x 3))>
#<alt (* 1/6 (pow x 3))>
#<alt (pow x 3)>
#<alt (pow x 3)>
#<alt (pow x 3)>
#<alt (pow x 3)>
#<alt (pow x 3)>
#<alt (pow x 3)>
#<alt (pow x 3)>
#<alt (pow x 3)>
#<alt (pow x 3)>
#<alt (pow x 3)>
#<alt (pow x 3)>
#<alt (pow x 3)>
#<alt (pow x 2)>
#<alt (pow x 2)>
#<alt (pow x 2)>
#<alt (pow x 2)>
#<alt (pow x 2)>
#<alt (pow x 2)>
#<alt (pow x 2)>
#<alt (pow x 2)>
#<alt (pow x 2)>
#<alt (pow x 2)>
#<alt (pow x 2)>
#<alt (pow x 2)>
#<alt (* x (sqrt 1/2))>
#<alt (* x (+ (sqrt 1/2) (* 1/12 (/ x (sqrt 1/2)))))>
#<alt (* x (+ (sqrt 1/2) (* x (+ (* -1/288 (/ x (pow (sqrt 1/2) 3))) (* 1/12 (/ 1 (sqrt 1/2)))))))>
#<alt (* x (+ (sqrt 1/2) (* x (+ (* x (- (* 1/3456 (/ x (pow (sqrt 1/2) 5))) (* 1/288 (/ 1 (pow (sqrt 1/2) 3))))) (* 1/12 (/ 1 (sqrt 1/2)))))))>
#<alt (* (sqrt (pow x 3)) (sqrt 1/6))>
#<alt (* (pow x 2) (+ (* 1/4 (* (sqrt (/ 1 (pow x 3))) (/ 1 (sqrt 1/6)))) (* (sqrt (/ 1 x)) (sqrt 1/6))))>
#<alt (* (pow x 2) (+ (* -1/32 (* (sqrt (/ 1 (pow x 5))) (/ 1 (pow (sqrt 1/6) 3)))) (+ (* 1/4 (* (sqrt (/ 1 (pow x 3))) (/ 1 (sqrt 1/6)))) (* (sqrt (/ 1 x)) (sqrt 1/6)))))>
#<alt (* (pow x 2) (+ (* -1/32 (* (sqrt (/ 1 (pow x 5))) (/ 1 (pow (sqrt 1/6) 3)))) (+ (* 1/128 (* (sqrt (/ 1 (pow x 7))) (/ 1 (pow (sqrt 1/6) 5)))) (+ (* 1/4 (* (sqrt (/ 1 (pow x 3))) (/ 1 (sqrt 1/6)))) (* (sqrt (/ 1 x)) (sqrt 1/6))))))>
#<alt (* (sqrt (pow x 3)) (* (sqrt -1) (sqrt -1/6)))>
#<alt (* (pow x 2) (+ (* 1/4 (* (sqrt (/ 1 (pow x 3))) (/ (sqrt -1) (sqrt -1/6)))) (* (sqrt (/ 1 x)) (* (sqrt -1) (sqrt -1/6)))))>
#<alt (* (pow x 2) (+ (* -1/32 (* (sqrt (/ 1 (pow x 5))) (/ (sqrt -1) (pow (sqrt -1/6) 3)))) (+ (* 1/4 (* (sqrt (/ 1 (pow x 3))) (/ (sqrt -1) (sqrt -1/6)))) (* (sqrt (/ 1 x)) (* (sqrt -1) (sqrt -1/6))))))>
#<alt (* (pow x 2) (+ (* -1/32 (* (sqrt (/ 1 (pow x 5))) (/ (sqrt -1) (pow (sqrt -1/6) 3)))) (+ (* 1/128 (* (sqrt (/ 1 (pow x 7))) (/ (sqrt -1) (pow (sqrt -1/6) 5)))) (+ (* 1/4 (* (sqrt (/ 1 (pow x 3))) (/ (sqrt -1) (sqrt -1/6)))) (* (sqrt (/ 1 x)) (* (sqrt -1) (sqrt -1/6)))))))>
#<alt (* 1/2 (pow x 2))>
#<alt (* (pow x 2) (+ 1/2 (* 1/6 x)))>
#<alt (* (pow x 2) (+ 1/2 (* 1/6 x)))>
#<alt (* (pow x 2) (+ 1/2 (* 1/6 x)))>
#<alt (* 1/6 (pow x 3))>
#<alt (* (pow x 3) (+ 1/6 (* 1/2 (/ 1 x))))>
#<alt (* (pow x 3) (+ 1/6 (* 1/2 (/ 1 x))))>
#<alt (* (pow x 3) (+ 1/6 (* 1/2 (/ 1 x))))>
#<alt (* 1/6 (pow x 3))>
#<alt (* (pow x 3) (+ 1/6 (* 1/2 (/ 1 x))))>
#<alt (* (pow x 3) (+ 1/6 (* 1/2 (/ 1 x))))>
#<alt (* (pow x 3) (+ 1/6 (* 1/2 (/ 1 x))))>
#<alt (* 1/2 x)>
#<alt (* x (+ 1/2 (* 1/6 x)))>
#<alt (* x (+ 1/2 (* 1/6 x)))>
#<alt (* x (+ 1/2 (* 1/6 x)))>
#<alt (* 1/6 (pow x 2))>
#<alt (* (pow x 2) (+ 1/6 (* 1/2 (/ 1 x))))>
#<alt (* (pow x 2) (+ 1/6 (* 1/2 (/ 1 x))))>
#<alt (* (pow x 2) (+ 1/6 (* 1/2 (/ 1 x))))>
#<alt (* 1/6 (pow x 2))>
#<alt (* (pow x 2) (+ 1/6 (* 1/2 (/ 1 x))))>
#<alt (* (pow x 2) (+ 1/6 (* 1/2 (/ 1 x))))>
#<alt (* (pow x 2) (+ 1/6 (* 1/2 (/ 1 x))))>
#<alt 1/2>
#<alt (+ 1/2 (* 1/6 x))>
#<alt (+ 1/2 (* 1/6 x))>
#<alt (+ 1/2 (* 1/6 x))>
#<alt (* 1/6 x)>
#<alt (* x (+ 1/6 (* 1/2 (/ 1 x))))>
#<alt (* x (+ 1/6 (* 1/2 (/ 1 x))))>
#<alt (* x (+ 1/6 (* 1/2 (/ 1 x))))>
#<alt (* 1/6 x)>
#<alt (* x (+ 1/6 (* 1/2 (/ 1 x))))>
#<alt (* x (+ 1/6 (* 1/2 (/ 1 x))))>
#<alt (* x (+ 1/6 (* 1/2 (/ 1 x))))>
#<alt (* 1/6 x)>
#<alt (* 1/6 x)>
#<alt (* 1/6 x)>
#<alt (* 1/6 x)>
#<alt (* 1/6 x)>
#<alt (* 1/6 x)>
#<alt (* 1/6 x)>
#<alt (* 1/6 x)>
#<alt (* 1/6 x)>
#<alt (* 1/6 x)>
#<alt (* 1/6 x)>
#<alt (* 1/6 x)>
#<alt x>
#<alt (* x (+ 1 (* 1/2 x)))>
#<alt (* x (+ 1 (* x (+ 1/2 (* 1/6 x)))))>
#<alt (* x (+ 1 (* x (+ 1/2 (* 1/6 x)))))>
#<alt (* 1/6 (pow x 3))>
#<alt (* (pow x 3) (+ 1/6 (* 1/2 (/ 1 x))))>
#<alt (* (pow x 3) (+ 1/6 (+ (* 1/2 (/ 1 x)) (/ 1 (pow x 2)))))>
#<alt (* (pow x 3) (+ 1/6 (+ (* 1/2 (/ 1 x)) (/ 1 (pow x 2)))))>
#<alt (* 1/6 (pow x 3))>
#<alt (* (pow x 3) (+ 1/6 (* 1/2 (/ 1 x))))>
#<alt (* -1 (* (pow x 3) (- (* -1 (/ (+ 1/2 (/ 1 x)) x)) 1/6)))>
#<alt (* -1 (* (pow x 3) (- (* -1 (/ (+ 1/2 (/ 1 x)) x)) 1/6)))>
Calls

48 calls:

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

rewrite350.0ms (4.8%)

Algorithm
batch-egg-rewrite
Rules
5278×*-lowering-*.f32
5278×*-lowering-*.f64
3190×/-lowering-/.f32
3190×/-lowering-/.f64
1862×+-lowering-+.f64
Iterations

Useful iterations: 2 (0.0ms)

IterNodesCost
023127
1122107
2862105
08499105
Stop Event
iter limit
node limit
Counts
17 → 523
Calls
Call 1
Inputs
(/ 1 (sqrt (/ 1 (+ 2 (* x (+ 1 (* x (+ 1/2 (* x 1/6)))))))))
(sqrt (/ 1 (+ 2 (* x (+ 1 (* x (+ 1/2 (* x 1/6))))))))
(/ 1 (+ 2 (* x (+ 1 (* x (+ 1/2 (* x 1/6)))))))
(+ 2 (* x (+ 1 (* x (+ 1/2 (* x 1/6))))))
(sqrt x)
(* x (sqrt 1/2))
(sqrt 1/2)
(sqrt (* (* x (* x x)) 1/6))
(* (* x (* x x)) 1/6)
(* x (* x x))
(* x x)
(sqrt (* x (* x (+ 1/2 (* x 1/6)))))
(* x (* x (+ 1/2 (* x 1/6))))
(* x (+ 1/2 (* x 1/6)))
(+ 1/2 (* x 1/6))
(* x 1/6)
(* x (+ 1 (* x (+ 1/2 (* x 1/6)))))
Outputs
(exp.f64 (*.f64 (*.f64 #s(literal -1/2 binary64) (log.f64 (+.f64 #s(literal 2 binary64) (*.f64 x (+.f64 #s(literal 1 binary64) (*.f64 x (+.f64 #s(literal 1/2 binary64) (*.f64 x #s(literal 1/6 binary64))))))))) #s(literal -1 binary64)))
(exp.f64 (*.f64 (log.f64 (+.f64 #s(literal 2 binary64) (*.f64 x (+.f64 #s(literal 1 binary64) (*.f64 x (+.f64 #s(literal 1/2 binary64) (*.f64 x #s(literal 1/6 binary64)))))))) #s(literal 1/2 binary64)))
(exp.f64 (*.f64 (log.f64 (/.f64 #s(literal 1 binary64) (+.f64 #s(literal 2 binary64) (*.f64 x (+.f64 #s(literal 1 binary64) (*.f64 x (+.f64 #s(literal 1/2 binary64) (*.f64 x #s(literal 1/6 binary64))))))))) #s(literal -1/2 binary64)))
(exp.f64 (neg.f64 (*.f64 #s(literal -1/2 binary64) (log.f64 (+.f64 #s(literal 2 binary64) (*.f64 x (+.f64 #s(literal 1 binary64) (*.f64 x (+.f64 #s(literal 1/2 binary64) (*.f64 x #s(literal 1/6 binary64)))))))))))
(-.f64 #s(literal 0 binary64) (-.f64 #s(literal 0 binary64) (sqrt.f64 (+.f64 #s(literal 2 binary64) (*.f64 x (+.f64 #s(literal 1 binary64) (*.f64 x (+.f64 #s(literal 1/2 binary64) (*.f64 x #s(literal 1/6 binary64))))))))))
(sqrt.f64 (+.f64 #s(literal 2 binary64) (*.f64 x (+.f64 #s(literal 1 binary64) (*.f64 x (+.f64 #s(literal 1/2 binary64) (*.f64 x #s(literal 1/6 binary64))))))))
(neg.f64 (-.f64 #s(literal 0 binary64) (sqrt.f64 (+.f64 #s(literal 2 binary64) (*.f64 x (+.f64 #s(literal 1 binary64) (*.f64 x (+.f64 #s(literal 1/2 binary64) (*.f64 x #s(literal 1/6 binary64))))))))))
(neg.f64 (/.f64 (-.f64 #s(literal 0 binary64) (sqrt.f64 (+.f64 #s(literal 2 binary64) (*.f64 x (+.f64 #s(literal 1 binary64) (*.f64 x (+.f64 #s(literal 1/2 binary64) (*.f64 x #s(literal 1/6 binary64))))))))) #s(literal 1 binary64)))
(/.f64 #s(literal 1 binary64) (pow.f64 (+.f64 #s(literal 2 binary64) (*.f64 x (+.f64 #s(literal 1 binary64) (*.f64 x (+.f64 #s(literal 1/2 binary64) (*.f64 x #s(literal 1/6 binary64))))))) #s(literal -1/2 binary64)))
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(/.f64 (*.f64 x (+.f64 #s(literal 1 binary64) (*.f64 (*.f64 x (*.f64 x (+.f64 #s(literal 1/2 binary64) (*.f64 x #s(literal 1/6 binary64))))) (+.f64 (*.f64 x #s(literal -1/6 binary64)) #s(literal -1/2 binary64))))) (-.f64 #s(literal 1 binary64) (*.f64 x (+.f64 #s(literal 1/2 binary64) (*.f64 x #s(literal 1/6 binary64))))))
(/.f64 (*.f64 (+.f64 #s(literal 1 binary64) (*.f64 x (*.f64 (+.f64 #s(literal 1/2 binary64) (*.f64 x #s(literal 1/6 binary64))) (*.f64 (*.f64 x (+.f64 #s(literal 1/2 binary64) (*.f64 x #s(literal 1/6 binary64)))) (*.f64 x (+.f64 #s(literal 1/2 binary64) (*.f64 x #s(literal 1/6 binary64)))))))) x) (+.f64 #s(literal 1 binary64) (*.f64 (+.f64 #s(literal 1/2 binary64) (*.f64 x #s(literal 1/6 binary64))) (*.f64 x (+.f64 (*.f64 x (+.f64 #s(literal 1/2 binary64) (*.f64 x #s(literal 1/6 binary64)))) #s(literal -1 binary64))))))
(/.f64 (*.f64 (+.f64 #s(literal 1 binary64) (*.f64 (*.f64 x (*.f64 x (+.f64 #s(literal 1/2 binary64) (*.f64 x #s(literal 1/6 binary64))))) (+.f64 (*.f64 x #s(literal -1/6 binary64)) #s(literal -1/2 binary64)))) x) (-.f64 #s(literal 1 binary64) (*.f64 x (+.f64 #s(literal 1/2 binary64) (*.f64 x #s(literal 1/6 binary64))))))
(/.f64 (neg.f64 (+.f64 (*.f64 x (*.f64 x x)) (*.f64 (*.f64 x (*.f64 x x)) (*.f64 x (*.f64 (+.f64 #s(literal 1/2 binary64) (*.f64 x #s(literal 1/6 binary64))) (*.f64 (*.f64 x (+.f64 #s(literal 1/2 binary64) (*.f64 x #s(literal 1/6 binary64)))) (*.f64 x (+.f64 #s(literal 1/2 binary64) (*.f64 x #s(literal 1/6 binary64)))))))))) (neg.f64 (+.f64 (*.f64 x x) (*.f64 (*.f64 x (*.f64 x (+.f64 #s(literal 1/2 binary64) (*.f64 x #s(literal 1/6 binary64))))) (-.f64 (*.f64 x (*.f64 x (+.f64 #s(literal 1/2 binary64) (*.f64 x #s(literal 1/6 binary64))))) x)))))
(/.f64 (neg.f64 (*.f64 (*.f64 x (+.f64 #s(literal 1 binary64) (*.f64 x (+.f64 #s(literal 1/2 binary64) (*.f64 x #s(literal 1/6 binary64)))))) (*.f64 x (-.f64 #s(literal 1 binary64) (*.f64 x (+.f64 #s(literal 1/2 binary64) (*.f64 x #s(literal 1/6 binary64)))))))) (neg.f64 (*.f64 x (-.f64 #s(literal 1 binary64) (*.f64 x (+.f64 #s(literal 1/2 binary64) (*.f64 x #s(literal 1/6 binary64))))))))
(/.f64 (neg.f64 (*.f64 x (+.f64 #s(literal 1 binary64) (*.f64 x (*.f64 (+.f64 #s(literal 1/2 binary64) (*.f64 x #s(literal 1/6 binary64))) (*.f64 (*.f64 x (+.f64 #s(literal 1/2 binary64) (*.f64 x #s(literal 1/6 binary64)))) (*.f64 x (+.f64 #s(literal 1/2 binary64) (*.f64 x #s(literal 1/6 binary64)))))))))) (-.f64 #s(literal 0 binary64) (+.f64 #s(literal 1 binary64) (*.f64 (+.f64 #s(literal 1/2 binary64) (*.f64 x #s(literal 1/6 binary64))) (*.f64 x (+.f64 (*.f64 x (+.f64 #s(literal 1/2 binary64) (*.f64 x #s(literal 1/6 binary64)))) #s(literal -1 binary64)))))))
(/.f64 (neg.f64 (*.f64 x (+.f64 #s(literal 1 binary64) (*.f64 (*.f64 x (*.f64 x (+.f64 #s(literal 1/2 binary64) (*.f64 x #s(literal 1/6 binary64))))) (+.f64 (*.f64 x #s(literal -1/6 binary64)) #s(literal -1/2 binary64)))))) (-.f64 #s(literal 0 binary64) (-.f64 #s(literal 1 binary64) (*.f64 x (+.f64 #s(literal 1/2 binary64) (*.f64 x #s(literal 1/6 binary64)))))))
(/.f64 (neg.f64 (*.f64 (+.f64 #s(literal 1 binary64) (*.f64 x (*.f64 (+.f64 #s(literal 1/2 binary64) (*.f64 x #s(literal 1/6 binary64))) (*.f64 (*.f64 x (+.f64 #s(literal 1/2 binary64) (*.f64 x #s(literal 1/6 binary64)))) (*.f64 x (+.f64 #s(literal 1/2 binary64) (*.f64 x #s(literal 1/6 binary64)))))))) x)) (-.f64 #s(literal 0 binary64) (+.f64 #s(literal 1 binary64) (*.f64 (+.f64 #s(literal 1/2 binary64) (*.f64 x #s(literal 1/6 binary64))) (*.f64 x (+.f64 (*.f64 x (+.f64 #s(literal 1/2 binary64) (*.f64 x #s(literal 1/6 binary64)))) #s(literal -1 binary64)))))))
(/.f64 (neg.f64 (*.f64 (+.f64 #s(literal 1 binary64) (*.f64 (*.f64 x (*.f64 x (+.f64 #s(literal 1/2 binary64) (*.f64 x #s(literal 1/6 binary64))))) (+.f64 (*.f64 x #s(literal -1/6 binary64)) #s(literal -1/2 binary64)))) x)) (-.f64 #s(literal 0 binary64) (-.f64 #s(literal 1 binary64) (*.f64 x (+.f64 #s(literal 1/2 binary64) (*.f64 x #s(literal 1/6 binary64)))))))
(/.f64 (+.f64 (*.f64 (*.f64 x (*.f64 x x)) (*.f64 x (*.f64 (+.f64 #s(literal 1/2 binary64) (*.f64 x #s(literal 1/6 binary64))) (*.f64 (*.f64 x (+.f64 #s(literal 1/2 binary64) (*.f64 x #s(literal 1/6 binary64)))) (*.f64 x (+.f64 #s(literal 1/2 binary64) (*.f64 x #s(literal 1/6 binary64)))))))) (*.f64 x (*.f64 x x))) (+.f64 (*.f64 (*.f64 x x) (*.f64 (*.f64 x (+.f64 #s(literal 1/2 binary64) (*.f64 x #s(literal 1/6 binary64)))) (*.f64 x (+.f64 #s(literal 1/2 binary64) (*.f64 x #s(literal 1/6 binary64)))))) (-.f64 (*.f64 x x) (*.f64 (*.f64 x (+.f64 #s(literal 1/2 binary64) (*.f64 x #s(literal 1/6 binary64)))) (*.f64 x x)))))
(/.f64 (-.f64 (*.f64 (*.f64 x x) (*.f64 (*.f64 x (+.f64 #s(literal 1/2 binary64) (*.f64 x #s(literal 1/6 binary64)))) (*.f64 x (+.f64 #s(literal 1/2 binary64) (*.f64 x #s(literal 1/6 binary64)))))) (*.f64 x x)) (-.f64 (*.f64 x (*.f64 x (+.f64 #s(literal 1/2 binary64) (*.f64 x #s(literal 1/6 binary64))))) x))
(/.f64 (*.f64 x (-.f64 #s(literal 0 binary64) (+.f64 #s(literal 1 binary64) (*.f64 x (*.f64 (+.f64 #s(literal 1/2 binary64) (*.f64 x #s(literal 1/6 binary64))) (*.f64 (*.f64 x (+.f64 #s(literal 1/2 binary64) (*.f64 x #s(literal 1/6 binary64)))) (*.f64 x (+.f64 #s(literal 1/2 binary64) (*.f64 x #s(literal 1/6 binary64)))))))))) (-.f64 #s(literal 0 binary64) (+.f64 #s(literal 1 binary64) (*.f64 (+.f64 #s(literal 1/2 binary64) (*.f64 x #s(literal 1/6 binary64))) (*.f64 x (+.f64 (*.f64 x (+.f64 #s(literal 1/2 binary64) (*.f64 x #s(literal 1/6 binary64)))) #s(literal -1 binary64)))))))
(/.f64 (*.f64 x (+.f64 #s(literal -1 binary64) (neg.f64 (*.f64 (*.f64 x (*.f64 x (+.f64 #s(literal 1/2 binary64) (*.f64 x #s(literal 1/6 binary64))))) (+.f64 (*.f64 x #s(literal -1/6 binary64)) #s(literal -1/2 binary64)))))) (-.f64 #s(literal 0 binary64) (-.f64 #s(literal 1 binary64) (*.f64 x (+.f64 #s(literal 1/2 binary64) (*.f64 x #s(literal 1/6 binary64)))))))
(/.f64 (*.f64 x (+.f64 (*.f64 (*.f64 x (+.f64 #s(literal 1/2 binary64) (*.f64 x #s(literal 1/6 binary64)))) (*.f64 x (+.f64 #s(literal 1/2 binary64) (*.f64 x #s(literal 1/6 binary64))))) #s(literal -1 binary64))) (+.f64 (*.f64 x (+.f64 #s(literal 1/2 binary64) (*.f64 x #s(literal 1/6 binary64)))) #s(literal -1 binary64)))
(*.f64 #s(literal 1 binary64) (*.f64 x (+.f64 #s(literal 1 binary64) (*.f64 x (+.f64 #s(literal 1/2 binary64) (*.f64 x #s(literal 1/6 binary64)))))))
(*.f64 x (+.f64 #s(literal 1 binary64) (*.f64 x (+.f64 #s(literal 1/2 binary64) (*.f64 x #s(literal 1/6 binary64))))))
(*.f64 (+.f64 #s(literal 1 binary64) (*.f64 x (+.f64 #s(literal 1/2 binary64) (*.f64 x #s(literal 1/6 binary64))))) x)
(*.f64 (*.f64 x (+.f64 #s(literal 1 binary64) (*.f64 x (+.f64 #s(literal 1/2 binary64) (*.f64 x #s(literal 1/6 binary64)))))) #s(literal 1 binary64))
(*.f64 (+.f64 #s(literal 1 binary64) (*.f64 x (*.f64 (+.f64 #s(literal 1/2 binary64) (*.f64 x #s(literal 1/6 binary64))) (*.f64 (*.f64 x (+.f64 #s(literal 1/2 binary64) (*.f64 x #s(literal 1/6 binary64)))) (*.f64 x (+.f64 #s(literal 1/2 binary64) (*.f64 x #s(literal 1/6 binary64)))))))) (*.f64 (/.f64 #s(literal 1 binary64) (+.f64 #s(literal 1 binary64) (*.f64 (+.f64 #s(literal 1/2 binary64) (*.f64 x #s(literal 1/6 binary64))) (*.f64 x (+.f64 (*.f64 x (+.f64 #s(literal 1/2 binary64) (*.f64 x #s(literal 1/6 binary64)))) #s(literal -1 binary64)))))) x))
(*.f64 (+.f64 #s(literal 1 binary64) (*.f64 (*.f64 x (*.f64 x (+.f64 #s(literal 1/2 binary64) (*.f64 x #s(literal 1/6 binary64))))) (+.f64 (*.f64 x #s(literal -1/6 binary64)) #s(literal -1/2 binary64)))) (*.f64 (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 1 binary64) (*.f64 x (+.f64 #s(literal 1/2 binary64) (*.f64 x #s(literal 1/6 binary64)))))) x))
(*.f64 (+.f64 (*.f64 x (*.f64 x x)) (*.f64 (*.f64 x (*.f64 x x)) (*.f64 x (*.f64 (+.f64 #s(literal 1/2 binary64) (*.f64 x #s(literal 1/6 binary64))) (*.f64 (*.f64 x (+.f64 #s(literal 1/2 binary64) (*.f64 x #s(literal 1/6 binary64)))) (*.f64 x (+.f64 #s(literal 1/2 binary64) (*.f64 x #s(literal 1/6 binary64))))))))) (/.f64 #s(literal 1 binary64) (+.f64 (*.f64 x x) (*.f64 (*.f64 x (*.f64 x (+.f64 #s(literal 1/2 binary64) (*.f64 x #s(literal 1/6 binary64))))) (-.f64 (*.f64 x (*.f64 x (+.f64 #s(literal 1/2 binary64) (*.f64 x #s(literal 1/6 binary64))))) x)))))
(*.f64 (*.f64 (*.f64 x (+.f64 #s(literal 1 binary64) (*.f64 x (+.f64 #s(literal 1/2 binary64) (*.f64 x #s(literal 1/6 binary64)))))) (*.f64 x (-.f64 #s(literal 1 binary64) (*.f64 x (+.f64 #s(literal 1/2 binary64) (*.f64 x #s(literal 1/6 binary64))))))) (/.f64 #s(literal 1 binary64) (*.f64 x (-.f64 #s(literal 1 binary64) (*.f64 x (+.f64 #s(literal 1/2 binary64) (*.f64 x #s(literal 1/6 binary64))))))))
(*.f64 (*.f64 x (+.f64 #s(literal 1 binary64) (*.f64 x (*.f64 (+.f64 #s(literal 1/2 binary64) (*.f64 x #s(literal 1/6 binary64))) (*.f64 (*.f64 x (+.f64 #s(literal 1/2 binary64) (*.f64 x #s(literal 1/6 binary64)))) (*.f64 x (+.f64 #s(literal 1/2 binary64) (*.f64 x #s(literal 1/6 binary64))))))))) (/.f64 #s(literal 1 binary64) (+.f64 #s(literal 1 binary64) (*.f64 (+.f64 #s(literal 1/2 binary64) (*.f64 x #s(literal 1/6 binary64))) (*.f64 x (+.f64 (*.f64 x (+.f64 #s(literal 1/2 binary64) (*.f64 x #s(literal 1/6 binary64)))) #s(literal -1 binary64)))))))
(*.f64 (*.f64 x (+.f64 #s(literal 1 binary64) (*.f64 (*.f64 x (*.f64 x (+.f64 #s(literal 1/2 binary64) (*.f64 x #s(literal 1/6 binary64))))) (+.f64 (*.f64 x #s(literal -1/6 binary64)) #s(literal -1/2 binary64))))) (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 1 binary64) (*.f64 x (+.f64 #s(literal 1/2 binary64) (*.f64 x #s(literal 1/6 binary64)))))))
(*.f64 (*.f64 (+.f64 #s(literal 1 binary64) (*.f64 x (*.f64 (+.f64 #s(literal 1/2 binary64) (*.f64 x #s(literal 1/6 binary64))) (*.f64 (*.f64 x (+.f64 #s(literal 1/2 binary64) (*.f64 x #s(literal 1/6 binary64)))) (*.f64 x (+.f64 #s(literal 1/2 binary64) (*.f64 x #s(literal 1/6 binary64)))))))) x) (/.f64 #s(literal 1 binary64) (+.f64 #s(literal 1 binary64) (*.f64 (+.f64 #s(literal 1/2 binary64) (*.f64 x #s(literal 1/6 binary64))) (*.f64 x (+.f64 (*.f64 x (+.f64 #s(literal 1/2 binary64) (*.f64 x #s(literal 1/6 binary64)))) #s(literal -1 binary64)))))))
(*.f64 (*.f64 (+.f64 #s(literal 1 binary64) (*.f64 (*.f64 x (*.f64 x (+.f64 #s(literal 1/2 binary64) (*.f64 x #s(literal 1/6 binary64))))) (+.f64 (*.f64 x #s(literal -1/6 binary64)) #s(literal -1/2 binary64)))) x) (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 1 binary64) (*.f64 x (+.f64 #s(literal 1/2 binary64) (*.f64 x #s(literal 1/6 binary64)))))))

simplify308.0ms (4.2%)

Algorithm
egg-herbie
Rules
4982×*-lowering-*.f32
4982×*-lowering-*.f64
3406×+-lowering-+.f64
3406×+-lowering-+.f32
2502×/-lowering-/.f32
Iterations

Useful iterations: 2 (0.0ms)

IterNodesCost
03461853
111011729
236481696
082491696
Stop Event
iter limit
node limit
Counts
192 → 192
Calls
Call 1
Inputs
(sqrt 2)
(+ (sqrt 2) (* 1/2 (/ x (sqrt 2))))
(+ (sqrt 2) (* x (+ (* 1/2 (/ (* x (- 1/2 (* 1/4 (/ 1 (pow (sqrt 2) 2))))) (sqrt 2))) (* 1/2 (/ 1 (sqrt 2))))))
(+ (sqrt 2) (* x (+ (* x (+ (* 1/2 (/ (* x (- 1/6 (* 1/2 (/ (- 1/2 (* 1/4 (/ 1 (pow (sqrt 2) 2)))) (pow (sqrt 2) 2))))) (sqrt 2))) (* 1/2 (/ (- 1/2 (* 1/4 (/ 1 (pow (sqrt 2) 2)))) (sqrt 2))))) (* 1/2 (/ 1 (sqrt 2))))))
(* (sqrt (pow x 3)) (sqrt 1/6))
(* (pow x 2) (+ (* 1/4 (* (sqrt (/ 1 (pow x 3))) (/ 1 (sqrt 1/6)))) (* (sqrt (/ 1 x)) (sqrt 1/6))))
(* (pow x 2) (+ (* 1/4 (* (sqrt (/ 1 (pow x 3))) (/ 1 (sqrt 1/6)))) (+ (* 1/2 (* (sqrt (/ 1 (pow x 5))) (/ 1 (sqrt 1/6)))) (* (sqrt (/ 1 x)) (sqrt 1/6)))))
(* (pow x 2) (+ (* 1/4 (* (sqrt (/ 1 (pow x 3))) (/ 1 (sqrt 1/6)))) (+ (* 1/2 (* (sqrt (/ 1 (pow x 5))) (/ 1 (sqrt 1/6)))) (+ (* 1/2 (* (sqrt (/ 1 (pow x 7))) (/ (- 2 (* 1/16 (/ x (pow (sqrt 1/6) 2)))) (sqrt 1/6)))) (* (sqrt (/ 1 x)) (sqrt 1/6))))))
(* (sqrt (pow x 3)) (* (sqrt -1) (sqrt -1/6)))
(* (pow x 2) (+ (* 1/4 (* (sqrt (/ 1 (pow x 3))) (/ (sqrt -1) (sqrt -1/6)))) (* (sqrt (/ 1 x)) (* (sqrt -1) (sqrt -1/6)))))
(* (pow x 2) (+ (* 1/4 (* (sqrt (/ 1 (pow x 3))) (/ (sqrt -1) (sqrt -1/6)))) (+ (* 1/2 (* (sqrt (/ 1 (pow x 5))) (/ (sqrt -1) (sqrt -1/6)))) (* (sqrt (/ 1 x)) (* (sqrt -1) (sqrt -1/6))))))
(* (pow x 2) (+ (* -1 (/ (+ (* -1/2 (* (sqrt x) (/ (sqrt -1) (sqrt -1/6)))) (* -1/2 (* (sqrt (/ 1 x)) (/ (* (sqrt -1) (- 2 (* -1/16 (/ x (pow (sqrt -1/6) 2))))) (sqrt -1/6))))) (pow x 3))) (+ (* 1/4 (* (sqrt (/ 1 (pow x 3))) (/ (sqrt -1) (sqrt -1/6)))) (* (sqrt (/ 1 x)) (* (sqrt -1) (sqrt -1/6))))))
(sqrt 1/2)
(+ (sqrt 1/2) (* -1/8 (/ x (sqrt 1/2))))
(+ (sqrt 1/2) (* x (- (* -1/128 (/ x (pow (sqrt 1/2) 3))) (* 1/8 (/ 1 (sqrt 1/2))))))
(+ (sqrt 1/2) (* x (- (* x (- (* 1/2 (/ (* x (- 1/48 (* 1/512 (/ 1 (pow (sqrt 1/2) 4))))) (sqrt 1/2))) (* 1/128 (/ 1 (pow (sqrt 1/2) 3))))) (* 1/8 (/ 1 (sqrt 1/2))))))
(* (sqrt (/ 1 (pow x 3))) (sqrt 6))
(/ (+ (* -9 (* (sqrt (/ 1 (pow x 3))) (/ 1 (sqrt 6)))) (* (sqrt (/ 1 x)) (sqrt 6))) x)
(/ (+ (* -9 (* (sqrt (/ 1 (pow x 3))) (/ 1 (sqrt 6)))) (+ (* 9 (* (sqrt (/ 1 (pow x 5))) (/ 1 (sqrt 6)))) (* (sqrt (/ 1 x)) (sqrt 6)))) x)
(/ (+ (* -9 (* (sqrt (/ 1 (pow x 3))) (/ 1 (sqrt 6)))) (+ (* -1/2 (* (sqrt (/ 1 (pow x 7))) (/ (+ 18 (* 81 (/ x (pow (sqrt 6) 2)))) (sqrt 6)))) (+ (* 9 (* (sqrt (/ 1 (pow x 5))) (/ 1 (sqrt 6)))) (* (sqrt (/ 1 x)) (sqrt 6))))) x)
(* -1 (* (sqrt (/ 1 (pow x 3))) (* (sqrt -6) (sqrt -1))))
(* -1 (/ (+ (* -9 (* (sqrt (/ 1 (pow x 3))) (/ (sqrt -1) (sqrt -6)))) (* (sqrt (/ 1 x)) (* (sqrt -6) (sqrt -1)))) x))
(* -1 (/ (+ (* -9 (* (sqrt (/ 1 (pow x 3))) (/ (sqrt -1) (sqrt -6)))) (+ (* 9 (* (sqrt (/ 1 (pow x 5))) (/ (sqrt -1) (sqrt -6)))) (* (sqrt (/ 1 x)) (* (sqrt -6) (sqrt -1))))) x))
(* -1 (/ (+ (* -9 (* (sqrt (/ 1 (pow x 3))) (/ (sqrt -1) (sqrt -6)))) (+ (* -1 (/ (+ (* -9 (* (sqrt x) (/ (sqrt -1) (sqrt -6)))) (* 1/2 (* (sqrt (/ 1 x)) (/ (* (sqrt -1) (+ 18 (* -81 (/ x (pow (sqrt -6) 2))))) (sqrt -6))))) (pow x 3))) (* (sqrt (/ 1 x)) (* (sqrt -6) (sqrt -1))))) x))
1/2
(+ 1/2 (* -1/4 x))
(+ 1/2 (* x (- (* 1/48 (pow x 2)) 1/4)))
(+ 1/2 (* x (- (* (pow x 2) (+ 1/48 (* 1/96 x))) 1/4)))
(/ 6 (pow x 3))
(/ (- 6 (* 18 (/ 1 x))) (pow x 3))
(/ (- (+ 6 (/ 18 (pow x 2))) (* 18 (/ 1 x))) (pow x 3))
(/ (- (+ 6 (/ 18 (pow x 2))) (+ (* 18 (/ 1 x)) (* 18 (/ 1 (pow x 3))))) (pow x 3))
(/ 6 (pow x 3))
(* -1 (/ (- (* 18 (/ 1 x)) 6) (pow x 3)))
(* -1 (/ (- (* -1 (/ (- (* 18 (/ 1 x)) 18) x)) 6) (pow x 3)))
(* -1 (/ (- (* -1 (/ (- (* -1 (/ (- (* 18 (/ 1 x)) 18) x)) 18) x)) 6) (pow x 3)))
2
(+ 2 x)
(+ 2 (* x (+ 1 (* 1/2 x))))
(+ 2 (* x (+ 1 (* x (+ 1/2 (* 1/6 x))))))
(* 1/6 (pow x 3))
(* (pow x 3) (+ 1/6 (* 1/2 (/ 1 x))))
(* (pow x 3) (+ 1/6 (+ (* 1/2 (/ 1 x)) (/ 1 (pow x 2)))))
(* (pow x 3) (+ 1/6 (+ (* 1/2 (/ 1 x)) (+ (/ 1 (pow x 2)) (* 2 (/ 1 (pow x 3)))))))
(* 1/6 (pow x 3))
(* (pow x 3) (+ 1/6 (* 1/2 (/ 1 x))))
(* -1 (* (pow x 3) (- (* -1 (/ (+ 1/2 (/ 1 x)) x)) 1/6)))
(* -1 (* (pow x 3) (- (* -1 (/ (+ 1/2 (+ (/ 1 x) (/ 2 (pow x 2)))) x)) 1/6)))
(sqrt x)
(sqrt x)
(sqrt x)
(sqrt x)
(sqrt x)
(sqrt x)
(sqrt x)
(sqrt x)
(* -1 (* (sqrt x) (pow (sqrt -1) 2)))
(* -1 (* (sqrt x) (pow (sqrt -1) 2)))
(* -1 (* (sqrt x) (pow (sqrt -1) 2)))
(* -1 (* (sqrt x) (pow (sqrt -1) 2)))
(* x (sqrt 1/2))
(* x (sqrt 1/2))
(* x (sqrt 1/2))
(* x (sqrt 1/2))
(* x (sqrt 1/2))
(* x (sqrt 1/2))
(* x (sqrt 1/2))
(* x (sqrt 1/2))
(* x (sqrt 1/2))
(* x (sqrt 1/2))
(* x (sqrt 1/2))
(* x (sqrt 1/2))
(* (sqrt (pow x 3)) (sqrt 1/6))
(* (sqrt (pow x 3)) (sqrt 1/6))
(* (sqrt (pow x 3)) (sqrt 1/6))
(* (sqrt (pow x 3)) (sqrt 1/6))
(* (sqrt (pow x 3)) (sqrt 1/6))
(* (sqrt (pow x 3)) (sqrt 1/6))
(* (sqrt (pow x 3)) (sqrt 1/6))
(* (sqrt (pow x 3)) (sqrt 1/6))
(* (sqrt (pow x 3)) (* (sqrt -1) (sqrt -1/6)))
(* (sqrt (pow x 3)) (* (sqrt -1) (sqrt -1/6)))
(* (sqrt (pow x 3)) (* (sqrt -1) (sqrt -1/6)))
(* (sqrt (pow x 3)) (* (sqrt -1) (sqrt -1/6)))
(* 1/6 (pow x 3))
(* 1/6 (pow x 3))
(* 1/6 (pow x 3))
(* 1/6 (pow x 3))
(* 1/6 (pow x 3))
(* 1/6 (pow x 3))
(* 1/6 (pow x 3))
(* 1/6 (pow x 3))
(* 1/6 (pow x 3))
(* 1/6 (pow x 3))
(* 1/6 (pow x 3))
(* 1/6 (pow x 3))
(pow x 3)
(pow x 3)
(pow x 3)
(pow x 3)
(pow x 3)
(pow x 3)
(pow x 3)
(pow x 3)
(pow x 3)
(pow x 3)
(pow x 3)
(pow x 3)
(pow x 2)
(pow x 2)
(pow x 2)
(pow x 2)
(pow x 2)
(pow x 2)
(pow x 2)
(pow x 2)
(pow x 2)
(pow x 2)
(pow x 2)
(pow x 2)
(* x (sqrt 1/2))
(* x (+ (sqrt 1/2) (* 1/12 (/ x (sqrt 1/2)))))
(* x (+ (sqrt 1/2) (* x (+ (* -1/288 (/ x (pow (sqrt 1/2) 3))) (* 1/12 (/ 1 (sqrt 1/2)))))))
(* x (+ (sqrt 1/2) (* x (+ (* x (- (* 1/3456 (/ x (pow (sqrt 1/2) 5))) (* 1/288 (/ 1 (pow (sqrt 1/2) 3))))) (* 1/12 (/ 1 (sqrt 1/2)))))))
(* (sqrt (pow x 3)) (sqrt 1/6))
(* (pow x 2) (+ (* 1/4 (* (sqrt (/ 1 (pow x 3))) (/ 1 (sqrt 1/6)))) (* (sqrt (/ 1 x)) (sqrt 1/6))))
(* (pow x 2) (+ (* -1/32 (* (sqrt (/ 1 (pow x 5))) (/ 1 (pow (sqrt 1/6) 3)))) (+ (* 1/4 (* (sqrt (/ 1 (pow x 3))) (/ 1 (sqrt 1/6)))) (* (sqrt (/ 1 x)) (sqrt 1/6)))))
(* (pow x 2) (+ (* -1/32 (* (sqrt (/ 1 (pow x 5))) (/ 1 (pow (sqrt 1/6) 3)))) (+ (* 1/128 (* (sqrt (/ 1 (pow x 7))) (/ 1 (pow (sqrt 1/6) 5)))) (+ (* 1/4 (* (sqrt (/ 1 (pow x 3))) (/ 1 (sqrt 1/6)))) (* (sqrt (/ 1 x)) (sqrt 1/6))))))
(* (sqrt (pow x 3)) (* (sqrt -1) (sqrt -1/6)))
(* (pow x 2) (+ (* 1/4 (* (sqrt (/ 1 (pow x 3))) (/ (sqrt -1) (sqrt -1/6)))) (* (sqrt (/ 1 x)) (* (sqrt -1) (sqrt -1/6)))))
(* (pow x 2) (+ (* -1/32 (* (sqrt (/ 1 (pow x 5))) (/ (sqrt -1) (pow (sqrt -1/6) 3)))) (+ (* 1/4 (* (sqrt (/ 1 (pow x 3))) (/ (sqrt -1) (sqrt -1/6)))) (* (sqrt (/ 1 x)) (* (sqrt -1) (sqrt -1/6))))))
(* (pow x 2) (+ (* -1/32 (* (sqrt (/ 1 (pow x 5))) (/ (sqrt -1) (pow (sqrt -1/6) 3)))) (+ (* 1/128 (* (sqrt (/ 1 (pow x 7))) (/ (sqrt -1) (pow (sqrt -1/6) 5)))) (+ (* 1/4 (* (sqrt (/ 1 (pow x 3))) (/ (sqrt -1) (sqrt -1/6)))) (* (sqrt (/ 1 x)) (* (sqrt -1) (sqrt -1/6)))))))
(* 1/2 (pow x 2))
(* (pow x 2) (+ 1/2 (* 1/6 x)))
(* (pow x 2) (+ 1/2 (* 1/6 x)))
(* (pow x 2) (+ 1/2 (* 1/6 x)))
(* 1/6 (pow x 3))
(* (pow x 3) (+ 1/6 (* 1/2 (/ 1 x))))
(* (pow x 3) (+ 1/6 (* 1/2 (/ 1 x))))
(* (pow x 3) (+ 1/6 (* 1/2 (/ 1 x))))
(* 1/6 (pow x 3))
(* (pow x 3) (+ 1/6 (* 1/2 (/ 1 x))))
(* (pow x 3) (+ 1/6 (* 1/2 (/ 1 x))))
(* (pow x 3) (+ 1/6 (* 1/2 (/ 1 x))))
(* 1/2 x)
(* x (+ 1/2 (* 1/6 x)))
(* x (+ 1/2 (* 1/6 x)))
(* x (+ 1/2 (* 1/6 x)))
(* 1/6 (pow x 2))
(* (pow x 2) (+ 1/6 (* 1/2 (/ 1 x))))
(* (pow x 2) (+ 1/6 (* 1/2 (/ 1 x))))
(* (pow x 2) (+ 1/6 (* 1/2 (/ 1 x))))
(* 1/6 (pow x 2))
(* (pow x 2) (+ 1/6 (* 1/2 (/ 1 x))))
(* (pow x 2) (+ 1/6 (* 1/2 (/ 1 x))))
(* (pow x 2) (+ 1/6 (* 1/2 (/ 1 x))))
1/2
(+ 1/2 (* 1/6 x))
(+ 1/2 (* 1/6 x))
(+ 1/2 (* 1/6 x))
(* 1/6 x)
(* x (+ 1/6 (* 1/2 (/ 1 x))))
(* x (+ 1/6 (* 1/2 (/ 1 x))))
(* x (+ 1/6 (* 1/2 (/ 1 x))))
(* 1/6 x)
(* x (+ 1/6 (* 1/2 (/ 1 x))))
(* x (+ 1/6 (* 1/2 (/ 1 x))))
(* x (+ 1/6 (* 1/2 (/ 1 x))))
(* 1/6 x)
(* 1/6 x)
(* 1/6 x)
(* 1/6 x)
(* 1/6 x)
(* 1/6 x)
(* 1/6 x)
(* 1/6 x)
(* 1/6 x)
(* 1/6 x)
(* 1/6 x)
(* 1/6 x)
x
(* x (+ 1 (* 1/2 x)))
(* x (+ 1 (* x (+ 1/2 (* 1/6 x)))))
(* x (+ 1 (* x (+ 1/2 (* 1/6 x)))))
(* 1/6 (pow x 3))
(* (pow x 3) (+ 1/6 (* 1/2 (/ 1 x))))
(* (pow x 3) (+ 1/6 (+ (* 1/2 (/ 1 x)) (/ 1 (pow x 2)))))
(* (pow x 3) (+ 1/6 (+ (* 1/2 (/ 1 x)) (/ 1 (pow x 2)))))
(* 1/6 (pow x 3))
(* (pow x 3) (+ 1/6 (* 1/2 (/ 1 x))))
(* -1 (* (pow x 3) (- (* -1 (/ (+ 1/2 (/ 1 x)) x)) 1/6)))
(* -1 (* (pow x 3) (- (* -1 (/ (+ 1/2 (/ 1 x)) x)) 1/6)))
Outputs
(sqrt 2)
(sqrt.f64 #s(literal 2 binary64))
(+ (sqrt 2) (* 1/2 (/ x (sqrt 2))))
(+.f64 (sqrt.f64 #s(literal 2 binary64)) (/.f64 (*.f64 #s(literal 1/2 binary64) x) (sqrt.f64 #s(literal 2 binary64))))
(+ (sqrt 2) (* x (+ (* 1/2 (/ (* x (- 1/2 (* 1/4 (/ 1 (pow (sqrt 2) 2))))) (sqrt 2))) (* 1/2 (/ 1 (sqrt 2))))))
(+.f64 (sqrt.f64 #s(literal 2 binary64)) (*.f64 x (+.f64 (/.f64 #s(literal 1/2 binary64) (sqrt.f64 #s(literal 2 binary64))) (*.f64 #s(literal 3/16 binary64) (/.f64 x (sqrt.f64 #s(literal 2 binary64)))))))
(+ (sqrt 2) (* x (+ (* x (+ (* 1/2 (/ (* x (- 1/6 (* 1/2 (/ (- 1/2 (* 1/4 (/ 1 (pow (sqrt 2) 2)))) (pow (sqrt 2) 2))))) (sqrt 2))) (* 1/2 (/ (- 1/2 (* 1/4 (/ 1 (pow (sqrt 2) 2)))) (sqrt 2))))) (* 1/2 (/ 1 (sqrt 2))))))
(+.f64 (sqrt.f64 #s(literal 2 binary64)) (*.f64 x (+.f64 (/.f64 #s(literal 1/2 binary64) (sqrt.f64 #s(literal 2 binary64))) (*.f64 x (+.f64 (*.f64 #s(literal 7/192 binary64) (/.f64 x (sqrt.f64 #s(literal 2 binary64)))) (/.f64 #s(literal 3/16 binary64) (sqrt.f64 #s(literal 2 binary64))))))))
(* (sqrt (pow x 3)) (sqrt 1/6))
(*.f64 (sqrt.f64 (*.f64 x (*.f64 x x))) (sqrt.f64 #s(literal 1/6 binary64)))
(* (pow x 2) (+ (* 1/4 (* (sqrt (/ 1 (pow x 3))) (/ 1 (sqrt 1/6)))) (* (sqrt (/ 1 x)) (sqrt 1/6))))
(*.f64 (*.f64 x x) (+.f64 (*.f64 #s(literal 1/4 binary64) (/.f64 (sqrt.f64 (/.f64 (/.f64 #s(literal 1 binary64) (*.f64 x x)) x)) (sqrt.f64 #s(literal 1/6 binary64)))) (*.f64 (sqrt.f64 #s(literal 1/6 binary64)) (sqrt.f64 (/.f64 #s(literal 1 binary64) x)))))
(* (pow x 2) (+ (* 1/4 (* (sqrt (/ 1 (pow x 3))) (/ 1 (sqrt 1/6)))) (+ (* 1/2 (* (sqrt (/ 1 (pow x 5))) (/ 1 (sqrt 1/6)))) (* (sqrt (/ 1 x)) (sqrt 1/6)))))
(*.f64 (*.f64 x x) (+.f64 (*.f64 (sqrt.f64 #s(literal 1/6 binary64)) (sqrt.f64 (/.f64 #s(literal 1 binary64) x))) (*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 #s(literal 1/6 binary64))) (+.f64 (*.f64 #s(literal 1/4 binary64) (sqrt.f64 (/.f64 (/.f64 #s(literal 1 binary64) (*.f64 x x)) x))) (*.f64 #s(literal 1/2 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 5 binary64)))))))))
(* (pow x 2) (+ (* 1/4 (* (sqrt (/ 1 (pow x 3))) (/ 1 (sqrt 1/6)))) (+ (* 1/2 (* (sqrt (/ 1 (pow x 5))) (/ 1 (sqrt 1/6)))) (+ (* 1/2 (* (sqrt (/ 1 (pow x 7))) (/ (- 2 (* 1/16 (/ x (pow (sqrt 1/6) 2)))) (sqrt 1/6)))) (* (sqrt (/ 1 x)) (sqrt 1/6))))))
(*.f64 (*.f64 x x) (+.f64 (*.f64 (sqrt.f64 #s(literal 1/6 binary64)) (sqrt.f64 (/.f64 #s(literal 1 binary64) x))) (+.f64 (*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 #s(literal 1/6 binary64))) (+.f64 (*.f64 #s(literal 1/4 binary64) (sqrt.f64 (/.f64 (/.f64 #s(literal 1 binary64) (*.f64 x x)) x))) (*.f64 #s(literal 1/2 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 5 binary64))))))) (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 7 binary64)))) (/.f64 (*.f64 (+.f64 #s(literal 2 binary64) (*.f64 x #s(literal -3/8 binary64))) #s(literal 1/2 binary64)) (sqrt.f64 #s(literal 1/6 binary64)))))))
(* (sqrt (pow x 3)) (* (sqrt -1) (sqrt -1/6)))
(*.f64 (sqrt.f64 (*.f64 x (*.f64 x x))) (*.f64 (sqrt.f64 #s(literal -1 binary64)) (sqrt.f64 #s(literal -1/6 binary64))))
(* (pow x 2) (+ (* 1/4 (* (sqrt (/ 1 (pow x 3))) (/ (sqrt -1) (sqrt -1/6)))) (* (sqrt (/ 1 x)) (* (sqrt -1) (sqrt -1/6)))))
(*.f64 (*.f64 x x) (+.f64 (*.f64 (sqrt.f64 (/.f64 (/.f64 #s(literal 1 binary64) (*.f64 x x)) x)) (/.f64 (*.f64 (sqrt.f64 #s(literal -1 binary64)) #s(literal 1/4 binary64)) (sqrt.f64 #s(literal -1/6 binary64)))) (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) (*.f64 (sqrt.f64 #s(literal -1 binary64)) (sqrt.f64 #s(literal -1/6 binary64))))))
(* (pow x 2) (+ (* 1/4 (* (sqrt (/ 1 (pow x 3))) (/ (sqrt -1) (sqrt -1/6)))) (+ (* 1/2 (* (sqrt (/ 1 (pow x 5))) (/ (sqrt -1) (sqrt -1/6)))) (* (sqrt (/ 1 x)) (* (sqrt -1) (sqrt -1/6))))))
(*.f64 (*.f64 x x) (+.f64 (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) (*.f64 (sqrt.f64 #s(literal -1 binary64)) (sqrt.f64 #s(literal -1/6 binary64)))) (*.f64 (/.f64 (sqrt.f64 #s(literal -1 binary64)) (sqrt.f64 #s(literal -1/6 binary64))) (+.f64 (*.f64 #s(literal 1/4 binary64) (sqrt.f64 (/.f64 (/.f64 #s(literal 1 binary64) (*.f64 x x)) x))) (*.f64 #s(literal 1/2 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 5 binary64)))))))))
(* (pow x 2) (+ (* -1 (/ (+ (* -1/2 (* (sqrt x) (/ (sqrt -1) (sqrt -1/6)))) (* -1/2 (* (sqrt (/ 1 x)) (/ (* (sqrt -1) (- 2 (* -1/16 (/ x (pow (sqrt -1/6) 2))))) (sqrt -1/6))))) (pow x 3))) (+ (* 1/4 (* (sqrt (/ 1 (pow x 3))) (/ (sqrt -1) (sqrt -1/6)))) (* (sqrt (/ 1 x)) (* (sqrt -1) (sqrt -1/6))))))
(*.f64 (*.f64 x x) (+.f64 (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) (*.f64 (sqrt.f64 #s(literal -1 binary64)) (sqrt.f64 #s(literal -1/6 binary64)))) (-.f64 (*.f64 (sqrt.f64 (/.f64 (/.f64 #s(literal 1 binary64) (*.f64 x x)) x)) (/.f64 (*.f64 (sqrt.f64 #s(literal -1 binary64)) #s(literal 1/4 binary64)) (sqrt.f64 #s(literal -1/6 binary64)))) (/.f64 (*.f64 (+.f64 (/.f64 (*.f64 (sqrt.f64 #s(literal -1 binary64)) (sqrt.f64 x)) (sqrt.f64 #s(literal -1/6 binary64))) (/.f64 (*.f64 (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) (sqrt.f64 #s(literal -1 binary64))) (+.f64 #s(literal 2 binary64) (*.f64 x #s(literal -3/8 binary64)))) (sqrt.f64 #s(literal -1/6 binary64)))) (/.f64 #s(literal -1/2 binary64) (*.f64 x x))) x))))
(sqrt 1/2)
(sqrt.f64 #s(literal 1/2 binary64))
(+ (sqrt 1/2) (* -1/8 (/ x (sqrt 1/2))))
(+.f64 (sqrt.f64 #s(literal 1/2 binary64)) (/.f64 (*.f64 x #s(literal -1/8 binary64)) (sqrt.f64 #s(literal 1/2 binary64))))
(+ (sqrt 1/2) (* x (- (* -1/128 (/ x (pow (sqrt 1/2) 3))) (* 1/8 (/ 1 (sqrt 1/2))))))
(+.f64 (sqrt.f64 #s(literal 1/2 binary64)) (*.f64 x (+.f64 (*.f64 (/.f64 x (sqrt.f64 #s(literal 1/2 binary64))) #s(literal -1/64 binary64)) (/.f64 #s(literal -1/8 binary64) (sqrt.f64 #s(literal 1/2 binary64))))))
(+ (sqrt 1/2) (* x (- (* x (- (* 1/2 (/ (* x (- 1/48 (* 1/512 (/ 1 (pow (sqrt 1/2) 4))))) (sqrt 1/2))) (* 1/128 (/ 1 (pow (sqrt 1/2) 3))))) (* 1/8 (/ 1 (sqrt 1/2))))))
(+.f64 (sqrt.f64 #s(literal 1/2 binary64)) (*.f64 x (+.f64 (*.f64 x (+.f64 (*.f64 (+.f64 #s(literal 1/96 binary64) (*.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/512 binary64) (pow.f64 (sqrt.f64 #s(literal 1/2 binary64)) #s(literal 4 binary64))))) (/.f64 x (sqrt.f64 #s(literal 1/2 binary64)))) (/.f64 #s(literal -1/64 binary64) (sqrt.f64 #s(literal 1/2 binary64))))) (/.f64 #s(literal -1/8 binary64) (sqrt.f64 #s(literal 1/2 binary64))))))
(* (sqrt (/ 1 (pow x 3))) (sqrt 6))
(*.f64 (sqrt.f64 (/.f64 (/.f64 #s(literal 1 binary64) (*.f64 x x)) x)) (sqrt.f64 #s(literal 6 binary64)))
(/ (+ (* -9 (* (sqrt (/ 1 (pow x 3))) (/ 1 (sqrt 6)))) (* (sqrt (/ 1 x)) (sqrt 6))) x)
(/.f64 (+.f64 (*.f64 (sqrt.f64 (/.f64 (/.f64 #s(literal 1 binary64) (*.f64 x x)) x)) (/.f64 #s(literal -9 binary64) (sqrt.f64 #s(literal 6 binary64)))) (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) (sqrt.f64 #s(literal 6 binary64)))) x)
(/ (+ (* -9 (* (sqrt (/ 1 (pow x 3))) (/ 1 (sqrt 6)))) (+ (* 9 (* (sqrt (/ 1 (pow x 5))) (/ 1 (sqrt 6)))) (* (sqrt (/ 1 x)) (sqrt 6)))) x)
(/.f64 (+.f64 (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) (sqrt.f64 #s(literal 6 binary64))) (*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 #s(literal 6 binary64))) (+.f64 (*.f64 (sqrt.f64 (/.f64 (/.f64 #s(literal 1 binary64) (*.f64 x x)) x)) #s(literal -9 binary64)) (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 5 binary64)))) #s(literal 9 binary64))))) x)
(/ (+ (* -9 (* (sqrt (/ 1 (pow x 3))) (/ 1 (sqrt 6)))) (+ (* -1/2 (* (sqrt (/ 1 (pow x 7))) (/ (+ 18 (* 81 (/ x (pow (sqrt 6) 2)))) (sqrt 6)))) (+ (* 9 (* (sqrt (/ 1 (pow x 5))) (/ 1 (sqrt 6)))) (* (sqrt (/ 1 x)) (sqrt 6))))) x)
(/.f64 (+.f64 (*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 #s(literal 6 binary64))) (+.f64 (*.f64 (sqrt.f64 (/.f64 (/.f64 #s(literal 1 binary64) (*.f64 x x)) x)) #s(literal -9 binary64)) (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 5 binary64)))) #s(literal 9 binary64)))) (+.f64 (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) (sqrt.f64 #s(literal 6 binary64))) (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 7 binary64)))) (/.f64 (*.f64 (+.f64 #s(literal 18 binary64) (*.f64 x #s(literal 27/2 binary64))) #s(literal -1/2 binary64)) (sqrt.f64 #s(literal 6 binary64)))))) x)
(* -1 (* (sqrt (/ 1 (pow x 3))) (* (sqrt -6) (sqrt -1))))
(*.f64 (*.f64 (sqrt.f64 (/.f64 (/.f64 #s(literal 1 binary64) (*.f64 x x)) x)) (sqrt.f64 #s(literal -6 binary64))) (-.f64 #s(literal 0 binary64) (sqrt.f64 #s(literal -1 binary64))))
(* -1 (/ (+ (* -9 (* (sqrt (/ 1 (pow x 3))) (/ (sqrt -1) (sqrt -6)))) (* (sqrt (/ 1 x)) (* (sqrt -6) (sqrt -1)))) x))
(/.f64 (+.f64 (*.f64 (sqrt.f64 (/.f64 (/.f64 #s(literal 1 binary64) (*.f64 x x)) x)) (/.f64 (*.f64 (sqrt.f64 #s(literal -1 binary64)) #s(literal -9 binary64)) (sqrt.f64 #s(literal -6 binary64)))) (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) (*.f64 (sqrt.f64 #s(literal -1 binary64)) (sqrt.f64 #s(literal -6 binary64))))) (-.f64 #s(literal 0 binary64) x))
(* -1 (/ (+ (* -9 (* (sqrt (/ 1 (pow x 3))) (/ (sqrt -1) (sqrt -6)))) (+ (* 9 (* (sqrt (/ 1 (pow x 5))) (/ (sqrt -1) (sqrt -6)))) (* (sqrt (/ 1 x)) (* (sqrt -6) (sqrt -1))))) x))
(/.f64 (+.f64 (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) (*.f64 (sqrt.f64 #s(literal -1 binary64)) (sqrt.f64 #s(literal -6 binary64)))) (*.f64 (/.f64 (sqrt.f64 #s(literal -1 binary64)) (sqrt.f64 #s(literal -6 binary64))) (+.f64 (*.f64 (sqrt.f64 (/.f64 (/.f64 #s(literal 1 binary64) (*.f64 x x)) x)) #s(literal -9 binary64)) (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 5 binary64)))) #s(literal 9 binary64))))) (-.f64 #s(literal 0 binary64) x))
(* -1 (/ (+ (* -9 (* (sqrt (/ 1 (pow x 3))) (/ (sqrt -1) (sqrt -6)))) (+ (* -1 (/ (+ (* -9 (* (sqrt x) (/ (sqrt -1) (sqrt -6)))) (* 1/2 (* (sqrt (/ 1 x)) (/ (* (sqrt -1) (+ 18 (* -81 (/ x (pow (sqrt -6) 2))))) (sqrt -6))))) (pow x 3))) (* (sqrt (/ 1 x)) (* (sqrt -6) (sqrt -1))))) x))
(/.f64 (+.f64 (*.f64 (sqrt.f64 (/.f64 (/.f64 #s(literal 1 binary64) (*.f64 x x)) x)) (/.f64 (*.f64 (sqrt.f64 #s(literal -1 binary64)) #s(literal -9 binary64)) (sqrt.f64 #s(literal -6 binary64)))) (-.f64 (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) (*.f64 (sqrt.f64 #s(literal -1 binary64)) (sqrt.f64 #s(literal -6 binary64)))) (/.f64 (+.f64 (/.f64 (*.f64 (*.f64 (sqrt.f64 x) #s(literal -9 binary64)) (sqrt.f64 #s(literal -1 binary64))) (sqrt.f64 #s(literal -6 binary64))) (*.f64 (*.f64 (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) (sqrt.f64 #s(literal -1 binary64))) (+.f64 #s(literal 18 binary64) (*.f64 x #s(literal 27/2 binary64)))) (/.f64 #s(literal 1/2 binary64) (sqrt.f64 #s(literal -6 binary64))))) (*.f64 x (*.f64 x x))))) (-.f64 #s(literal 0 binary64) x))
1/2
#s(literal 1/2 binary64)
(+ 1/2 (* -1/4 x))
(+.f64 #s(literal 1/2 binary64) (*.f64 x #s(literal -1/4 binary64)))
(+ 1/2 (* x (- (* 1/48 (pow x 2)) 1/4)))
(+.f64 #s(literal 1/2 binary64) (*.f64 x (+.f64 #s(literal -1/4 binary64) (*.f64 (*.f64 x x) #s(literal 1/48 binary64)))))
(+ 1/2 (* x (- (* (pow x 2) (+ 1/48 (* 1/96 x))) 1/4)))
(+.f64 #s(literal 1/2 binary64) (*.f64 x (+.f64 #s(literal -1/4 binary64) (*.f64 (*.f64 x x) (+.f64 #s(literal 1/48 binary64) (*.f64 x #s(literal 1/96 binary64)))))))
(/ 6 (pow x 3))
(/.f64 (/.f64 #s(literal 6 binary64) (*.f64 x x)) x)
(/ (- 6 (* 18 (/ 1 x))) (pow x 3))
(/.f64 (+.f64 #s(literal 6 binary64) (/.f64 #s(literal -18 binary64) x)) (*.f64 x (*.f64 x x)))
(/ (- (+ 6 (/ 18 (pow x 2))) (* 18 (/ 1 x))) (pow x 3))
(/.f64 (+.f64 #s(literal 6 binary64) (/.f64 (+.f64 (/.f64 #s(literal 18 binary64) x) #s(literal -18 binary64)) x)) (*.f64 x (*.f64 x x)))
(/ (- (+ 6 (/ 18 (pow x 2))) (+ (* 18 (/ 1 x)) (* 18 (/ 1 (pow x 3))))) (pow x 3))
(/.f64 (+.f64 (/.f64 (+.f64 (/.f64 #s(literal 18 binary64) x) #s(literal -18 binary64)) x) (+.f64 #s(literal 6 binary64) (/.f64 #s(literal -18 binary64) (*.f64 x (*.f64 x x))))) (*.f64 x (*.f64 x x)))
(/ 6 (pow x 3))
(/.f64 (/.f64 #s(literal 6 binary64) (*.f64 x x)) x)
(* -1 (/ (- (* 18 (/ 1 x)) 6) (pow x 3)))
(/.f64 (+.f64 #s(literal 6 binary64) (/.f64 #s(literal -18 binary64) x)) (*.f64 x (*.f64 x x)))
(* -1 (/ (- (* -1 (/ (- (* 18 (/ 1 x)) 18) x)) 6) (pow x 3)))
(/.f64 (+.f64 #s(literal -6 binary64) (/.f64 (+.f64 #s(literal 18 binary64) (/.f64 #s(literal -18 binary64) x)) x)) (*.f64 x (*.f64 #s(literal -1 binary64) (*.f64 x x))))
(* -1 (/ (- (* -1 (/ (- (* -1 (/ (- (* 18 (/ 1 x)) 18) x)) 18) x)) 6) (pow x 3)))
(/.f64 (-.f64 #s(literal -6 binary64) (/.f64 (+.f64 (/.f64 (+.f64 #s(literal 18 binary64) (/.f64 #s(literal -18 binary64) x)) x) #s(literal -18 binary64)) x)) (*.f64 x (*.f64 #s(literal -1 binary64) (*.f64 x x))))
2
#s(literal 2 binary64)
(+ 2 x)
(+.f64 #s(literal 2 binary64) x)
(+ 2 (* x (+ 1 (* 1/2 x))))
(+.f64 #s(literal 2 binary64) (*.f64 x (+.f64 #s(literal 1 binary64) (*.f64 #s(literal 1/2 binary64) x))))
(+ 2 (* x (+ 1 (* x (+ 1/2 (* 1/6 x))))))
(+.f64 #s(literal 2 binary64) (*.f64 x (+.f64 #s(literal 1 binary64) (*.f64 x (+.f64 #s(literal 1/2 binary64) (/.f64 x #s(literal 6 binary64)))))))
(* 1/6 (pow x 3))
(*.f64 x (*.f64 x (/.f64 x #s(literal 6 binary64))))
(* (pow x 3) (+ 1/6 (* 1/2 (/ 1 x))))
(*.f64 (*.f64 x x) (+.f64 #s(literal 1/2 binary64) (/.f64 x #s(literal 6 binary64))))
(* (pow x 3) (+ 1/6 (+ (* 1/2 (/ 1 x)) (/ 1 (pow x 2)))))
(*.f64 (*.f64 x x) (+.f64 #s(literal 1/2 binary64) (*.f64 x (+.f64 (/.f64 #s(literal 1 binary64) (*.f64 x x)) #s(literal 1/6 binary64)))))
(* (pow x 3) (+ 1/6 (+ (* 1/2 (/ 1 x)) (+ (/ 1 (pow x 2)) (* 2 (/ 1 (pow x 3)))))))
(*.f64 (*.f64 x x) (+.f64 #s(literal 1/2 binary64) (*.f64 x (+.f64 (/.f64 (/.f64 #s(literal 2 binary64) (*.f64 x x)) x) (+.f64 (/.f64 #s(literal 1 binary64) (*.f64 x x)) #s(literal 1/6 binary64))))))
(* 1/6 (pow x 3))
(*.f64 x (*.f64 x (/.f64 x #s(literal 6 binary64))))
(* (pow x 3) (+ 1/6 (* 1/2 (/ 1 x))))
(*.f64 (*.f64 x x) (+.f64 #s(literal 1/2 binary64) (/.f64 x #s(literal 6 binary64))))
(* -1 (* (pow x 3) (- (* -1 (/ (+ 1/2 (/ 1 x)) x)) 1/6)))
(-.f64 #s(literal 0 binary64) (*.f64 (*.f64 x (*.f64 x x)) (+.f64 #s(literal -1/6 binary64) (/.f64 (+.f64 #s(literal -1/2 binary64) (/.f64 #s(literal -1 binary64) x)) x))))
(* -1 (* (pow x 3) (- (* -1 (/ (+ 1/2 (+ (/ 1 x) (/ 2 (pow x 2)))) x)) 1/6)))
(-.f64 #s(literal 0 binary64) (*.f64 (*.f64 x (*.f64 x x)) (+.f64 #s(literal -1/6 binary64) (/.f64 (+.f64 (+.f64 #s(literal -1/2 binary64) (/.f64 #s(literal -1 binary64) x)) (/.f64 #s(literal -2 binary64) (*.f64 x x))) x))))
(sqrt x)
(sqrt.f64 x)
(sqrt x)
(sqrt.f64 x)
(sqrt x)
(sqrt.f64 x)
(sqrt x)
(sqrt.f64 x)
(sqrt x)
(sqrt.f64 x)
(sqrt x)
(sqrt.f64 x)
(sqrt x)
(sqrt.f64 x)
(sqrt x)
(sqrt.f64 x)
(* -1 (* (sqrt x) (pow (sqrt -1) 2)))
(sqrt.f64 x)
(* -1 (* (sqrt x) (pow (sqrt -1) 2)))
(sqrt.f64 x)
(* -1 (* (sqrt x) (pow (sqrt -1) 2)))
(sqrt.f64 x)
(* -1 (* (sqrt x) (pow (sqrt -1) 2)))
(sqrt.f64 x)
(* x (sqrt 1/2))
(*.f64 x (sqrt.f64 #s(literal 1/2 binary64)))
(* x (sqrt 1/2))
(*.f64 x (sqrt.f64 #s(literal 1/2 binary64)))
(* x (sqrt 1/2))
(*.f64 x (sqrt.f64 #s(literal 1/2 binary64)))
(* x (sqrt 1/2))
(*.f64 x (sqrt.f64 #s(literal 1/2 binary64)))
(* x (sqrt 1/2))
(*.f64 x (sqrt.f64 #s(literal 1/2 binary64)))
(* x (sqrt 1/2))
(*.f64 x (sqrt.f64 #s(literal 1/2 binary64)))
(* x (sqrt 1/2))
(*.f64 x (sqrt.f64 #s(literal 1/2 binary64)))
(* x (sqrt 1/2))
(*.f64 x (sqrt.f64 #s(literal 1/2 binary64)))
(* x (sqrt 1/2))
(*.f64 x (sqrt.f64 #s(literal 1/2 binary64)))
(* x (sqrt 1/2))
(*.f64 x (sqrt.f64 #s(literal 1/2 binary64)))
(* x (sqrt 1/2))
(*.f64 x (sqrt.f64 #s(literal 1/2 binary64)))
(* x (sqrt 1/2))
(*.f64 x (sqrt.f64 #s(literal 1/2 binary64)))
(* (sqrt (pow x 3)) (sqrt 1/6))
(*.f64 (sqrt.f64 (*.f64 x (*.f64 x x))) (sqrt.f64 #s(literal 1/6 binary64)))
(* (sqrt (pow x 3)) (sqrt 1/6))
(*.f64 (sqrt.f64 (*.f64 x (*.f64 x x))) (sqrt.f64 #s(literal 1/6 binary64)))
(* (sqrt (pow x 3)) (sqrt 1/6))
(*.f64 (sqrt.f64 (*.f64 x (*.f64 x x))) (sqrt.f64 #s(literal 1/6 binary64)))
(* (sqrt (pow x 3)) (sqrt 1/6))
(*.f64 (sqrt.f64 (*.f64 x (*.f64 x x))) (sqrt.f64 #s(literal 1/6 binary64)))
(* (sqrt (pow x 3)) (sqrt 1/6))
(*.f64 (sqrt.f64 (*.f64 x (*.f64 x x))) (sqrt.f64 #s(literal 1/6 binary64)))
(* (sqrt (pow x 3)) (sqrt 1/6))
(*.f64 (sqrt.f64 (*.f64 x (*.f64 x x))) (sqrt.f64 #s(literal 1/6 binary64)))
(* (sqrt (pow x 3)) (sqrt 1/6))
(*.f64 (sqrt.f64 (*.f64 x (*.f64 x x))) (sqrt.f64 #s(literal 1/6 binary64)))
(* (sqrt (pow x 3)) (sqrt 1/6))
(*.f64 (sqrt.f64 (*.f64 x (*.f64 x x))) (sqrt.f64 #s(literal 1/6 binary64)))
(* (sqrt (pow x 3)) (* (sqrt -1) (sqrt -1/6)))
(*.f64 (sqrt.f64 (*.f64 x (*.f64 x x))) (*.f64 (sqrt.f64 #s(literal -1 binary64)) (sqrt.f64 #s(literal -1/6 binary64))))
(* (sqrt (pow x 3)) (* (sqrt -1) (sqrt -1/6)))
(*.f64 (sqrt.f64 (*.f64 x (*.f64 x x))) (*.f64 (sqrt.f64 #s(literal -1 binary64)) (sqrt.f64 #s(literal -1/6 binary64))))
(* (sqrt (pow x 3)) (* (sqrt -1) (sqrt -1/6)))
(*.f64 (sqrt.f64 (*.f64 x (*.f64 x x))) (*.f64 (sqrt.f64 #s(literal -1 binary64)) (sqrt.f64 #s(literal -1/6 binary64))))
(* (sqrt (pow x 3)) (* (sqrt -1) (sqrt -1/6)))
(*.f64 (sqrt.f64 (*.f64 x (*.f64 x x))) (*.f64 (sqrt.f64 #s(literal -1 binary64)) (sqrt.f64 #s(literal -1/6 binary64))))
(* 1/6 (pow x 3))
(*.f64 x (*.f64 x (/.f64 x #s(literal 6 binary64))))
(* 1/6 (pow x 3))
(*.f64 x (*.f64 x (/.f64 x #s(literal 6 binary64))))
(* 1/6 (pow x 3))
(*.f64 x (*.f64 x (/.f64 x #s(literal 6 binary64))))
(* 1/6 (pow x 3))
(*.f64 x (*.f64 x (/.f64 x #s(literal 6 binary64))))
(* 1/6 (pow x 3))
(*.f64 x (*.f64 x (/.f64 x #s(literal 6 binary64))))
(* 1/6 (pow x 3))
(*.f64 x (*.f64 x (/.f64 x #s(literal 6 binary64))))
(* 1/6 (pow x 3))
(*.f64 x (*.f64 x (/.f64 x #s(literal 6 binary64))))
(* 1/6 (pow x 3))
(*.f64 x (*.f64 x (/.f64 x #s(literal 6 binary64))))
(* 1/6 (pow x 3))
(*.f64 x (*.f64 x (/.f64 x #s(literal 6 binary64))))
(* 1/6 (pow x 3))
(*.f64 x (*.f64 x (/.f64 x #s(literal 6 binary64))))
(* 1/6 (pow x 3))
(*.f64 x (*.f64 x (/.f64 x #s(literal 6 binary64))))
(* 1/6 (pow x 3))
(*.f64 x (*.f64 x (/.f64 x #s(literal 6 binary64))))
(pow x 3)
(*.f64 x (*.f64 x x))
(pow x 3)
(*.f64 x (*.f64 x x))
(pow x 3)
(*.f64 x (*.f64 x x))
(pow x 3)
(*.f64 x (*.f64 x x))
(pow x 3)
(*.f64 x (*.f64 x x))
(pow x 3)
(*.f64 x (*.f64 x x))
(pow x 3)
(*.f64 x (*.f64 x x))
(pow x 3)
(*.f64 x (*.f64 x x))
(pow x 3)
(*.f64 x (*.f64 x x))
(pow x 3)
(*.f64 x (*.f64 x x))
(pow x 3)
(*.f64 x (*.f64 x x))
(pow x 3)
(*.f64 x (*.f64 x x))
(pow x 2)
(*.f64 x x)
(pow x 2)
(*.f64 x x)
(pow x 2)
(*.f64 x x)
(pow x 2)
(*.f64 x x)
(pow x 2)
(*.f64 x x)
(pow x 2)
(*.f64 x x)
(pow x 2)
(*.f64 x x)
(pow x 2)
(*.f64 x x)
(pow x 2)
(*.f64 x x)
(pow x 2)
(*.f64 x x)
(pow x 2)
(*.f64 x x)
(pow x 2)
(*.f64 x x)
(* x (sqrt 1/2))
(*.f64 x (sqrt.f64 #s(literal 1/2 binary64)))
(* x (+ (sqrt 1/2) (* 1/12 (/ x (sqrt 1/2)))))
(*.f64 x (+.f64 (sqrt.f64 #s(literal 1/2 binary64)) (*.f64 x (/.f64 #s(literal 1/12 binary64) (sqrt.f64 #s(literal 1/2 binary64))))))
(* x (+ (sqrt 1/2) (* x (+ (* -1/288 (/ x (pow (sqrt 1/2) 3))) (* 1/12 (/ 1 (sqrt 1/2)))))))
(*.f64 x (+.f64 (sqrt.f64 #s(literal 1/2 binary64)) (*.f64 x (+.f64 (/.f64 (*.f64 x #s(literal -1/144 binary64)) (sqrt.f64 #s(literal 1/2 binary64))) (/.f64 #s(literal 1/12 binary64) (sqrt.f64 #s(literal 1/2 binary64)))))))
(* x (+ (sqrt 1/2) (* x (+ (* x (- (* 1/3456 (/ x (pow (sqrt 1/2) 5))) (* 1/288 (/ 1 (pow (sqrt 1/2) 3))))) (* 1/12 (/ 1 (sqrt 1/2)))))))
(*.f64 x (+.f64 (sqrt.f64 #s(literal 1/2 binary64)) (*.f64 x (+.f64 (/.f64 #s(literal 1/12 binary64) (sqrt.f64 #s(literal 1/2 binary64))) (*.f64 x (+.f64 (/.f64 (*.f64 x #s(literal 1/3456 binary64)) (pow.f64 (sqrt.f64 #s(literal 1/2 binary64)) #s(literal 5 binary64))) (/.f64 #s(literal -1/144 binary64) (sqrt.f64 #s(literal 1/2 binary64)))))))))
(* (sqrt (pow x 3)) (sqrt 1/6))
(*.f64 (sqrt.f64 (*.f64 x (*.f64 x x))) (sqrt.f64 #s(literal 1/6 binary64)))
(* (pow x 2) (+ (* 1/4 (* (sqrt (/ 1 (pow x 3))) (/ 1 (sqrt 1/6)))) (* (sqrt (/ 1 x)) (sqrt 1/6))))
(*.f64 (*.f64 x x) (+.f64 (*.f64 #s(literal 1/4 binary64) (/.f64 (sqrt.f64 (/.f64 (/.f64 #s(literal 1 binary64) (*.f64 x x)) x)) (sqrt.f64 #s(literal 1/6 binary64)))) (*.f64 (sqrt.f64 #s(literal 1/6 binary64)) (sqrt.f64 (/.f64 #s(literal 1 binary64) x)))))
(* (pow x 2) (+ (* -1/32 (* (sqrt (/ 1 (pow x 5))) (/ 1 (pow (sqrt 1/6) 3)))) (+ (* 1/4 (* (sqrt (/ 1 (pow x 3))) (/ 1 (sqrt 1/6)))) (* (sqrt (/ 1 x)) (sqrt 1/6)))))
(*.f64 (*.f64 x x) (+.f64 (+.f64 (*.f64 #s(literal 1/4 binary64) (/.f64 (sqrt.f64 (/.f64 (/.f64 #s(literal 1 binary64) (*.f64 x x)) x)) (sqrt.f64 #s(literal 1/6 binary64)))) (*.f64 (sqrt.f64 #s(literal 1/6 binary64)) (sqrt.f64 (/.f64 #s(literal 1 binary64) x)))) (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 5 binary64)))) (/.f64 #s(literal -3/16 binary64) (sqrt.f64 #s(literal 1/6 binary64))))))
(* (pow x 2) (+ (* -1/32 (* (sqrt (/ 1 (pow x 5))) (/ 1 (pow (sqrt 1/6) 3)))) (+ (* 1/128 (* (sqrt (/ 1 (pow x 7))) (/ 1 (pow (sqrt 1/6) 5)))) (+ (* 1/4 (* (sqrt (/ 1 (pow x 3))) (/ 1 (sqrt 1/6)))) (* (sqrt (/ 1 x)) (sqrt 1/6))))))
(*.f64 (*.f64 x x) (+.f64 (*.f64 (sqrt.f64 #s(literal 1/6 binary64)) (sqrt.f64 (/.f64 #s(literal 1 binary64) x))) (+.f64 (*.f64 #s(literal 1/4 binary64) (/.f64 (sqrt.f64 (/.f64 (/.f64 #s(literal 1 binary64) (*.f64 x x)) x)) (sqrt.f64 #s(literal 1/6 binary64)))) (+.f64 (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 5 binary64)))) (/.f64 #s(literal -3/16 binary64) (sqrt.f64 #s(literal 1/6 binary64)))) (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 7 binary64)))) (/.f64 #s(literal 1/128 binary64) (pow.f64 (sqrt.f64 #s(literal 1/6 binary64)) #s(literal 5 binary64))))))))
(* (sqrt (pow x 3)) (* (sqrt -1) (sqrt -1/6)))
(*.f64 (sqrt.f64 (*.f64 x (*.f64 x x))) (*.f64 (sqrt.f64 #s(literal -1 binary64)) (sqrt.f64 #s(literal -1/6 binary64))))
(* (pow x 2) (+ (* 1/4 (* (sqrt (/ 1 (pow x 3))) (/ (sqrt -1) (sqrt -1/6)))) (* (sqrt (/ 1 x)) (* (sqrt -1) (sqrt -1/6)))))
(*.f64 (*.f64 x x) (+.f64 (*.f64 (sqrt.f64 (/.f64 (/.f64 #s(literal 1 binary64) (*.f64 x x)) x)) (/.f64 (*.f64 (sqrt.f64 #s(literal -1 binary64)) #s(literal 1/4 binary64)) (sqrt.f64 #s(literal -1/6 binary64)))) (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) (*.f64 (sqrt.f64 #s(literal -1 binary64)) (sqrt.f64 #s(literal -1/6 binary64))))))
(* (pow x 2) (+ (* -1/32 (* (sqrt (/ 1 (pow x 5))) (/ (sqrt -1) (pow (sqrt -1/6) 3)))) (+ (* 1/4 (* (sqrt (/ 1 (pow x 3))) (/ (sqrt -1) (sqrt -1/6)))) (* (sqrt (/ 1 x)) (* (sqrt -1) (sqrt -1/6))))))
(*.f64 (*.f64 x x) (+.f64 (*.f64 (sqrt.f64 (/.f64 (/.f64 #s(literal 1 binary64) (*.f64 x x)) x)) (/.f64 (*.f64 (sqrt.f64 #s(literal -1 binary64)) #s(literal 1/4 binary64)) (sqrt.f64 #s(literal -1/6 binary64)))) (+.f64 (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) (*.f64 (sqrt.f64 #s(literal -1 binary64)) (sqrt.f64 #s(literal -1/6 binary64)))) (*.f64 (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 5 binary64)))) (/.f64 (sqrt.f64 #s(literal -1 binary64)) (sqrt.f64 #s(literal -1/6 binary64)))) #s(literal 3/16 binary64)))))
(* (pow x 2) (+ (* -1/32 (* (sqrt (/ 1 (pow x 5))) (/ (sqrt -1) (pow (sqrt -1/6) 3)))) (+ (* 1/128 (* (sqrt (/ 1 (pow x 7))) (/ (sqrt -1) (pow (sqrt -1/6) 5)))) (+ (* 1/4 (* (sqrt (/ 1 (pow x 3))) (/ (sqrt -1) (sqrt -1/6)))) (* (sqrt (/ 1 x)) (* (sqrt -1) (sqrt -1/6)))))))
(*.f64 (*.f64 x x) (+.f64 (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) (*.f64 (sqrt.f64 #s(literal -1 binary64)) (sqrt.f64 #s(literal -1/6 binary64)))) (+.f64 (+.f64 (*.f64 (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 5 binary64)))) (/.f64 (sqrt.f64 #s(literal -1 binary64)) (sqrt.f64 #s(literal -1/6 binary64)))) #s(literal 3/16 binary64)) (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 7 binary64)))) (/.f64 (*.f64 (sqrt.f64 #s(literal -1 binary64)) #s(literal 1/128 binary64)) (pow.f64 (sqrt.f64 #s(literal -1/6 binary64)) #s(literal 5 binary64))))) (*.f64 (sqrt.f64 (/.f64 (/.f64 #s(literal 1 binary64) (*.f64 x x)) x)) (/.f64 (*.f64 (sqrt.f64 #s(literal -1 binary64)) #s(literal 1/4 binary64)) (sqrt.f64 #s(literal -1/6 binary64)))))))
(* 1/2 (pow x 2))
(*.f64 #s(literal 1/2 binary64) (*.f64 x x))
(* (pow x 2) (+ 1/2 (* 1/6 x)))
(*.f64 (*.f64 x x) (+.f64 #s(literal 1/2 binary64) (/.f64 x #s(literal 6 binary64))))
(* (pow x 2) (+ 1/2 (* 1/6 x)))
(*.f64 (*.f64 x x) (+.f64 #s(literal 1/2 binary64) (/.f64 x #s(literal 6 binary64))))
(* (pow x 2) (+ 1/2 (* 1/6 x)))
(*.f64 (*.f64 x x) (+.f64 #s(literal 1/2 binary64) (/.f64 x #s(literal 6 binary64))))
(* 1/6 (pow x 3))
(*.f64 x (*.f64 x (/.f64 x #s(literal 6 binary64))))
(* (pow x 3) (+ 1/6 (* 1/2 (/ 1 x))))
(*.f64 (*.f64 x x) (+.f64 #s(literal 1/2 binary64) (/.f64 x #s(literal 6 binary64))))
(* (pow x 3) (+ 1/6 (* 1/2 (/ 1 x))))
(*.f64 (*.f64 x x) (+.f64 #s(literal 1/2 binary64) (/.f64 x #s(literal 6 binary64))))
(* (pow x 3) (+ 1/6 (* 1/2 (/ 1 x))))
(*.f64 (*.f64 x x) (+.f64 #s(literal 1/2 binary64) (/.f64 x #s(literal 6 binary64))))
(* 1/6 (pow x 3))
(*.f64 x (*.f64 x (/.f64 x #s(literal 6 binary64))))
(* (pow x 3) (+ 1/6 (* 1/2 (/ 1 x))))
(*.f64 (*.f64 x x) (+.f64 #s(literal 1/2 binary64) (/.f64 x #s(literal 6 binary64))))
(* (pow x 3) (+ 1/6 (* 1/2 (/ 1 x))))
(*.f64 (*.f64 x x) (+.f64 #s(literal 1/2 binary64) (/.f64 x #s(literal 6 binary64))))
(* (pow x 3) (+ 1/6 (* 1/2 (/ 1 x))))
(*.f64 (*.f64 x x) (+.f64 #s(literal 1/2 binary64) (/.f64 x #s(literal 6 binary64))))
(* 1/2 x)
(*.f64 #s(literal 1/2 binary64) x)
(* x (+ 1/2 (* 1/6 x)))
(*.f64 x (+.f64 #s(literal 1/2 binary64) (/.f64 x #s(literal 6 binary64))))
(* x (+ 1/2 (* 1/6 x)))
(*.f64 x (+.f64 #s(literal 1/2 binary64) (/.f64 x #s(literal 6 binary64))))
(* x (+ 1/2 (* 1/6 x)))
(*.f64 x (+.f64 #s(literal 1/2 binary64) (/.f64 x #s(literal 6 binary64))))
(* 1/6 (pow x 2))
(*.f64 x (/.f64 x #s(literal 6 binary64)))
(* (pow x 2) (+ 1/6 (* 1/2 (/ 1 x))))
(*.f64 x (+.f64 #s(literal 1/2 binary64) (/.f64 x #s(literal 6 binary64))))
(* (pow x 2) (+ 1/6 (* 1/2 (/ 1 x))))
(*.f64 x (+.f64 #s(literal 1/2 binary64) (/.f64 x #s(literal 6 binary64))))
(* (pow x 2) (+ 1/6 (* 1/2 (/ 1 x))))
(*.f64 x (+.f64 #s(literal 1/2 binary64) (/.f64 x #s(literal 6 binary64))))
(* 1/6 (pow x 2))
(*.f64 x (/.f64 x #s(literal 6 binary64)))
(* (pow x 2) (+ 1/6 (* 1/2 (/ 1 x))))
(*.f64 x (+.f64 #s(literal 1/2 binary64) (/.f64 x #s(literal 6 binary64))))
(* (pow x 2) (+ 1/6 (* 1/2 (/ 1 x))))
(*.f64 x (+.f64 #s(literal 1/2 binary64) (/.f64 x #s(literal 6 binary64))))
(* (pow x 2) (+ 1/6 (* 1/2 (/ 1 x))))
(*.f64 x (+.f64 #s(literal 1/2 binary64) (/.f64 x #s(literal 6 binary64))))
1/2
#s(literal 1/2 binary64)
(+ 1/2 (* 1/6 x))
(+.f64 #s(literal 1/2 binary64) (/.f64 x #s(literal 6 binary64)))
(+ 1/2 (* 1/6 x))
(+.f64 #s(literal 1/2 binary64) (/.f64 x #s(literal 6 binary64)))
(+ 1/2 (* 1/6 x))
(+.f64 #s(literal 1/2 binary64) (/.f64 x #s(literal 6 binary64)))
(* 1/6 x)
(/.f64 x #s(literal 6 binary64))
(* x (+ 1/6 (* 1/2 (/ 1 x))))
(+.f64 #s(literal 1/2 binary64) (/.f64 x #s(literal 6 binary64)))
(* x (+ 1/6 (* 1/2 (/ 1 x))))
(+.f64 #s(literal 1/2 binary64) (/.f64 x #s(literal 6 binary64)))
(* x (+ 1/6 (* 1/2 (/ 1 x))))
(+.f64 #s(literal 1/2 binary64) (/.f64 x #s(literal 6 binary64)))
(* 1/6 x)
(/.f64 x #s(literal 6 binary64))
(* x (+ 1/6 (* 1/2 (/ 1 x))))
(+.f64 #s(literal 1/2 binary64) (/.f64 x #s(literal 6 binary64)))
(* x (+ 1/6 (* 1/2 (/ 1 x))))
(+.f64 #s(literal 1/2 binary64) (/.f64 x #s(literal 6 binary64)))
(* x (+ 1/6 (* 1/2 (/ 1 x))))
(+.f64 #s(literal 1/2 binary64) (/.f64 x #s(literal 6 binary64)))
(* 1/6 x)
(/.f64 x #s(literal 6 binary64))
(* 1/6 x)
(/.f64 x #s(literal 6 binary64))
(* 1/6 x)
(/.f64 x #s(literal 6 binary64))
(* 1/6 x)
(/.f64 x #s(literal 6 binary64))
(* 1/6 x)
(/.f64 x #s(literal 6 binary64))
(* 1/6 x)
(/.f64 x #s(literal 6 binary64))
(* 1/6 x)
(/.f64 x #s(literal 6 binary64))
(* 1/6 x)
(/.f64 x #s(literal 6 binary64))
(* 1/6 x)
(/.f64 x #s(literal 6 binary64))
(* 1/6 x)
(/.f64 x #s(literal 6 binary64))
(* 1/6 x)
(/.f64 x #s(literal 6 binary64))
(* 1/6 x)
(/.f64 x #s(literal 6 binary64))
x
(* x (+ 1 (* 1/2 x)))
(*.f64 x (+.f64 #s(literal 1 binary64) (*.f64 #s(literal 1/2 binary64) x)))
(* x (+ 1 (* x (+ 1/2 (* 1/6 x)))))
(*.f64 x (+.f64 #s(literal 1 binary64) (*.f64 x (+.f64 #s(literal 1/2 binary64) (/.f64 x #s(literal 6 binary64))))))
(* x (+ 1 (* x (+ 1/2 (* 1/6 x)))))
(*.f64 x (+.f64 #s(literal 1 binary64) (*.f64 x (+.f64 #s(literal 1/2 binary64) (/.f64 x #s(literal 6 binary64))))))
(* 1/6 (pow x 3))
(*.f64 x (*.f64 x (/.f64 x #s(literal 6 binary64))))
(* (pow x 3) (+ 1/6 (* 1/2 (/ 1 x))))
(*.f64 (*.f64 x x) (+.f64 #s(literal 1/2 binary64) (/.f64 x #s(literal 6 binary64))))
(* (pow x 3) (+ 1/6 (+ (* 1/2 (/ 1 x)) (/ 1 (pow x 2)))))
(*.f64 (*.f64 x x) (+.f64 #s(literal 1/2 binary64) (*.f64 x (+.f64 (/.f64 #s(literal 1 binary64) (*.f64 x x)) #s(literal 1/6 binary64)))))
(* (pow x 3) (+ 1/6 (+ (* 1/2 (/ 1 x)) (/ 1 (pow x 2)))))
(*.f64 (*.f64 x x) (+.f64 #s(literal 1/2 binary64) (*.f64 x (+.f64 (/.f64 #s(literal 1 binary64) (*.f64 x x)) #s(literal 1/6 binary64)))))
(* 1/6 (pow x 3))
(*.f64 x (*.f64 x (/.f64 x #s(literal 6 binary64))))
(* (pow x 3) (+ 1/6 (* 1/2 (/ 1 x))))
(*.f64 (*.f64 x x) (+.f64 #s(literal 1/2 binary64) (/.f64 x #s(literal 6 binary64))))
(* -1 (* (pow x 3) (- (* -1 (/ (+ 1/2 (/ 1 x)) x)) 1/6)))
(-.f64 #s(literal 0 binary64) (*.f64 (*.f64 x (*.f64 x x)) (+.f64 #s(literal -1/6 binary64) (/.f64 (+.f64 #s(literal -1/2 binary64) (/.f64 #s(literal -1 binary64) x)) x))))
(* -1 (* (pow x 3) (- (* -1 (/ (+ 1/2 (/ 1 x)) x)) 1/6)))
(-.f64 #s(literal 0 binary64) (*.f64 (*.f64 x (*.f64 x x)) (+.f64 #s(literal -1/6 binary64) (/.f64 (+.f64 #s(literal -1/2 binary64) (/.f64 #s(literal -1 binary64) x)) x))))

eval140.0ms (1.9%)

Compiler

Compiled 23183 to 3056 computations (86.8% saved)

prune93.0ms (1.3%)

Pruning

14 alts after pruning (7 fresh and 7 done)

PrunedKeptTotal
New8516857
Fresh011
Picked235
Done145
Total85414868
Accuracy
100.0%
Counts
868 → 14
Alt Table
Click to see full alt table
StatusAccuracyProgram
0.2%
(/.f64 #s(literal 1 binary64) (sqrt.f64 (/.f64 (+.f64 #s(literal 6 binary64) (/.f64 #s(literal -18 binary64) x)) (*.f64 x (*.f64 x x)))))
63.0%
(/.f64 #s(literal 1 binary64) (sqrt.f64 (+.f64 #s(literal 1/2 binary64) (*.f64 x (+.f64 #s(literal -1/4 binary64) (*.f64 (*.f64 x x) #s(literal 1/48 binary64)))))))
65.3%
(/.f64 #s(literal 1 binary64) (sqrt.f64 (+.f64 #s(literal 1/2 binary64) (*.f64 x #s(literal -1/4 binary64)))))
69.3%
(/.f64 #s(literal 1 binary64) (sqrt.f64 #s(literal 1/2 binary64)))
2.6%
(*.f64 (pow.f64 (+.f64 #s(literal 1/2 binary64) (*.f64 x #s(literal 1/6 binary64))) #s(literal 1/2 binary64)) x)
1.6%
(*.f64 (sqrt.f64 (*.f64 x #s(literal 1/6 binary64))) x)
2.9%
(*.f64 x (sqrt.f64 #s(literal 1/2 binary64)))
65.6%
(sqrt.f64 (+.f64 #s(literal 2 binary64) (*.f64 x (+.f64 #s(literal 1 binary64) (*.f64 #s(literal 1/2 binary64) x)))))
63.5%
(sqrt.f64 (+.f64 #s(literal 2 binary64) x))
100.0%
(sqrt.f64 (+.f64 #s(literal 1 binary64) (exp.f64 x)))
2.3%
(sqrt.f64 (*.f64 x (+.f64 #s(literal 1 binary64) (*.f64 x (+.f64 #s(literal 1/2 binary64) (*.f64 x #s(literal 1/6 binary64)))))))
3.3%
(sqrt.f64 (*.f64 x (*.f64 x (+.f64 #s(literal 1/2 binary64) (*.f64 x #s(literal 1/6 binary64))))))
2.3%
(sqrt.f64 x)
70.2%
(sqrt.f64 #s(literal 2 binary64))
Compiler

Compiled 192 to 151 computations (21.4% saved)

simplify16.0ms (0.2%)

Algorithm
egg-herbie
Localize:

Found 17 expressions of interest:

NewMetricScoreProgram
cost-diff0
(*.f64 x (+.f64 #s(literal 1/2 binary64) (*.f64 x #s(literal 1/6 binary64))))
cost-diff0
(+.f64 #s(literal 1 binary64) (*.f64 x (+.f64 #s(literal 1/2 binary64) (*.f64 x #s(literal 1/6 binary64)))))
cost-diff0
(*.f64 x (+.f64 #s(literal 1 binary64) (*.f64 x (+.f64 #s(literal 1/2 binary64) (*.f64 x #s(literal 1/6 binary64))))))
cost-diff0
(sqrt.f64 (*.f64 x (+.f64 #s(literal 1 binary64) (*.f64 x (+.f64 #s(literal 1/2 binary64) (*.f64 x #s(literal 1/6 binary64)))))))
cost-diff0
(*.f64 x #s(literal 1/6 binary64))
cost-diff0
(+.f64 #s(literal 1/2 binary64) (*.f64 x #s(literal 1/6 binary64)))
cost-diff0
(pow.f64 (+.f64 #s(literal 1/2 binary64) (*.f64 x #s(literal 1/6 binary64))) #s(literal 1/2 binary64))
cost-diff0
(*.f64 (pow.f64 (+.f64 #s(literal 1/2 binary64) (*.f64 x #s(literal 1/6 binary64))) #s(literal 1/2 binary64)) x)
cost-diff0
(*.f64 x #s(literal -1/4 binary64))
cost-diff0
(+.f64 #s(literal 1/2 binary64) (*.f64 x #s(literal -1/4 binary64)))
cost-diff0
(sqrt.f64 (+.f64 #s(literal 1/2 binary64) (*.f64 x #s(literal -1/4 binary64))))
cost-diff0
(/.f64 #s(literal 1 binary64) (sqrt.f64 (+.f64 #s(literal 1/2 binary64) (*.f64 x #s(literal -1/4 binary64)))))
cost-diff0
(*.f64 x #s(literal 1/6 binary64))
cost-diff0
(sqrt.f64 (*.f64 x #s(literal 1/6 binary64)))
cost-diff0
(*.f64 (sqrt.f64 (*.f64 x #s(literal 1/6 binary64))) x)
cost-diff0
(sqrt.f64 #s(literal 1/2 binary64))
cost-diff0
(/.f64 #s(literal 1 binary64) (sqrt.f64 #s(literal 1/2 binary64)))
Rules
268×fma-define
216×fma-lowering-fma.f32
216×fma-lowering-fma.f64
166×*-lowering-*.f32
166×*-lowering-*.f64
Iterations

Useful iterations: 1 (0.0ms)

IterNodesCost
021121
149107
2101107
3213107
4337107
5379107
0379107
Stop Event
iter limit
saturated
Calls
Call 1
Inputs
(/ 1 (sqrt 1/2))
1
(sqrt 1/2)
1/2
(* (sqrt (* x 1/6)) x)
(sqrt (* x 1/6))
(* x 1/6)
x
1/6
(/ 1 (sqrt (+ 1/2 (* x -1/4))))
1
(sqrt (+ 1/2 (* x -1/4)))
(+ 1/2 (* x -1/4))
1/2
(* x -1/4)
x
-1/4
(* (pow (+ 1/2 (* x 1/6)) 1/2) x)
(pow (+ 1/2 (* x 1/6)) 1/2)
(+ 1/2 (* x 1/6))
1/2
(* x 1/6)
x
1/6
(sqrt (* x (+ 1 (* x (+ 1/2 (* x 1/6))))))
(* x (+ 1 (* x (+ 1/2 (* x 1/6)))))
x
(+ 1 (* x (+ 1/2 (* x 1/6))))
1
(* x (+ 1/2 (* x 1/6)))
(+ 1/2 (* x 1/6))
1/2
(* x 1/6)
1/6
Outputs
(/ 1 (sqrt 1/2))
(/.f64 #s(literal 1 binary64) (sqrt.f64 #s(literal 1/2 binary64)))
1
#s(literal 1 binary64)
(sqrt 1/2)
(sqrt.f64 #s(literal 1/2 binary64))
1/2
#s(literal 1/2 binary64)
(* (sqrt (* x 1/6)) x)
(*.f64 x (sqrt.f64 (*.f64 x #s(literal 1/6 binary64))))
(sqrt (* x 1/6))
(sqrt.f64 (*.f64 x #s(literal 1/6 binary64)))
(* x 1/6)
(*.f64 x #s(literal 1/6 binary64))
x
1/6
#s(literal 1/6 binary64)
(/ 1 (sqrt (+ 1/2 (* x -1/4))))
(/.f64 #s(literal 1 binary64) (sqrt.f64 (+.f64 #s(literal 1/2 binary64) (*.f64 x #s(literal -1/4 binary64)))))
1
#s(literal 1 binary64)
(sqrt (+ 1/2 (* x -1/4)))
(sqrt.f64 (+.f64 #s(literal 1/2 binary64) (*.f64 x #s(literal -1/4 binary64))))
(+ 1/2 (* x -1/4))
(+.f64 #s(literal 1/2 binary64) (*.f64 x #s(literal -1/4 binary64)))
1/2
#s(literal 1/2 binary64)
(* x -1/4)
(*.f64 x #s(literal -1/4 binary64))
x
-1/4
#s(literal -1/4 binary64)
(* (pow (+ 1/2 (* x 1/6)) 1/2) x)
(*.f64 x (pow.f64 (+.f64 #s(literal 1/2 binary64) (*.f64 x #s(literal 1/6 binary64))) #s(literal 1/2 binary64)))
(pow (+ 1/2 (* x 1/6)) 1/2)
(pow.f64 (+.f64 #s(literal 1/2 binary64) (*.f64 x #s(literal 1/6 binary64))) #s(literal 1/2 binary64))
(+ 1/2 (* x 1/6))
(+.f64 #s(literal 1/2 binary64) (*.f64 x #s(literal 1/6 binary64)))
1/2
#s(literal 1/2 binary64)
(* x 1/6)
(*.f64 x #s(literal 1/6 binary64))
x
1/6
#s(literal 1/6 binary64)
(sqrt (* x (+ 1 (* x (+ 1/2 (* x 1/6))))))
(sqrt.f64 (*.f64 x (+.f64 #s(literal 1 binary64) (*.f64 x (+.f64 #s(literal 1/2 binary64) (*.f64 x #s(literal 1/6 binary64)))))))
(* x (+ 1 (* x (+ 1/2 (* x 1/6)))))
(*.f64 x (+.f64 #s(literal 1 binary64) (*.f64 x (+.f64 #s(literal 1/2 binary64) (*.f64 x #s(literal 1/6 binary64))))))
x
(+ 1 (* x (+ 1/2 (* x 1/6))))
(+.f64 #s(literal 1 binary64) (*.f64 x (+.f64 #s(literal 1/2 binary64) (*.f64 x #s(literal 1/6 binary64)))))
1
#s(literal 1 binary64)
(* x (+ 1/2 (* x 1/6)))
(*.f64 x (+.f64 #s(literal 1/2 binary64) (*.f64 x #s(literal 1/6 binary64))))
(+ 1/2 (* x 1/6))
(+.f64 #s(literal 1/2 binary64) (*.f64 x #s(literal 1/6 binary64)))
1/2
#s(literal 1/2 binary64)
(* x 1/6)
(*.f64 x #s(literal 1/6 binary64))
1/6
#s(literal 1/6 binary64)

localize126.0ms (1.7%)

Localize:

Found 17 expressions of interest:

NewMetricScoreProgram
accuracy100.0%
(sqrt.f64 (*.f64 x (+.f64 #s(literal 1 binary64) (*.f64 x (+.f64 #s(literal 1/2 binary64) (*.f64 x #s(literal 1/6 binary64)))))))
accuracy100.0%
(*.f64 x (+.f64 #s(literal 1/2 binary64) (*.f64 x #s(literal 1/6 binary64))))
accuracy100.0%
(*.f64 x (+.f64 #s(literal 1 binary64) (*.f64 x (+.f64 #s(literal 1/2 binary64) (*.f64 x #s(literal 1/6 binary64))))))
accuracy99.9%
(*.f64 x #s(literal 1/6 binary64))
accuracy100.0%
(+.f64 #s(literal 1/2 binary64) (*.f64 x #s(literal 1/6 binary64)))
accuracy100.0%
(pow.f64 (+.f64 #s(literal 1/2 binary64) (*.f64 x #s(literal 1/6 binary64))) #s(literal 1/2 binary64))
accuracy99.9%
(*.f64 x #s(literal 1/6 binary64))
accuracy99.8%
(*.f64 (pow.f64 (+.f64 #s(literal 1/2 binary64) (*.f64 x #s(literal 1/6 binary64))) #s(literal 1/2 binary64)) x)
accuracy100.0%
(+.f64 #s(literal 1/2 binary64) (*.f64 x #s(literal -1/4 binary64)))
accuracy100.0%
(*.f64 x #s(literal -1/4 binary64))
accuracy100.0%
(sqrt.f64 (+.f64 #s(literal 1/2 binary64) (*.f64 x #s(literal -1/4 binary64))))
accuracy99.5%
(/.f64 #s(literal 1 binary64) (sqrt.f64 (+.f64 #s(literal 1/2 binary64) (*.f64 x #s(literal -1/4 binary64)))))
accuracy100.0%
(sqrt.f64 (*.f64 x #s(literal 1/6 binary64)))
accuracy99.9%
(*.f64 (sqrt.f64 (*.f64 x #s(literal 1/6 binary64))) x)
accuracy99.9%
(*.f64 x #s(literal 1/6 binary64))
accuracy100.0%
(sqrt.f64 #s(literal 1/2 binary64))
accuracy99.5%
(/.f64 #s(literal 1 binary64) (sqrt.f64 #s(literal 1/2 binary64)))
Results
71.0ms176×0invalid
23.0ms80×0valid
Compiler

Compiled 129 to 22 computations (82.9% saved)

Precisions
Click to see histograms. Total time spent on operations: 60.0ms
ival-mult: 34.0ms (56.7% of total)
ival-sqrt: 8.0ms (13.3% of total)
ival-add: 5.0ms (8.3% of total)
ival-div: 4.0ms (6.7% of total)
...c/correct-round.rkt:119:19: 4.0ms (6.7% of total)
ival-pow: 4.0ms (6.7% of total)
const: 1.0ms (1.7% of total)
backward-pass: 0.0ms (0% of total)

series13.0ms (0.2%)

Counts
16 → 168
Calls
Call 1
Inputs
#<alt (/ 1 (sqrt 1/2))>
#<alt (sqrt 1/2)>
#<alt (* (sqrt (* x 1/6)) x)>
#<alt (sqrt (* x 1/6))>
#<alt (* x 1/6)>
#<alt (/ 1 (sqrt (+ 1/2 (* x -1/4))))>
#<alt (sqrt (+ 1/2 (* x -1/4)))>
#<alt (+ 1/2 (* x -1/4))>
#<alt (* x -1/4)>
#<alt (* (pow (+ 1/2 (* x 1/6)) 1/2) x)>
#<alt (pow (+ 1/2 (* x 1/6)) 1/2)>
#<alt (+ 1/2 (* x 1/6))>
#<alt (sqrt (* x (+ 1 (* x (+ 1/2 (* x 1/6))))))>
#<alt (* x (+ 1 (* x (+ 1/2 (* x 1/6)))))>
#<alt (+ 1 (* x (+ 1/2 (* x 1/6))))>
#<alt (* x (+ 1/2 (* x 1/6)))>
Outputs
#<alt (* (sqrt (pow x 3)) (sqrt 1/6))>
#<alt (* (sqrt (pow x 3)) (sqrt 1/6))>
#<alt (* (sqrt (pow x 3)) (sqrt 1/6))>
#<alt (* (sqrt (pow x 3)) (sqrt 1/6))>
#<alt (* (sqrt (pow x 3)) (sqrt 1/6))>
#<alt (* (sqrt (pow x 3)) (sqrt 1/6))>
#<alt (* (sqrt (pow x 3)) (sqrt 1/6))>
#<alt (* (sqrt (pow x 3)) (sqrt 1/6))>
#<alt (* -1 (* (sqrt (pow x 3)) (* (sqrt -1) (sqrt -1/6))))>
#<alt (* -1 (* (sqrt (pow x 3)) (* (sqrt -1) (sqrt -1/6))))>
#<alt (* -1 (* (sqrt (pow x 3)) (* (sqrt -1) (sqrt -1/6))))>
#<alt (* -1 (* (sqrt (pow x 3)) (* (sqrt -1) (sqrt -1/6))))>
#<alt (* (sqrt x) (sqrt 1/6))>
#<alt (* (sqrt x) (sqrt 1/6))>
#<alt (* (sqrt x) (sqrt 1/6))>
#<alt (* (sqrt x) (sqrt 1/6))>
#<alt (* (sqrt x) (sqrt 1/6))>
#<alt (* (sqrt x) (sqrt 1/6))>
#<alt (* (sqrt x) (sqrt 1/6))>
#<alt (* (sqrt x) (sqrt 1/6))>
#<alt (* -1 (* (sqrt x) (* (sqrt -1) (sqrt -1/6))))>
#<alt (* -1 (* (sqrt x) (* (sqrt -1) (sqrt -1/6))))>
#<alt (* -1 (* (sqrt x) (* (sqrt -1) (sqrt -1/6))))>
#<alt (* -1 (* (sqrt x) (* (sqrt -1) (sqrt -1/6))))>
#<alt (* 1/6 x)>
#<alt (* 1/6 x)>
#<alt (* 1/6 x)>
#<alt (* 1/6 x)>
#<alt (* 1/6 x)>
#<alt (* 1/6 x)>
#<alt (* 1/6 x)>
#<alt (* 1/6 x)>
#<alt (* 1/6 x)>
#<alt (* 1/6 x)>
#<alt (* 1/6 x)>
#<alt (* 1/6 x)>
#<alt (sqrt 2)>
#<alt (+ (sqrt 2) (* 1/2 (/ x (sqrt 2))))>
#<alt (+ (sqrt 2) (* x (+ (* 1/2 (/ (* x (- 1/2 (* 1/4 (/ 1 (pow (sqrt 2) 2))))) (sqrt 2))) (* 1/2 (/ 1 (sqrt 2))))))>
#<alt (+ (sqrt 2) (* x (+ (* x (+ (* 1/2 (/ (* x (- 1/4 (* 1/2 (/ (- 1/2 (* 1/4 (/ 1 (pow (sqrt 2) 2)))) (pow (sqrt 2) 2))))) (sqrt 2))) (* 1/2 (/ (- 1/2 (* 1/4 (/ 1 (pow (sqrt 2) 2)))) (sqrt 2))))) (* 1/2 (/ 1 (sqrt 2))))))>
#<alt (* (sqrt (/ 1 x)) (sqrt -4))>
#<alt (+ (* -4 (* (sqrt (/ 1 (pow x 3))) (/ 1 (sqrt -4)))) (* (sqrt (/ 1 x)) (sqrt -4)))>
#<alt (+ (* -8 (* (sqrt (/ 1 (pow x 5))) (/ 1 (sqrt -4)))) (+ (* -4 (* (sqrt (/ 1 (pow x 3))) (/ 1 (sqrt -4)))) (* (sqrt (/ 1 x)) (sqrt -4))))>
#<alt (+ (* -8 (* (sqrt (/ 1 (pow x 5))) (/ 1 (sqrt -4)))) (+ (* -4 (* (sqrt (/ 1 (pow x 3))) (/ 1 (sqrt -4)))) (+ (* -1/2 (* (sqrt (/ 1 (pow x 7))) (/ (+ 32 (* 16 (/ x (pow (sqrt -4) 2)))) (sqrt -4)))) (* (sqrt (/ 1 x)) (sqrt -4)))))>
#<alt (* 2 (* (sqrt (/ 1 x)) (sqrt -1)))>
#<alt (+ (* -2 (* (sqrt (/ 1 (pow x 3))) (sqrt -1))) (* 2 (* (sqrt (/ 1 x)) (sqrt -1))))>
#<alt (+ (* -4 (* (sqrt (/ 1 (pow x 5))) (sqrt -1))) (+ (* -2 (* (sqrt (/ 1 (pow x 3))) (sqrt -1))) (* 2 (* (sqrt (/ 1 x)) (sqrt -1)))))>
#<alt (+ (* -2 (* (sqrt (/ 1 (pow x 3))) (sqrt -1))) (+ (* -1 (/ (+ (* 1/4 (* (sqrt (/ 1 x)) (* (sqrt -1) (+ 32 (* -4 x))))) (* 4 (* (sqrt x) (sqrt -1)))) (pow x 3))) (* 2 (* (sqrt (/ 1 x)) (sqrt -1)))))>
#<alt (sqrt 1/2)>
#<alt (+ (sqrt 1/2) (* -1/8 (/ x (sqrt 1/2))))>
#<alt (+ (sqrt 1/2) (* x (- (* -1/128 (/ x (pow (sqrt 1/2) 3))) (* 1/8 (/ 1 (sqrt 1/2))))))>
#<alt (+ (sqrt 1/2) (* x (- (* x (- (* -1/1024 (/ x (pow (sqrt 1/2) 5))) (* 1/128 (/ 1 (pow (sqrt 1/2) 3))))) (* 1/8 (/ 1 (sqrt 1/2))))))>
#<alt (* (sqrt x) (sqrt -1/4))>
#<alt (* x (+ (* 1/4 (* (sqrt (/ 1 (pow x 3))) (/ 1 (sqrt -1/4)))) (* (sqrt (/ 1 x)) (sqrt -1/4))))>
#<alt (* x (+ (* -1/32 (* (sqrt (/ 1 (pow x 5))) (/ 1 (pow (sqrt -1/4) 3)))) (+ (* 1/4 (* (sqrt (/ 1 (pow x 3))) (/ 1 (sqrt -1/4)))) (* (sqrt (/ 1 x)) (sqrt -1/4)))))>
#<alt (* x (+ (* -1/32 (* (sqrt (/ 1 (pow x 5))) (/ 1 (pow (sqrt -1/4) 3)))) (+ (* 1/128 (* (sqrt (/ 1 (pow x 7))) (/ 1 (pow (sqrt -1/4) 5)))) (+ (* 1/4 (* (sqrt (/ 1 (pow x 3))) (/ 1 (sqrt -1/4)))) (* (sqrt (/ 1 x)) (sqrt -1/4))))))>
#<alt (* -1/2 (* (sqrt x) (sqrt -1)))>
#<alt (* -1 (* x (+ (* 1/2 (* (sqrt (/ 1 x)) (sqrt -1))) (* 1/2 (* (sqrt (/ 1 (pow x 3))) (sqrt -1))))))>
#<alt (* -1 (* x (+ (* -1/4 (* (sqrt (/ 1 (pow x 5))) (sqrt -1))) (+ (* 1/2 (* (sqrt (/ 1 x)) (sqrt -1))) (* 1/2 (* (sqrt (/ 1 (pow x 3))) (sqrt -1)))))))>
#<alt (* -1 (* x (+ (* -1/4 (* (sqrt (/ 1 (pow x 5))) (sqrt -1))) (+ (* 1/4 (* (sqrt (/ 1 (pow x 7))) (sqrt -1))) (+ (* 1/2 (* (sqrt (/ 1 x)) (sqrt -1))) (* 1/2 (* (sqrt (/ 1 (pow x 3))) (sqrt -1))))))))>
#<alt 1/2>
#<alt (+ 1/2 (* -1/4 x))>
#<alt (+ 1/2 (* -1/4 x))>
#<alt (+ 1/2 (* -1/4 x))>
#<alt (* -1/4 x)>
#<alt (* x (- (* 1/2 (/ 1 x)) 1/4))>
#<alt (* x (- (* 1/2 (/ 1 x)) 1/4))>
#<alt (* x (- (* 1/2 (/ 1 x)) 1/4))>
#<alt (* -1/4 x)>
#<alt (* -1 (* x (- 1/4 (* 1/2 (/ 1 x)))))>
#<alt (* -1 (* x (- 1/4 (* 1/2 (/ 1 x)))))>
#<alt (* -1 (* x (- 1/4 (* 1/2 (/ 1 x)))))>
#<alt (* -1/4 x)>
#<alt (* -1/4 x)>
#<alt (* -1/4 x)>
#<alt (* -1/4 x)>
#<alt (* -1/4 x)>
#<alt (* -1/4 x)>
#<alt (* -1/4 x)>
#<alt (* -1/4 x)>
#<alt (* -1/4 x)>
#<alt (* -1/4 x)>
#<alt (* -1/4 x)>
#<alt (* -1/4 x)>
#<alt (* x (sqrt 1/2))>
#<alt (* x (+ (sqrt 1/2) (* 1/12 (/ x (sqrt 1/2)))))>
#<alt (* x (+ (sqrt 1/2) (* x (+ (* -1/288 (/ x (pow (sqrt 1/2) 3))) (* 1/12 (/ 1 (sqrt 1/2)))))))>
#<alt (* x (+ (sqrt 1/2) (* x (+ (* x (- (* 1/3456 (/ x (pow (sqrt 1/2) 5))) (* 1/288 (/ 1 (pow (sqrt 1/2) 3))))) (* 1/12 (/ 1 (sqrt 1/2)))))))>
#<alt (* (sqrt (pow x 3)) (sqrt 1/6))>
#<alt (* (pow x 2) (+ (* 1/4 (* (sqrt (/ 1 (pow x 3))) (/ 1 (sqrt 1/6)))) (* (sqrt (/ 1 x)) (sqrt 1/6))))>
#<alt (* (pow x 2) (+ (* -1/32 (* (sqrt (/ 1 (pow x 5))) (/ 1 (pow (sqrt 1/6) 3)))) (+ (* 1/4 (* (sqrt (/ 1 (pow x 3))) (/ 1 (sqrt 1/6)))) (* (sqrt (/ 1 x)) (sqrt 1/6)))))>
#<alt (* (pow x 2) (+ (* -1/32 (* (sqrt (/ 1 (pow x 5))) (/ 1 (pow (sqrt 1/6) 3)))) (+ (* 1/128 (* (sqrt (/ 1 (pow x 7))) (/ 1 (pow (sqrt 1/6) 5)))) (+ (* 1/4 (* (sqrt (/ 1 (pow x 3))) (/ 1 (sqrt 1/6)))) (* (sqrt (/ 1 x)) (sqrt 1/6))))))>
#<alt (* -1 (* (sqrt (pow x 3)) (* (sqrt -1) (sqrt -1/6))))>
#<alt (* (pow x 2) (+ (* -1 (* (sqrt (/ 1 x)) (* (sqrt -1) (sqrt -1/6)))) (* -1/4 (* (sqrt (/ 1 (pow x 3))) (/ (sqrt -1) (sqrt -1/6))))))>
#<alt (* (pow x 2) (+ (* -1 (* (sqrt (/ 1 x)) (* (sqrt -1) (sqrt -1/6)))) (+ (* -1/4 (* (sqrt (/ 1 (pow x 3))) (/ (sqrt -1) (sqrt -1/6)))) (* 1/32 (* (sqrt (/ 1 (pow x 5))) (/ (sqrt -1) (pow (sqrt -1/6) 3)))))))>
#<alt (* (pow x 2) (+ (* -1 (* (sqrt (/ 1 x)) (* (sqrt -1) (sqrt -1/6)))) (+ (* -1/4 (* (sqrt (/ 1 (pow x 3))) (/ (sqrt -1) (sqrt -1/6)))) (+ (* -1/128 (* (sqrt (/ 1 (pow x 7))) (/ (sqrt -1) (pow (sqrt -1/6) 5)))) (* 1/32 (* (sqrt (/ 1 (pow x 5))) (/ (sqrt -1) (pow (sqrt -1/6) 3))))))))>
#<alt (sqrt 1/2)>
#<alt (+ (sqrt 1/2) (* 1/12 (/ x (sqrt 1/2))))>
#<alt (+ (sqrt 1/2) (* x (+ (* -1/288 (/ x (pow (sqrt 1/2) 3))) (* 1/12 (/ 1 (sqrt 1/2))))))>
#<alt (+ (sqrt 1/2) (* x (+ (* x (- (* 1/3456 (/ x (pow (sqrt 1/2) 5))) (* 1/288 (/ 1 (pow (sqrt 1/2) 3))))) (* 1/12 (/ 1 (sqrt 1/2))))))>
#<alt (* (sqrt x) (sqrt 1/6))>
#<alt (* x (+ (* 1/4 (* (sqrt (/ 1 (pow x 3))) (/ 1 (sqrt 1/6)))) (* (sqrt (/ 1 x)) (sqrt 1/6))))>
#<alt (* x (+ (* -1/32 (* (sqrt (/ 1 (pow x 5))) (/ 1 (pow (sqrt 1/6) 3)))) (+ (* 1/4 (* (sqrt (/ 1 (pow x 3))) (/ 1 (sqrt 1/6)))) (* (sqrt (/ 1 x)) (sqrt 1/6)))))>
#<alt (* x (+ (* -1/32 (* (sqrt (/ 1 (pow x 5))) (/ 1 (pow (sqrt 1/6) 3)))) (+ (* 1/128 (* (sqrt (/ 1 (pow x 7))) (/ 1 (pow (sqrt 1/6) 5)))) (+ (* 1/4 (* (sqrt (/ 1 (pow x 3))) (/ 1 (sqrt 1/6)))) (* (sqrt (/ 1 x)) (sqrt 1/6))))))>
#<alt (* -1 (* (sqrt x) (* (sqrt -1) (sqrt -1/6))))>
#<alt (* -1 (* x (+ (* 1/4 (* (sqrt (/ 1 (pow x 3))) (/ (sqrt -1) (sqrt -1/6)))) (* (sqrt (/ 1 x)) (* (sqrt -1) (sqrt -1/6))))))>
#<alt (* -1 (* x (+ (* -1/32 (* (sqrt (/ 1 (pow x 5))) (/ (sqrt -1) (pow (sqrt -1/6) 3)))) (+ (* 1/4 (* (sqrt (/ 1 (pow x 3))) (/ (sqrt -1) (sqrt -1/6)))) (* (sqrt (/ 1 x)) (* (sqrt -1) (sqrt -1/6)))))))>
#<alt (* -1 (* x (+ (* -1/32 (* (sqrt (/ 1 (pow x 5))) (/ (sqrt -1) (pow (sqrt -1/6) 3)))) (+ (* 1/128 (* (sqrt (/ 1 (pow x 7))) (/ (sqrt -1) (pow (sqrt -1/6) 5)))) (+ (* 1/4 (* (sqrt (/ 1 (pow x 3))) (/ (sqrt -1) (sqrt -1/6)))) (* (sqrt (/ 1 x)) (* (sqrt -1) (sqrt -1/6))))))))>
#<alt 1/2>
#<alt (+ 1/2 (* 1/6 x))>
#<alt (+ 1/2 (* 1/6 x))>
#<alt (+ 1/2 (* 1/6 x))>
#<alt (* 1/6 x)>
#<alt (* x (+ 1/6 (* 1/2 (/ 1 x))))>
#<alt (* x (+ 1/6 (* 1/2 (/ 1 x))))>
#<alt (* x (+ 1/6 (* 1/2 (/ 1 x))))>
#<alt (* 1/6 x)>
#<alt (* x (+ 1/6 (* 1/2 (/ 1 x))))>
#<alt (* x (+ 1/6 (* 1/2 (/ 1 x))))>
#<alt (* x (+ 1/6 (* 1/2 (/ 1 x))))>
#<alt (sqrt x)>
#<alt (+ (sqrt x) (* 1/4 (sqrt (pow x 3))))>
#<alt (+ (sqrt x) (* (pow x 2) (+ (* 1/12 (sqrt x)) (* 1/4 (sqrt (/ 1 x))))))>
#<alt (+ (sqrt x) (* (pow x 2) (+ (* 1/4 (sqrt (/ 1 x))) (* x (+ (* -1/32 (sqrt (/ 1 x))) (* 1/12 (sqrt (/ 1 x))))))))>
#<alt (* (sqrt (pow x 3)) (sqrt 1/6))>
#<alt (* (pow x 2) (+ (* 1/4 (* (sqrt (/ 1 (pow x 3))) (/ 1 (sqrt 1/6)))) (* (sqrt (/ 1 x)) (sqrt 1/6))))>
#<alt (* (pow x 2) (+ (* 1/4 (* (sqrt (/ 1 (pow x 3))) (/ 1 (sqrt 1/6)))) (+ (* 1/2 (* (sqrt (/ 1 (pow x 5))) (/ 1 (sqrt 1/6)))) (* (sqrt (/ 1 x)) (sqrt 1/6)))))>
#<alt (* (pow x 2) (+ (* -1/32 (* (sqrt (/ 1 (pow x 5))) (/ 1 (pow (sqrt 1/6) 3)))) (+ (* 1/4 (* (sqrt (/ 1 (pow x 3))) (/ 1 (sqrt 1/6)))) (+ (* 1/2 (* (sqrt (/ 1 (pow x 5))) (/ 1 (sqrt 1/6)))) (* (sqrt (/ 1 x)) (sqrt 1/6))))))>
#<alt (* (sqrt (pow x 3)) (* (pow (sqrt -1) 2) (sqrt 1/6)))>
#<alt (* (pow x 2) (+ (* -1/4 (* (sqrt (/ 1 (pow x 3))) (/ (pow (sqrt -1) 2) (sqrt 1/6)))) (* (sqrt (/ 1 x)) (* (pow (sqrt -1) 2) (sqrt 1/6)))))>
#<alt (* (pow x 2) (+ (* -1/2 (* (sqrt (/ 1 (pow x 5))) (/ (pow (sqrt -1) 2) (sqrt 1/6)))) (+ (* -1/4 (* (sqrt (/ 1 (pow x 3))) (/ (pow (sqrt -1) 2) (sqrt 1/6)))) (* (sqrt (/ 1 x)) (* (pow (sqrt -1) 2) (sqrt 1/6))))))>
#<alt (* (pow x 2) (+ (* -1 (/ (+ (* 1/32 (* (sqrt x) (/ (pow (sqrt -1) 2) (pow (sqrt 1/6) 3)))) (* 1/2 (* (sqrt x) (/ (pow (sqrt -1) 2) (sqrt 1/6))))) (pow x 3))) (+ (* -1/4 (* (sqrt (/ 1 (pow x 3))) (/ (pow (sqrt -1) 2) (sqrt 1/6)))) (* (sqrt (/ 1 x)) (* (pow (sqrt -1) 2) (sqrt 1/6))))))>
#<alt x>
#<alt (* x (+ 1 (* 1/2 x)))>
#<alt (* x (+ 1 (* x (+ 1/2 (* 1/6 x)))))>
#<alt (* x (+ 1 (* x (+ 1/2 (* 1/6 x)))))>
#<alt (* 1/6 (pow x 3))>
#<alt (* (pow x 3) (+ 1/6 (* 1/2 (/ 1 x))))>
#<alt (* (pow x 3) (+ 1/6 (+ (* 1/2 (/ 1 x)) (/ 1 (pow x 2)))))>
#<alt (* (pow x 3) (+ 1/6 (+ (* 1/2 (/ 1 x)) (/ 1 (pow x 2)))))>
#<alt (* 1/6 (pow x 3))>
#<alt (* (pow x 3) (+ 1/6 (* 1/2 (/ 1 x))))>
#<alt (* -1 (* (pow x 3) (- (* -1 (/ (+ 1/2 (/ 1 x)) x)) 1/6)))>
#<alt (* -1 (* (pow x 3) (- (* -1 (/ (+ 1/2 (/ 1 x)) x)) 1/6)))>
#<alt 1>
#<alt (+ 1 (* 1/2 x))>
#<alt (+ 1 (* x (+ 1/2 (* 1/6 x))))>
#<alt (+ 1 (* x (+ 1/2 (* 1/6 x))))>
#<alt (* 1/6 (pow x 2))>
#<alt (* (pow x 2) (+ 1/6 (* 1/2 (/ 1 x))))>
#<alt (* (pow x 2) (+ 1/6 (+ (* 1/2 (/ 1 x)) (/ 1 (pow x 2)))))>
#<alt (* (pow x 2) (+ 1/6 (+ (* 1/2 (/ 1 x)) (/ 1 (pow x 2)))))>
#<alt (* 1/6 (pow x 2))>
#<alt (* (pow x 2) (+ 1/6 (* 1/2 (/ 1 x))))>
#<alt (* (pow x 2) (+ 1/6 (+ (* 1/2 (/ 1 x)) (/ 1 (pow x 2)))))>
#<alt (* (pow x 2) (+ 1/6 (+ (* 1/2 (/ 1 x)) (/ 1 (pow x 2)))))>
#<alt (* 1/2 x)>
#<alt (* x (+ 1/2 (* 1/6 x)))>
#<alt (* x (+ 1/2 (* 1/6 x)))>
#<alt (* x (+ 1/2 (* 1/6 x)))>
#<alt (* 1/6 (pow x 2))>
#<alt (* (pow x 2) (+ 1/6 (* 1/2 (/ 1 x))))>
#<alt (* (pow x 2) (+ 1/6 (* 1/2 (/ 1 x))))>
#<alt (* (pow x 2) (+ 1/6 (* 1/2 (/ 1 x))))>
#<alt (* 1/6 (pow x 2))>
#<alt (* (pow x 2) (+ 1/6 (* 1/2 (/ 1 x))))>
#<alt (* (pow x 2) (+ 1/6 (* 1/2 (/ 1 x))))>
#<alt (* (pow x 2) (+ 1/6 (* 1/2 (/ 1 x))))>
Calls

42 calls:

TimeVariablePointExpression
3.0ms
x
@0
(sqrt (* x (+ 1 (* x (+ 1/2 (* x 1/6))))))
1.0ms
x
@-inf
(/ 1 (sqrt (+ 1/2 (* x -1/4))))
1.0ms
x
@inf
(/ 1 (sqrt (+ 1/2 (* x -1/4))))
1.0ms
x
@-inf
(sqrt (* x (+ 1 (* x (+ 1/2 (* x 1/6))))))
1.0ms
x
@inf
(sqrt (+ 1/2 (* x -1/4)))

rewrite310.0ms (4.3%)

Algorithm
batch-egg-rewrite
Rules
4088×*-lowering-*.f32
4088×*-lowering-*.f64
2514×/-lowering-/.f32
2514×/-lowering-/.f64
1686×sum3-define
Iterations

Useful iterations: 1 (0.0ms)

IterNodesCost
02195
111682
278582
3729482
0868382
Stop Event
iter limit
node limit
Counts
16 → 486
Calls
Call 1
Inputs
(/ 1 (sqrt 1/2))
(sqrt 1/2)
(* (sqrt (* x 1/6)) x)
(sqrt (* x 1/6))
(* x 1/6)
(/ 1 (sqrt (+ 1/2 (* x -1/4))))
(sqrt (+ 1/2 (* x -1/4)))
(+ 1/2 (* x -1/4))
(* x -1/4)
(* (pow (+ 1/2 (* x 1/6)) 1/2) x)
(pow (+ 1/2 (* x 1/6)) 1/2)
(+ 1/2 (* x 1/6))
(sqrt (* x (+ 1 (* x (+ 1/2 (* x 1/6))))))
(* x (+ 1 (* x (+ 1/2 (* x 1/6)))))
(+ 1 (* x (+ 1/2 (* x 1/6))))
(* x (+ 1/2 (* x 1/6)))
Outputs
(exp.f64 (*.f64 #s(literal -1 binary64) (*.f64 #s(literal 1/2 binary64) (log.f64 #s(literal 1/2 binary64)))))
(exp.f64 (*.f64 (log.f64 #s(literal 1/2 binary64)) #s(literal -1/2 binary64)))
(exp.f64 (neg.f64 (*.f64 #s(literal 1/2 binary64) (log.f64 #s(literal 1/2 binary64)))))
(-.f64 #s(literal 0 binary64) (/.f64 #s(literal -1 binary64) (sqrt.f64 #s(literal 1/2 binary64))))
(neg.f64 (/.f64 #s(literal -1 binary64) (sqrt.f64 #s(literal 1/2 binary64))))
(/.f64 #s(literal 1 binary64) (sqrt.f64 #s(literal 1/2 binary64)))
(/.f64 (pow.f64 #s(literal 1/2 binary64) #s(literal -1/2 binary64)) #s(literal 1 binary64))
(/.f64 #s(literal -1 binary64) (-.f64 #s(literal 0 binary64) (sqrt.f64 #s(literal 1/2 binary64))))
(/.f64 (/.f64 #s(literal 1 binary64) (pow.f64 #s(literal 1/2 binary64) #s(literal 1/4 binary64))) (pow.f64 #s(literal 1/2 binary64) #s(literal 1/4 binary64)))
(pow.f64 #s(literal 1/2 binary64) #s(literal -1/2 binary64))
(pow.f64 (sqrt.f64 #s(literal 1/2 binary64)) #s(literal -1 binary64))
(pow.f64 (pow.f64 #s(literal 1/2 binary64) #s(literal -1/4 binary64)) #s(literal 2 binary64))
(pow.f64 (*.f64 (sqrt.f64 #s(literal 1/2 binary64)) (sqrt.f64 #s(literal 1/2 binary64))) #s(literal -1/2 binary64))
(*.f64 #s(literal 1 binary64) (pow.f64 #s(literal 1/2 binary64) #s(literal -1/2 binary64)))
(*.f64 (pow.f64 #s(literal 1/2 binary64) #s(literal -1/2 binary64)) #s(literal 1 binary64))
(*.f64 #s(literal -1 binary64) (/.f64 #s(literal -1 binary64) (sqrt.f64 #s(literal 1/2 binary64))))
(*.f64 (pow.f64 #s(literal 1/2 binary64) #s(literal -1/4 binary64)) (pow.f64 #s(literal 1/2 binary64) #s(literal -1/4 binary64)))
(*.f64 (pow.f64 #s(literal 1/2 binary64) #s(literal -1/4 binary64)) (*.f64 (pow.f64 #s(literal 1/2 binary64) #s(literal -1/4 binary64)) #s(literal 1 binary64)))
(*.f64 (/.f64 #s(literal -1 binary64) (sqrt.f64 #s(literal 1/2 binary64))) #s(literal -1 binary64))
(*.f64 (pow.f64 (pow.f64 #s(literal 1/2 binary64) #s(literal 1/4 binary64)) #s(literal -1 binary64)) (pow.f64 (pow.f64 #s(literal 1/2 binary64) #s(literal 1/4 binary64)) #s(literal -1 binary64)))
(*.f64 (*.f64 #s(literal 1 binary64) (pow.f64 #s(literal 1/2 binary64) #s(literal -1/4 binary64))) (pow.f64 #s(literal 1/2 binary64) #s(literal -1/4 binary64)))
(exp.f64 (*.f64 #s(literal 1/2 binary64) (log.f64 #s(literal 1/2 binary64))))
(exp.f64 (neg.f64 (*.f64 #s(literal -1 binary64) (*.f64 #s(literal 1/2 binary64) (log.f64 #s(literal 1/2 binary64))))))
(-.f64 #s(literal 0 binary64) (-.f64 #s(literal 0 binary64) (sqrt.f64 #s(literal 1/2 binary64))))
(sqrt.f64 #s(literal 1/2 binary64))
(neg.f64 (-.f64 #s(literal 0 binary64) (sqrt.f64 #s(literal 1/2 binary64))))
(/.f64 #s(literal 1 binary64) (pow.f64 #s(literal 1/2 binary64) #s(literal -1/2 binary64)))
(/.f64 (sqrt.f64 #s(literal 1/2 binary64)) #s(literal 1 binary64))
(/.f64 #s(literal -1 binary64) (/.f64 #s(literal -1 binary64) (sqrt.f64 #s(literal 1/2 binary64))))
(/.f64 (-.f64 #s(literal 0 binary64) (sqrt.f64 #s(literal 1/2 binary64))) #s(literal -1 binary64))
(/.f64 (/.f64 #s(literal 1 binary64) (pow.f64 #s(literal 1/2 binary64) #s(literal -1/4 binary64))) (pow.f64 #s(literal 1/2 binary64) #s(literal -1/4 binary64)))
(pow.f64 #s(literal 1/2 binary64) #s(literal 1/2 binary64))
(pow.f64 (sqrt.f64 #s(literal 1/2 binary64)) #s(literal 1 binary64))
(pow.f64 (pow.f64 #s(literal 1/2 binary64) #s(literal -1/2 binary64)) #s(literal -1 binary64))
(pow.f64 #s(literal 1/4 binary64) #s(literal 1/4 binary64))
(pow.f64 (pow.f64 #s(literal 1/2 binary64) #s(literal 1/4 binary64)) #s(literal 2 binary64))
(pow.f64 (exp.f64 (log.f64 #s(literal 1/2 binary64))) #s(literal 1/2 binary64))
(*.f64 #s(literal 1 binary64) (sqrt.f64 #s(literal 1/2 binary64)))
(*.f64 (sqrt.f64 #s(literal 1/2 binary64)) #s(literal 1 binary64))
(*.f64 #s(literal -1 binary64) (-.f64 #s(literal 0 binary64) (sqrt.f64 #s(literal 1/2 binary64))))
(*.f64 (-.f64 #s(literal 0 binary64) (sqrt.f64 #s(literal 1/2 binary64))) #s(literal -1 binary64))
(*.f64 (pow.f64 #s(literal 1/2 binary64) #s(literal 1/4 binary64)) (pow.f64 #s(literal 1/2 binary64) #s(literal 1/4 binary64)))
(*.f64 (pow.f64 #s(literal 1/2 binary64) #s(literal 1/4 binary64)) (*.f64 (pow.f64 #s(literal 1/2 binary64) #s(literal 1/4 binary64)) #s(literal 1 binary64)))
(*.f64 (pow.f64 #s(literal 1/2 binary64) #s(literal 1/4 binary64)) (/.f64 (pow.f64 #s(literal 1/2 binary64) #s(literal 1/4 binary64)) #s(literal 1 binary64)))
(*.f64 #s(literal 1 binary64) (*.f64 x (pow.f64 (*.f64 x #s(literal 1/6 binary64)) #s(literal 1/2 binary64))))
(*.f64 x (pow.f64 (*.f64 x #s(literal 1/6 binary64)) #s(literal 1/2 binary64)))
(*.f64 x (*.f64 #s(literal 1 binary64) (pow.f64 (*.f64 x #s(literal 1/6 binary64)) #s(literal 1/2 binary64))))
(*.f64 (pow.f64 (*.f64 x #s(literal 1/6 binary64)) #s(literal 1/2 binary64)) x)
(*.f64 (*.f64 x (pow.f64 (*.f64 x #s(literal 1/6 binary64)) #s(literal 1/2 binary64))) #s(literal 1 binary64))
(*.f64 (sqrt.f64 x) (*.f64 x (sqrt.f64 #s(literal 1/6 binary64))))
(*.f64 (sqrt.f64 #s(literal 1/6 binary64)) (*.f64 x (sqrt.f64 x)))
(*.f64 (pow.f64 (*.f64 x #s(literal 1/6 binary64)) #s(literal 1/4 binary64)) (*.f64 (pow.f64 (*.f64 x #s(literal 1/6 binary64)) #s(literal 1/4 binary64)) x))
(*.f64 (*.f64 x (sqrt.f64 x)) (sqrt.f64 #s(literal 1/6 binary64)))
(*.f64 (*.f64 x (sqrt.f64 #s(literal 1/6 binary64))) (sqrt.f64 x))
(*.f64 (*.f64 x (pow.f64 (*.f64 x #s(literal 1/6 binary64)) #s(literal 1/4 binary64))) (pow.f64 (*.f64 x #s(literal 1/6 binary64)) #s(literal 1/4 binary64)))
(*.f64 (*.f64 (pow.f64 (*.f64 x #s(literal 1/6 binary64)) #s(literal 1/2 binary64)) #s(literal 1 binary64)) x)
(exp.f64 (*.f64 #s(literal 1/2 binary64) (log.f64 (*.f64 x #s(literal 1/6 binary64)))))
(sqrt.f64 (*.f64 x #s(literal 1/6 binary64)))
(pow.f64 (*.f64 x #s(literal 1/6 binary64)) #s(literal 1/2 binary64))
(pow.f64 (*.f64 (*.f64 x x) #s(literal 1/36 binary64)) #s(literal 1/4 binary64))
(pow.f64 (pow.f64 (*.f64 x #s(literal 1/6 binary64)) #s(literal 1/4 binary64)) #s(literal 2 binary64))
(pow.f64 (exp.f64 (log.f64 (*.f64 x #s(literal 1/6 binary64)))) #s(literal 1/2 binary64))
(*.f64 (sqrt.f64 x) (sqrt.f64 #s(literal 1/6 binary64)))
(*.f64 (sqrt.f64 #s(literal 1/6 binary64)) (sqrt.f64 x))
(*.f64 (pow.f64 (*.f64 x #s(literal 1/6 binary64)) #s(literal 1/4 binary64)) (pow.f64 (*.f64 x #s(literal 1/6 binary64)) #s(literal 1/4 binary64)))
(*.f64 #s(literal 1 binary64) (*.f64 x #s(literal 1/6 binary64)))
(*.f64 x #s(literal 1/6 binary64))
(*.f64 #s(literal 1/6 binary64) x)
(*.f64 (*.f64 x #s(literal 1/6 binary64)) #s(literal 1 binary64))
(exp.f64 (*.f64 #s(literal -1 binary64) (*.f64 #s(literal 1/2 binary64) (log.f64 (+.f64 #s(literal 1/2 binary64) (*.f64 x #s(literal -1/4 binary64)))))))
(exp.f64 (*.f64 (log.f64 (+.f64 #s(literal 1/2 binary64) (*.f64 x #s(literal -1/4 binary64)))) #s(literal -1/2 binary64)))
(exp.f64 (neg.f64 (*.f64 #s(literal 1/2 binary64) (log.f64 (+.f64 #s(literal 1/2 binary64) (*.f64 x #s(literal -1/4 binary64)))))))
(-.f64 #s(literal 0 binary64) (neg.f64 (pow.f64 (+.f64 #s(literal 1/2 binary64) (*.f64 x #s(literal -1/4 binary64))) #s(literal -1/2 binary64))))
(neg.f64 (neg.f64 (pow.f64 (+.f64 #s(literal 1/2 binary64) (*.f64 x #s(literal -1/4 binary64))) #s(literal -1/2 binary64))))
(/.f64 #s(literal 1 binary64) (sqrt.f64 (+.f64 #s(literal 1/2 binary64) (*.f64 x #s(literal -1/4 binary64)))))
(/.f64 (pow.f64 (+.f64 #s(literal 1/2 binary64) (*.f64 x #s(literal -1/4 binary64))) #s(literal -1/2 binary64)) #s(literal 1 binary64))
(/.f64 #s(literal -1 binary64) (-.f64 #s(literal 0 binary64) (sqrt.f64 (+.f64 #s(literal 1/2 binary64) (*.f64 x #s(literal -1/4 binary64))))))
(/.f64 (/.f64 #s(literal 1 binary64) (pow.f64 (+.f64 #s(literal 1/2 binary64) (*.f64 x #s(literal -1/4 binary64))) #s(literal 1/4 binary64))) (pow.f64 (+.f64 #s(literal 1/2 binary64) (*.f64 x #s(literal -1/4 binary64))) #s(literal 1/4 binary64)))
(pow.f64 (+.f64 #s(literal 1/2 binary64) (*.f64 x #s(literal -1/4 binary64))) #s(literal -1/2 binary64))
(pow.f64 (sqrt.f64 (+.f64 #s(literal 1/2 binary64) (*.f64 x #s(literal -1/4 binary64)))) #s(literal -1 binary64))
(pow.f64 (pow.f64 (+.f64 #s(literal 1/2 binary64) (*.f64 x #s(literal -1/4 binary64))) #s(literal -1/4 binary64)) #s(literal 2 binary64))
(pow.f64 (*.f64 (sqrt.f64 (+.f64 #s(literal 1/2 binary64) (*.f64 x #s(literal -1/4 binary64)))) (sqrt.f64 (+.f64 #s(literal 1/2 binary64) (*.f64 x #s(literal -1/4 binary64))))) #s(literal -1/2 binary64))
(*.f64 #s(literal 1 binary64) (pow.f64 (+.f64 #s(literal 1/2 binary64) (*.f64 x #s(literal -1/4 binary64))) #s(literal -1/2 binary64)))
(*.f64 (pow.f64 (+.f64 #s(literal 1/2 binary64) (*.f64 x #s(literal -1/4 binary64))) #s(literal -1/2 binary64)) #s(literal 1 binary64))
(*.f64 #s(literal -1 binary64) (neg.f64 (pow.f64 (+.f64 #s(literal 1/2 binary64) (*.f64 x #s(literal -1/4 binary64))) #s(literal -1/2 binary64))))
(*.f64 (pow.f64 (+.f64 #s(literal 1/2 binary64) (*.f64 x #s(literal -1/4 binary64))) #s(literal -1/4 binary64)) (pow.f64 (+.f64 #s(literal 1/2 binary64) (*.f64 x #s(literal -1/4 binary64))) #s(literal -1/4 binary64)))
(*.f64 (pow.f64 (+.f64 #s(literal 1/2 binary64) (*.f64 x #s(literal -1/4 binary64))) #s(literal -1/4 binary64)) (*.f64 (pow.f64 (+.f64 #s(literal 1/2 binary64) (*.f64 x #s(literal -1/4 binary64))) #s(literal -1/4 binary64)) #s(literal 1 binary64)))
(*.f64 (neg.f64 (pow.f64 (+.f64 #s(literal 1/2 binary64) (*.f64 x #s(literal -1/4 binary64))) #s(literal -1/2 binary64))) #s(literal -1 binary64))
(*.f64 (pow.f64 (+.f64 #s(literal 1/8 binary64) (*.f64 (*.f64 x (*.f64 x x)) #s(literal -1/64 binary64))) #s(literal -1/2 binary64)) (pow.f64 (/.f64 #s(literal 1 binary64) (+.f64 #s(literal 1/4 binary64) (*.f64 x (-.f64 (*.f64 x #s(literal 1/16 binary64)) #s(literal -1/8 binary64))))) #s(literal -1/2 binary64)))
(*.f64 (pow.f64 (+.f64 #s(literal 1/4 binary64) (*.f64 (*.f64 x x) #s(literal -1/16 binary64))) #s(literal -1/2 binary64)) (pow.f64 (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 1/2 binary64) (*.f64 x #s(literal -1/4 binary64)))) #s(literal -1/2 binary64)))
(*.f64 (pow.f64 (pow.f64 (+.f64 #s(literal 1/2 binary64) (*.f64 x #s(literal -1/4 binary64))) #s(literal 1/4 binary64)) #s(literal -1 binary64)) (pow.f64 (pow.f64 (+.f64 #s(literal 1/2 binary64) (*.f64 x #s(literal -1/4 binary64))) #s(literal 1/4 binary64)) #s(literal -1 binary64)))
(*.f64 (*.f64 #s(literal 1 binary64) (pow.f64 (+.f64 #s(literal 1/2 binary64) (*.f64 x #s(literal -1/4 binary64))) #s(literal -1/4 binary64))) (pow.f64 (+.f64 #s(literal 1/2 binary64) (*.f64 x #s(literal -1/4 binary64))) #s(literal -1/4 binary64)))
(*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 (+.f64 #s(literal 1/8 binary64) (*.f64 (*.f64 x (*.f64 x x)) #s(literal -1/64 binary64))))) (sqrt.f64 (+.f64 #s(literal 1/4 binary64) (*.f64 x (-.f64 (*.f64 x #s(literal 1/16 binary64)) #s(literal -1/8 binary64))))))
(*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 (+.f64 #s(literal 1/4 binary64) (*.f64 (*.f64 x x) #s(literal -1/16 binary64))))) (pow.f64 (-.f64 #s(literal 1/2 binary64) (*.f64 x #s(literal -1/4 binary64))) #s(literal 1/2 binary64)))
(exp.f64 (*.f64 #s(literal 1/2 binary64) (log.f64 (+.f64 #s(literal 1/2 binary64) (*.f64 x #s(literal -1/4 binary64))))))
(exp.f64 (neg.f64 (*.f64 #s(literal -1 binary64) (*.f64 #s(literal 1/2 binary64) (log.f64 (+.f64 #s(literal 1/2 binary64) (*.f64 x #s(literal -1/4 binary64))))))))
(-.f64 #s(literal 0 binary64) (-.f64 #s(literal 0 binary64) (sqrt.f64 (+.f64 #s(literal 1/2 binary64) (*.f64 x #s(literal -1/4 binary64))))))
(sqrt.f64 (+.f64 #s(literal 1/2 binary64) (*.f64 x #s(literal -1/4 binary64))))
(neg.f64 (-.f64 #s(literal 0 binary64) (sqrt.f64 (+.f64 #s(literal 1/2 binary64) (*.f64 x #s(literal -1/4 binary64))))))
(/.f64 #s(literal 1 binary64) (pow.f64 (+.f64 #s(literal 1/2 binary64) (*.f64 x #s(literal -1/4 binary64))) #s(literal -1/2 binary64)))
(/.f64 #s(literal 1 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) (+.f64 #s(literal 1/2 binary64) (*.f64 x #s(literal -1/4 binary64))))))
(/.f64 #s(literal 1 binary64) (/.f64 (sqrt.f64 (+.f64 #s(literal 1/4 binary64) (*.f64 x (-.f64 (*.f64 x #s(literal 1/16 binary64)) #s(literal -1/8 binary64))))) (sqrt.f64 (+.f64 #s(literal 1/8 binary64) (*.f64 (*.f64 x (*.f64 x x)) #s(literal -1/64 binary64))))))
(/.f64 #s(literal 1 binary64) (/.f64 (pow.f64 (-.f64 #s(literal 1/2 binary64) (*.f64 x #s(literal -1/4 binary64))) #s(literal 1/2 binary64)) (sqrt.f64 (+.f64 #s(literal 1/4 binary64) (*.f64 (*.f64 x x) #s(literal -1/16 binary64))))))
(/.f64 (sqrt.f64 (+.f64 #s(literal 1/2 binary64) (*.f64 x #s(literal -1/4 binary64)))) #s(literal 1 binary64))
(/.f64 #s(literal -1 binary64) (neg.f64 (pow.f64 (+.f64 #s(literal 1/2 binary64) (*.f64 x #s(literal -1/4 binary64))) #s(literal -1/2 binary64))))
(/.f64 (-.f64 #s(literal 0 binary64) (sqrt.f64 (+.f64 #s(literal 1/2 binary64) (*.f64 x #s(literal -1/4 binary64))))) #s(literal -1 binary64))
(/.f64 (sqrt.f64 (+.f64 #s(literal 1/8 binary64) (*.f64 (*.f64 x (*.f64 x x)) #s(literal -1/64 binary64)))) (sqrt.f64 (+.f64 #s(literal 1/4 binary64) (*.f64 x (-.f64 (*.f64 x #s(literal 1/16 binary64)) #s(literal -1/8 binary64))))))
(/.f64 (sqrt.f64 (+.f64 #s(literal 1/8 binary64) (*.f64 (*.f64 x (*.f64 x x)) #s(literal -1/64 binary64)))) (*.f64 #s(literal 1 binary64) (sqrt.f64 (+.f64 #s(literal 1/4 binary64) (*.f64 x (-.f64 (*.f64 x #s(literal 1/16 binary64)) #s(literal -1/8 binary64)))))))
(/.f64 (sqrt.f64 (+.f64 #s(literal 1/4 binary64) (*.f64 (*.f64 x x) #s(literal -1/16 binary64)))) (pow.f64 (-.f64 #s(literal 1/2 binary64) (*.f64 x #s(literal -1/4 binary64))) #s(literal 1/2 binary64)))
(/.f64 (sqrt.f64 (+.f64 #s(literal 1/4 binary64) (*.f64 (*.f64 x x) #s(literal -1/16 binary64)))) (*.f64 #s(literal 1 binary64) (pow.f64 (-.f64 #s(literal 1/2 binary64) (*.f64 x #s(literal -1/4 binary64))) #s(literal 1/2 binary64))))
(/.f64 (sqrt.f64 (+.f64 #s(literal -1/8 binary64) (neg.f64 (*.f64 (*.f64 x (*.f64 x x)) #s(literal -1/64 binary64))))) (sqrt.f64 (+.f64 #s(literal -1/4 binary64) (neg.f64 (*.f64 x (-.f64 (*.f64 x #s(literal 1/16 binary64)) #s(literal -1/8 binary64)))))))
(/.f64 (sqrt.f64 (+.f64 #s(literal -1/4 binary64) (neg.f64 (*.f64 (*.f64 x x) #s(literal -1/16 binary64))))) (sqrt.f64 (-.f64 #s(literal 0 binary64) (-.f64 #s(literal 1/2 binary64) (*.f64 x #s(literal -1/4 binary64))))))
(/.f64 (sqrt.f64 (+.f64 (*.f64 x (*.f64 x #s(literal 1/16 binary64))) #s(literal -1/4 binary64))) (sqrt.f64 (+.f64 (*.f64 x #s(literal -1/4 binary64)) #s(literal -1/2 binary64))))
(/.f64 (neg.f64 (sqrt.f64 (+.f64 #s(literal 1/8 binary64) (*.f64 (*.f64 x (*.f64 x x)) #s(literal -1/64 binary64))))) (neg.f64 (sqrt.f64 (+.f64 #s(literal 1/4 binary64) (*.f64 x (-.f64 (*.f64 x #s(literal 1/16 binary64)) #s(literal -1/8 binary64)))))))
(/.f64 (neg.f64 (sqrt.f64 (+.f64 #s(literal 1/4 binary64) (*.f64 (*.f64 x x) #s(literal -1/16 binary64))))) (neg.f64 (pow.f64 (-.f64 #s(literal 1/2 binary64) (*.f64 x #s(literal -1/4 binary64))) #s(literal 1/2 binary64))))
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(fma.f64 #s(literal 1/2 binary64) x (*.f64 x (*.f64 x #s(literal 1/6 binary64))))
(fma.f64 x #s(literal 1/2 binary64) (*.f64 x (*.f64 x #s(literal 1/6 binary64))))
(fma.f64 x (*.f64 x #s(literal 1/6 binary64)) (*.f64 #s(literal 1/2 binary64) x))
(fma.f64 #s(literal 1/6 binary64) (*.f64 x x) (*.f64 #s(literal 1/2 binary64) x))
(fma.f64 (*.f64 x #s(literal 1/6 binary64)) x (*.f64 #s(literal 1/2 binary64) x))
(fma.f64 (*.f64 #s(literal 1/2 binary64) x) #s(literal 1 binary64) (*.f64 x (*.f64 x #s(literal 1/6 binary64))))
(fma.f64 (*.f64 x x) #s(literal 1/6 binary64) (*.f64 #s(literal 1/2 binary64) x))
(/.f64 #s(literal 1 binary64) (/.f64 (+.f64 (*.f64 #s(literal 1/4 binary64) (*.f64 x x)) (*.f64 (*.f64 x (*.f64 x #s(literal 1/6 binary64))) (-.f64 (*.f64 x (*.f64 x #s(literal 1/6 binary64))) (*.f64 #s(literal 1/2 binary64) x)))) (+.f64 (*.f64 #s(literal 1/8 binary64) (*.f64 x (*.f64 x x))) (*.f64 (*.f64 (*.f64 x (*.f64 x x)) #s(literal 1/216 binary64)) (*.f64 x (*.f64 x x))))))
(/.f64 #s(literal 1 binary64) (/.f64 (*.f64 x (+.f64 #s(literal 1/2 binary64) (*.f64 x #s(literal -1/6 binary64)))) (*.f64 (*.f64 x (+.f64 #s(literal 1/2 binary64) (*.f64 x #s(literal 1/6 binary64)))) (*.f64 x (+.f64 #s(literal 1/2 binary64) (*.f64 x #s(literal -1/6 binary64)))))))
(/.f64 #s(literal 1 binary64) (/.f64 (+.f64 #s(literal 1/4 binary64) (*.f64 x (-.f64 (*.f64 x #s(literal 1/36 binary64)) #s(literal 1/12 binary64)))) (*.f64 x (+.f64 #s(literal 1/8 binary64) (*.f64 (*.f64 x (*.f64 x x)) #s(literal 1/216 binary64))))))
(/.f64 #s(literal 1 binary64) (/.f64 (+.f64 #s(literal 1/2 binary64) (*.f64 x #s(literal -1/6 binary64))) (*.f64 x (+.f64 #s(literal 1/4 binary64) (*.f64 (*.f64 x x) #s(literal -1/36 binary64))))))
(/.f64 x (/.f64 #s(literal 1 binary64) (+.f64 #s(literal 1/2 binary64) (*.f64 x #s(literal 1/6 binary64)))))
(/.f64 (+.f64 (*.f64 #s(literal 1/8 binary64) (*.f64 x (*.f64 x x))) (*.f64 (*.f64 (*.f64 x (*.f64 x x)) #s(literal 1/216 binary64)) (*.f64 x (*.f64 x x)))) (+.f64 (*.f64 #s(literal 1/4 binary64) (*.f64 x x)) (*.f64 (*.f64 x (*.f64 x #s(literal 1/6 binary64))) (-.f64 (*.f64 x (*.f64 x #s(literal 1/6 binary64))) (*.f64 #s(literal 1/2 binary64) x)))))
(/.f64 (+.f64 (*.f64 #s(literal 1/8 binary64) (*.f64 x (*.f64 x x))) (*.f64 (*.f64 (*.f64 x (*.f64 x x)) #s(literal 1/216 binary64)) (*.f64 x (*.f64 x x)))) (+.f64 (*.f64 (*.f64 (*.f64 x x) #s(literal 1/36 binary64)) (*.f64 x x)) (-.f64 (*.f64 #s(literal 1/4 binary64) (*.f64 x x)) (*.f64 (*.f64 x #s(literal 1/12 binary64)) (*.f64 x x)))))
(/.f64 (*.f64 (*.f64 x (+.f64 #s(literal 1/2 binary64) (*.f64 x #s(literal 1/6 binary64)))) (*.f64 x (+.f64 #s(literal 1/2 binary64) (*.f64 x #s(literal -1/6 binary64))))) (*.f64 x (+.f64 #s(literal 1/2 binary64) (*.f64 x #s(literal -1/6 binary64)))))
(/.f64 (*.f64 x (+.f64 #s(literal 1/8 binary64) (*.f64 (*.f64 x (*.f64 x x)) #s(literal 1/216 binary64)))) (+.f64 #s(literal 1/4 binary64) (*.f64 x (-.f64 (*.f64 x #s(literal 1/36 binary64)) #s(literal 1/12 binary64)))))
(/.f64 (*.f64 x (+.f64 #s(literal 1/4 binary64) (*.f64 (*.f64 x x) #s(literal -1/36 binary64)))) (+.f64 #s(literal 1/2 binary64) (*.f64 x #s(literal -1/6 binary64))))
(/.f64 (*.f64 (+.f64 (*.f64 #s(literal 1/8 binary64) (*.f64 x (*.f64 x x))) (*.f64 (*.f64 (*.f64 x (*.f64 x x)) #s(literal 1/216 binary64)) (*.f64 x (*.f64 x x)))) #s(literal 1 binary64)) (+.f64 (*.f64 #s(literal 1/4 binary64) (*.f64 x x)) (*.f64 (*.f64 x (*.f64 x #s(literal 1/6 binary64))) (-.f64 (*.f64 x (*.f64 x #s(literal 1/6 binary64))) (*.f64 #s(literal 1/2 binary64) x)))))
(/.f64 (*.f64 (*.f64 (*.f64 x (+.f64 #s(literal 1/2 binary64) (*.f64 x #s(literal 1/6 binary64)))) (*.f64 x (+.f64 #s(literal 1/2 binary64) (*.f64 x #s(literal -1/6 binary64))))) #s(literal 1 binary64)) (*.f64 x (+.f64 #s(literal 1/2 binary64) (*.f64 x #s(literal -1/6 binary64)))))
(/.f64 (*.f64 #s(literal 1 binary64) (+.f64 (*.f64 #s(literal 1/8 binary64) (*.f64 x (*.f64 x x))) (*.f64 (*.f64 (*.f64 x (*.f64 x x)) #s(literal 1/216 binary64)) (*.f64 x (*.f64 x x))))) (+.f64 (*.f64 #s(literal 1/4 binary64) (*.f64 x x)) (*.f64 (*.f64 x (*.f64 x #s(literal 1/6 binary64))) (-.f64 (*.f64 x (*.f64 x #s(literal 1/6 binary64))) (*.f64 #s(literal 1/2 binary64) x)))))
(/.f64 (*.f64 #s(literal 1 binary64) (*.f64 (*.f64 x (+.f64 #s(literal 1/2 binary64) (*.f64 x #s(literal 1/6 binary64)))) (*.f64 x (+.f64 #s(literal 1/2 binary64) (*.f64 x #s(literal -1/6 binary64)))))) (*.f64 x (+.f64 #s(literal 1/2 binary64) (*.f64 x #s(literal -1/6 binary64)))))
(/.f64 (neg.f64 (+.f64 (*.f64 #s(literal 1/8 binary64) (*.f64 x (*.f64 x x))) (*.f64 (*.f64 (*.f64 x (*.f64 x x)) #s(literal 1/216 binary64)) (*.f64 x (*.f64 x x))))) (neg.f64 (+.f64 (*.f64 #s(literal 1/4 binary64) (*.f64 x x)) (*.f64 (*.f64 x (*.f64 x #s(literal 1/6 binary64))) (-.f64 (*.f64 x (*.f64 x #s(literal 1/6 binary64))) (*.f64 #s(literal 1/2 binary64) x))))))
(/.f64 (neg.f64 (*.f64 (*.f64 x (+.f64 #s(literal 1/2 binary64) (*.f64 x #s(literal 1/6 binary64)))) (*.f64 x (+.f64 #s(literal 1/2 binary64) (*.f64 x #s(literal -1/6 binary64)))))) (neg.f64 (*.f64 x (+.f64 #s(literal 1/2 binary64) (*.f64 x #s(literal -1/6 binary64))))))
(/.f64 (neg.f64 (*.f64 x (+.f64 #s(literal 1/8 binary64) (*.f64 (*.f64 x (*.f64 x x)) #s(literal 1/216 binary64))))) (+.f64 #s(literal -1/4 binary64) (neg.f64 (*.f64 x (-.f64 (*.f64 x #s(literal 1/36 binary64)) #s(literal 1/12 binary64))))))
(/.f64 (neg.f64 (*.f64 x (+.f64 #s(literal 1/4 binary64) (*.f64 (*.f64 x x) #s(literal -1/36 binary64))))) (-.f64 #s(literal 0 binary64) (+.f64 #s(literal 1/2 binary64) (*.f64 x #s(literal -1/6 binary64)))))
(/.f64 (-.f64 (*.f64 (*.f64 (*.f64 x x) #s(literal 1/36 binary64)) (*.f64 x x)) (*.f64 #s(literal 1/4 binary64) (*.f64 x x))) (-.f64 (*.f64 x (*.f64 x #s(literal 1/6 binary64))) (*.f64 #s(literal 1/2 binary64) x)))
(/.f64 (*.f64 x (+.f64 #s(literal -1/8 binary64) (neg.f64 (*.f64 (*.f64 x (*.f64 x x)) #s(literal 1/216 binary64))))) (+.f64 #s(literal -1/4 binary64) (neg.f64 (*.f64 x (-.f64 (*.f64 x #s(literal 1/36 binary64)) #s(literal 1/12 binary64))))))
(/.f64 (*.f64 x (-.f64 #s(literal 0 binary64) (+.f64 #s(literal 1/4 binary64) (*.f64 (*.f64 x x) #s(literal -1/36 binary64))))) (-.f64 #s(literal 0 binary64) (+.f64 #s(literal 1/2 binary64) (*.f64 x #s(literal -1/6 binary64)))))
(/.f64 (*.f64 x (+.f64 (*.f64 (*.f64 x x) #s(literal 1/36 binary64)) #s(literal -1/4 binary64))) (+.f64 (*.f64 x #s(literal 1/6 binary64)) #s(literal -1/2 binary64)))
(/.f64 (*.f64 (+.f64 #s(literal -1/8 binary64) (neg.f64 (*.f64 (*.f64 x (*.f64 x x)) #s(literal 1/216 binary64)))) x) (+.f64 #s(literal -1/4 binary64) (neg.f64 (*.f64 x (-.f64 (*.f64 x #s(literal 1/36 binary64)) #s(literal 1/12 binary64))))))
(/.f64 (*.f64 (-.f64 #s(literal 0 binary64) (+.f64 #s(literal 1/4 binary64) (*.f64 (*.f64 x x) #s(literal -1/36 binary64)))) x) (-.f64 #s(literal 0 binary64) (+.f64 #s(literal 1/2 binary64) (*.f64 x #s(literal -1/6 binary64)))))
(/.f64 (*.f64 (+.f64 (*.f64 (*.f64 x x) #s(literal 1/36 binary64)) #s(literal -1/4 binary64)) x) (+.f64 (*.f64 x #s(literal 1/6 binary64)) #s(literal -1/2 binary64)))
(*.f64 #s(literal 1 binary64) (*.f64 x (+.f64 #s(literal 1/2 binary64) (*.f64 x #s(literal 1/6 binary64)))))
(*.f64 x (+.f64 #s(literal 1/2 binary64) (*.f64 x #s(literal 1/6 binary64))))
(*.f64 (+.f64 #s(literal 1/2 binary64) (*.f64 x #s(literal 1/6 binary64))) x)
(*.f64 (*.f64 x (+.f64 #s(literal 1/2 binary64) (*.f64 x #s(literal 1/6 binary64)))) #s(literal 1 binary64))
(*.f64 (+.f64 #s(literal 1/8 binary64) (*.f64 (*.f64 x (*.f64 x x)) #s(literal 1/216 binary64))) (*.f64 (/.f64 #s(literal 1 binary64) (+.f64 #s(literal 1/4 binary64) (*.f64 x (-.f64 (*.f64 x #s(literal 1/36 binary64)) #s(literal 1/12 binary64))))) x))
(*.f64 (+.f64 #s(literal 1/8 binary64) (*.f64 (*.f64 x (*.f64 x x)) #s(literal 1/216 binary64))) (/.f64 x (+.f64 #s(literal 1/4 binary64) (*.f64 x (-.f64 (*.f64 x #s(literal 1/36 binary64)) #s(literal 1/12 binary64))))))
(*.f64 (+.f64 #s(literal 1/4 binary64) (*.f64 (*.f64 x x) #s(literal -1/36 binary64))) (*.f64 (/.f64 #s(literal 1 binary64) (+.f64 #s(literal 1/2 binary64) (*.f64 x #s(literal -1/6 binary64)))) x))
(*.f64 (+.f64 #s(literal 1/4 binary64) (*.f64 (*.f64 x x) #s(literal -1/36 binary64))) (/.f64 x (+.f64 #s(literal 1/2 binary64) (*.f64 x #s(literal -1/6 binary64)))))
(*.f64 (+.f64 (*.f64 #s(literal 1/8 binary64) (*.f64 x (*.f64 x x))) (*.f64 (*.f64 (*.f64 x (*.f64 x x)) #s(literal 1/216 binary64)) (*.f64 x (*.f64 x x)))) (/.f64 #s(literal 1 binary64) (+.f64 (*.f64 #s(literal 1/4 binary64) (*.f64 x x)) (*.f64 (*.f64 x (*.f64 x #s(literal 1/6 binary64))) (-.f64 (*.f64 x (*.f64 x #s(literal 1/6 binary64))) (*.f64 #s(literal 1/2 binary64) x))))))
(*.f64 (*.f64 (*.f64 x (+.f64 #s(literal 1/2 binary64) (*.f64 x #s(literal 1/6 binary64)))) (*.f64 x (+.f64 #s(literal 1/2 binary64) (*.f64 x #s(literal -1/6 binary64))))) (/.f64 #s(literal 1 binary64) (*.f64 x (+.f64 #s(literal 1/2 binary64) (*.f64 x #s(literal -1/6 binary64))))))
(*.f64 (*.f64 x (+.f64 #s(literal 1/8 binary64) (*.f64 (*.f64 x (*.f64 x x)) #s(literal 1/216 binary64)))) (/.f64 #s(literal 1 binary64) (+.f64 #s(literal 1/4 binary64) (*.f64 x (-.f64 (*.f64 x #s(literal 1/36 binary64)) #s(literal 1/12 binary64))))))
(*.f64 (*.f64 x (+.f64 #s(literal 1/4 binary64) (*.f64 (*.f64 x x) #s(literal -1/36 binary64)))) (/.f64 #s(literal 1 binary64) (+.f64 #s(literal 1/2 binary64) (*.f64 x #s(literal -1/6 binary64)))))
(*.f64 (/.f64 (*.f64 x (+.f64 #s(literal 1/8 binary64) (*.f64 (*.f64 x (*.f64 x x)) #s(literal 1/216 binary64)))) (+.f64 #s(literal 1/64 binary64) (*.f64 (*.f64 x (-.f64 (*.f64 x #s(literal 1/36 binary64)) #s(literal 1/12 binary64))) (*.f64 (*.f64 x (-.f64 (*.f64 x #s(literal 1/36 binary64)) #s(literal 1/12 binary64))) (*.f64 x (-.f64 (*.f64 x #s(literal 1/36 binary64)) #s(literal 1/12 binary64))))))) (+.f64 #s(literal 1/16 binary64) (*.f64 (*.f64 x (-.f64 (*.f64 x #s(literal 1/36 binary64)) #s(literal 1/12 binary64))) (-.f64 (*.f64 x (-.f64 (*.f64 x #s(literal 1/36 binary64)) #s(literal 1/12 binary64))) #s(literal 1/4 binary64)))))
(*.f64 (/.f64 (*.f64 x (+.f64 #s(literal 1/8 binary64) (*.f64 (*.f64 x (*.f64 x x)) #s(literal 1/216 binary64)))) (-.f64 #s(literal 1/16 binary64) (*.f64 (*.f64 x (-.f64 (*.f64 x #s(literal 1/36 binary64)) #s(literal 1/12 binary64))) (*.f64 x (-.f64 (*.f64 x #s(literal 1/36 binary64)) #s(literal 1/12 binary64)))))) (-.f64 #s(literal 1/4 binary64) (*.f64 x (-.f64 (*.f64 x #s(literal 1/36 binary64)) #s(literal 1/12 binary64)))))
(*.f64 (/.f64 (*.f64 x (+.f64 #s(literal 1/4 binary64) (*.f64 (*.f64 x x) #s(literal -1/36 binary64)))) (+.f64 #s(literal 1/4 binary64) (*.f64 (*.f64 x x) #s(literal -1/36 binary64)))) (+.f64 #s(literal 1/2 binary64) (*.f64 x #s(literal 1/6 binary64))))
(*.f64 (/.f64 (*.f64 x (+.f64 #s(literal 1/4 binary64) (*.f64 (*.f64 x x) #s(literal -1/36 binary64)))) (+.f64 #s(literal 1/8 binary64) (*.f64 #s(literal -1/216 binary64) (*.f64 x (*.f64 x x))))) (+.f64 #s(literal 1/4 binary64) (*.f64 x (+.f64 (*.f64 x #s(literal 1/36 binary64)) #s(literal 1/12 binary64)))))

simplify288.0ms (3.9%)

Algorithm
egg-herbie
Rules
5150×*-lowering-*.f32
5150×*-lowering-*.f64
4268×+-lowering-+.f64
4268×+-lowering-+.f32
1236×distribute-lft-in
Iterations

Useful iterations: 2 (0.0ms)

IterNodesCost
03332056
111341878
241591795
082891795
Stop Event
iter limit
node limit
Counts
168 → 168
Calls
Call 1
Inputs
(* (sqrt (pow x 3)) (sqrt 1/6))
(* (sqrt (pow x 3)) (sqrt 1/6))
(* (sqrt (pow x 3)) (sqrt 1/6))
(* (sqrt (pow x 3)) (sqrt 1/6))
(* (sqrt (pow x 3)) (sqrt 1/6))
(* (sqrt (pow x 3)) (sqrt 1/6))
(* (sqrt (pow x 3)) (sqrt 1/6))
(* (sqrt (pow x 3)) (sqrt 1/6))
(* -1 (* (sqrt (pow x 3)) (* (sqrt -1) (sqrt -1/6))))
(* -1 (* (sqrt (pow x 3)) (* (sqrt -1) (sqrt -1/6))))
(* -1 (* (sqrt (pow x 3)) (* (sqrt -1) (sqrt -1/6))))
(* -1 (* (sqrt (pow x 3)) (* (sqrt -1) (sqrt -1/6))))
(* (sqrt x) (sqrt 1/6))
(* (sqrt x) (sqrt 1/6))
(* (sqrt x) (sqrt 1/6))
(* (sqrt x) (sqrt 1/6))
(* (sqrt x) (sqrt 1/6))
(* (sqrt x) (sqrt 1/6))
(* (sqrt x) (sqrt 1/6))
(* (sqrt x) (sqrt 1/6))
(* -1 (* (sqrt x) (* (sqrt -1) (sqrt -1/6))))
(* -1 (* (sqrt x) (* (sqrt -1) (sqrt -1/6))))
(* -1 (* (sqrt x) (* (sqrt -1) (sqrt -1/6))))
(* -1 (* (sqrt x) (* (sqrt -1) (sqrt -1/6))))
(* 1/6 x)
(* 1/6 x)
(* 1/6 x)
(* 1/6 x)
(* 1/6 x)
(* 1/6 x)
(* 1/6 x)
(* 1/6 x)
(* 1/6 x)
(* 1/6 x)
(* 1/6 x)
(* 1/6 x)
(sqrt 2)
(+ (sqrt 2) (* 1/2 (/ x (sqrt 2))))
(+ (sqrt 2) (* x (+ (* 1/2 (/ (* x (- 1/2 (* 1/4 (/ 1 (pow (sqrt 2) 2))))) (sqrt 2))) (* 1/2 (/ 1 (sqrt 2))))))
(+ (sqrt 2) (* x (+ (* x (+ (* 1/2 (/ (* x (- 1/4 (* 1/2 (/ (- 1/2 (* 1/4 (/ 1 (pow (sqrt 2) 2)))) (pow (sqrt 2) 2))))) (sqrt 2))) (* 1/2 (/ (- 1/2 (* 1/4 (/ 1 (pow (sqrt 2) 2)))) (sqrt 2))))) (* 1/2 (/ 1 (sqrt 2))))))
(* (sqrt (/ 1 x)) (sqrt -4))
(+ (* -4 (* (sqrt (/ 1 (pow x 3))) (/ 1 (sqrt -4)))) (* (sqrt (/ 1 x)) (sqrt -4)))
(+ (* -8 (* (sqrt (/ 1 (pow x 5))) (/ 1 (sqrt -4)))) (+ (* -4 (* (sqrt (/ 1 (pow x 3))) (/ 1 (sqrt -4)))) (* (sqrt (/ 1 x)) (sqrt -4))))
(+ (* -8 (* (sqrt (/ 1 (pow x 5))) (/ 1 (sqrt -4)))) (+ (* -4 (* (sqrt (/ 1 (pow x 3))) (/ 1 (sqrt -4)))) (+ (* -1/2 (* (sqrt (/ 1 (pow x 7))) (/ (+ 32 (* 16 (/ x (pow (sqrt -4) 2)))) (sqrt -4)))) (* (sqrt (/ 1 x)) (sqrt -4)))))
(* 2 (* (sqrt (/ 1 x)) (sqrt -1)))
(+ (* -2 (* (sqrt (/ 1 (pow x 3))) (sqrt -1))) (* 2 (* (sqrt (/ 1 x)) (sqrt -1))))
(+ (* -4 (* (sqrt (/ 1 (pow x 5))) (sqrt -1))) (+ (* -2 (* (sqrt (/ 1 (pow x 3))) (sqrt -1))) (* 2 (* (sqrt (/ 1 x)) (sqrt -1)))))
(+ (* -2 (* (sqrt (/ 1 (pow x 3))) (sqrt -1))) (+ (* -1 (/ (+ (* 1/4 (* (sqrt (/ 1 x)) (* (sqrt -1) (+ 32 (* -4 x))))) (* 4 (* (sqrt x) (sqrt -1)))) (pow x 3))) (* 2 (* (sqrt (/ 1 x)) (sqrt -1)))))
(sqrt 1/2)
(+ (sqrt 1/2) (* -1/8 (/ x (sqrt 1/2))))
(+ (sqrt 1/2) (* x (- (* -1/128 (/ x (pow (sqrt 1/2) 3))) (* 1/8 (/ 1 (sqrt 1/2))))))
(+ (sqrt 1/2) (* x (- (* x (- (* -1/1024 (/ x (pow (sqrt 1/2) 5))) (* 1/128 (/ 1 (pow (sqrt 1/2) 3))))) (* 1/8 (/ 1 (sqrt 1/2))))))
(* (sqrt x) (sqrt -1/4))
(* x (+ (* 1/4 (* (sqrt (/ 1 (pow x 3))) (/ 1 (sqrt -1/4)))) (* (sqrt (/ 1 x)) (sqrt -1/4))))
(* x (+ (* -1/32 (* (sqrt (/ 1 (pow x 5))) (/ 1 (pow (sqrt -1/4) 3)))) (+ (* 1/4 (* (sqrt (/ 1 (pow x 3))) (/ 1 (sqrt -1/4)))) (* (sqrt (/ 1 x)) (sqrt -1/4)))))
(* x (+ (* -1/32 (* (sqrt (/ 1 (pow x 5))) (/ 1 (pow (sqrt -1/4) 3)))) (+ (* 1/128 (* (sqrt (/ 1 (pow x 7))) (/ 1 (pow (sqrt -1/4) 5)))) (+ (* 1/4 (* (sqrt (/ 1 (pow x 3))) (/ 1 (sqrt -1/4)))) (* (sqrt (/ 1 x)) (sqrt -1/4))))))
(* -1/2 (* (sqrt x) (sqrt -1)))
(* -1 (* x (+ (* 1/2 (* (sqrt (/ 1 x)) (sqrt -1))) (* 1/2 (* (sqrt (/ 1 (pow x 3))) (sqrt -1))))))
(* -1 (* x (+ (* -1/4 (* (sqrt (/ 1 (pow x 5))) (sqrt -1))) (+ (* 1/2 (* (sqrt (/ 1 x)) (sqrt -1))) (* 1/2 (* (sqrt (/ 1 (pow x 3))) (sqrt -1)))))))
(* -1 (* x (+ (* -1/4 (* (sqrt (/ 1 (pow x 5))) (sqrt -1))) (+ (* 1/4 (* (sqrt (/ 1 (pow x 7))) (sqrt -1))) (+ (* 1/2 (* (sqrt (/ 1 x)) (sqrt -1))) (* 1/2 (* (sqrt (/ 1 (pow x 3))) (sqrt -1))))))))
1/2
(+ 1/2 (* -1/4 x))
(+ 1/2 (* -1/4 x))
(+ 1/2 (* -1/4 x))
(* -1/4 x)
(* x (- (* 1/2 (/ 1 x)) 1/4))
(* x (- (* 1/2 (/ 1 x)) 1/4))
(* x (- (* 1/2 (/ 1 x)) 1/4))
(* -1/4 x)
(* -1 (* x (- 1/4 (* 1/2 (/ 1 x)))))
(* -1 (* x (- 1/4 (* 1/2 (/ 1 x)))))
(* -1 (* x (- 1/4 (* 1/2 (/ 1 x)))))
(* -1/4 x)
(* -1/4 x)
(* -1/4 x)
(* -1/4 x)
(* -1/4 x)
(* -1/4 x)
(* -1/4 x)
(* -1/4 x)
(* -1/4 x)
(* -1/4 x)
(* -1/4 x)
(* -1/4 x)
(* x (sqrt 1/2))
(* x (+ (sqrt 1/2) (* 1/12 (/ x (sqrt 1/2)))))
(* x (+ (sqrt 1/2) (* x (+ (* -1/288 (/ x (pow (sqrt 1/2) 3))) (* 1/12 (/ 1 (sqrt 1/2)))))))
(* x (+ (sqrt 1/2) (* x (+ (* x (- (* 1/3456 (/ x (pow (sqrt 1/2) 5))) (* 1/288 (/ 1 (pow (sqrt 1/2) 3))))) (* 1/12 (/ 1 (sqrt 1/2)))))))
(* (sqrt (pow x 3)) (sqrt 1/6))
(* (pow x 2) (+ (* 1/4 (* (sqrt (/ 1 (pow x 3))) (/ 1 (sqrt 1/6)))) (* (sqrt (/ 1 x)) (sqrt 1/6))))
(* (pow x 2) (+ (* -1/32 (* (sqrt (/ 1 (pow x 5))) (/ 1 (pow (sqrt 1/6) 3)))) (+ (* 1/4 (* (sqrt (/ 1 (pow x 3))) (/ 1 (sqrt 1/6)))) (* (sqrt (/ 1 x)) (sqrt 1/6)))))
(* (pow x 2) (+ (* -1/32 (* (sqrt (/ 1 (pow x 5))) (/ 1 (pow (sqrt 1/6) 3)))) (+ (* 1/128 (* (sqrt (/ 1 (pow x 7))) (/ 1 (pow (sqrt 1/6) 5)))) (+ (* 1/4 (* (sqrt (/ 1 (pow x 3))) (/ 1 (sqrt 1/6)))) (* (sqrt (/ 1 x)) (sqrt 1/6))))))
(* -1 (* (sqrt (pow x 3)) (* (sqrt -1) (sqrt -1/6))))
(* (pow x 2) (+ (* -1 (* (sqrt (/ 1 x)) (* (sqrt -1) (sqrt -1/6)))) (* -1/4 (* (sqrt (/ 1 (pow x 3))) (/ (sqrt -1) (sqrt -1/6))))))
(* (pow x 2) (+ (* -1 (* (sqrt (/ 1 x)) (* (sqrt -1) (sqrt -1/6)))) (+ (* -1/4 (* (sqrt (/ 1 (pow x 3))) (/ (sqrt -1) (sqrt -1/6)))) (* 1/32 (* (sqrt (/ 1 (pow x 5))) (/ (sqrt -1) (pow (sqrt -1/6) 3)))))))
(* (pow x 2) (+ (* -1 (* (sqrt (/ 1 x)) (* (sqrt -1) (sqrt -1/6)))) (+ (* -1/4 (* (sqrt (/ 1 (pow x 3))) (/ (sqrt -1) (sqrt -1/6)))) (+ (* -1/128 (* (sqrt (/ 1 (pow x 7))) (/ (sqrt -1) (pow (sqrt -1/6) 5)))) (* 1/32 (* (sqrt (/ 1 (pow x 5))) (/ (sqrt -1) (pow (sqrt -1/6) 3))))))))
(sqrt 1/2)
(+ (sqrt 1/2) (* 1/12 (/ x (sqrt 1/2))))
(+ (sqrt 1/2) (* x (+ (* -1/288 (/ x (pow (sqrt 1/2) 3))) (* 1/12 (/ 1 (sqrt 1/2))))))
(+ (sqrt 1/2) (* x (+ (* x (- (* 1/3456 (/ x (pow (sqrt 1/2) 5))) (* 1/288 (/ 1 (pow (sqrt 1/2) 3))))) (* 1/12 (/ 1 (sqrt 1/2))))))
(* (sqrt x) (sqrt 1/6))
(* x (+ (* 1/4 (* (sqrt (/ 1 (pow x 3))) (/ 1 (sqrt 1/6)))) (* (sqrt (/ 1 x)) (sqrt 1/6))))
(* x (+ (* -1/32 (* (sqrt (/ 1 (pow x 5))) (/ 1 (pow (sqrt 1/6) 3)))) (+ (* 1/4 (* (sqrt (/ 1 (pow x 3))) (/ 1 (sqrt 1/6)))) (* (sqrt (/ 1 x)) (sqrt 1/6)))))
(* x (+ (* -1/32 (* (sqrt (/ 1 (pow x 5))) (/ 1 (pow (sqrt 1/6) 3)))) (+ (* 1/128 (* (sqrt (/ 1 (pow x 7))) (/ 1 (pow (sqrt 1/6) 5)))) (+ (* 1/4 (* (sqrt (/ 1 (pow x 3))) (/ 1 (sqrt 1/6)))) (* (sqrt (/ 1 x)) (sqrt 1/6))))))
(* -1 (* (sqrt x) (* (sqrt -1) (sqrt -1/6))))
(* -1 (* x (+ (* 1/4 (* (sqrt (/ 1 (pow x 3))) (/ (sqrt -1) (sqrt -1/6)))) (* (sqrt (/ 1 x)) (* (sqrt -1) (sqrt -1/6))))))
(* -1 (* x (+ (* -1/32 (* (sqrt (/ 1 (pow x 5))) (/ (sqrt -1) (pow (sqrt -1/6) 3)))) (+ (* 1/4 (* (sqrt (/ 1 (pow x 3))) (/ (sqrt -1) (sqrt -1/6)))) (* (sqrt (/ 1 x)) (* (sqrt -1) (sqrt -1/6)))))))
(* -1 (* x (+ (* -1/32 (* (sqrt (/ 1 (pow x 5))) (/ (sqrt -1) (pow (sqrt -1/6) 3)))) (+ (* 1/128 (* (sqrt (/ 1 (pow x 7))) (/ (sqrt -1) (pow (sqrt -1/6) 5)))) (+ (* 1/4 (* (sqrt (/ 1 (pow x 3))) (/ (sqrt -1) (sqrt -1/6)))) (* (sqrt (/ 1 x)) (* (sqrt -1) (sqrt -1/6))))))))
1/2
(+ 1/2 (* 1/6 x))
(+ 1/2 (* 1/6 x))
(+ 1/2 (* 1/6 x))
(* 1/6 x)
(* x (+ 1/6 (* 1/2 (/ 1 x))))
(* x (+ 1/6 (* 1/2 (/ 1 x))))
(* x (+ 1/6 (* 1/2 (/ 1 x))))
(* 1/6 x)
(* x (+ 1/6 (* 1/2 (/ 1 x))))
(* x (+ 1/6 (* 1/2 (/ 1 x))))
(* x (+ 1/6 (* 1/2 (/ 1 x))))
(sqrt x)
(+ (sqrt x) (* 1/4 (sqrt (pow x 3))))
(+ (sqrt x) (* (pow x 2) (+ (* 1/12 (sqrt x)) (* 1/4 (sqrt (/ 1 x))))))
(+ (sqrt x) (* (pow x 2) (+ (* 1/4 (sqrt (/ 1 x))) (* x (+ (* -1/32 (sqrt (/ 1 x))) (* 1/12 (sqrt (/ 1 x))))))))
(* (sqrt (pow x 3)) (sqrt 1/6))
(* (pow x 2) (+ (* 1/4 (* (sqrt (/ 1 (pow x 3))) (/ 1 (sqrt 1/6)))) (* (sqrt (/ 1 x)) (sqrt 1/6))))
(* (pow x 2) (+ (* 1/4 (* (sqrt (/ 1 (pow x 3))) (/ 1 (sqrt 1/6)))) (+ (* 1/2 (* (sqrt (/ 1 (pow x 5))) (/ 1 (sqrt 1/6)))) (* (sqrt (/ 1 x)) (sqrt 1/6)))))
(* (pow x 2) (+ (* -1/32 (* (sqrt (/ 1 (pow x 5))) (/ 1 (pow (sqrt 1/6) 3)))) (+ (* 1/4 (* (sqrt (/ 1 (pow x 3))) (/ 1 (sqrt 1/6)))) (+ (* 1/2 (* (sqrt (/ 1 (pow x 5))) (/ 1 (sqrt 1/6)))) (* (sqrt (/ 1 x)) (sqrt 1/6))))))
(* (sqrt (pow x 3)) (* (pow (sqrt -1) 2) (sqrt 1/6)))
(* (pow x 2) (+ (* -1/4 (* (sqrt (/ 1 (pow x 3))) (/ (pow (sqrt -1) 2) (sqrt 1/6)))) (* (sqrt (/ 1 x)) (* (pow (sqrt -1) 2) (sqrt 1/6)))))
(* (pow x 2) (+ (* -1/2 (* (sqrt (/ 1 (pow x 5))) (/ (pow (sqrt -1) 2) (sqrt 1/6)))) (+ (* -1/4 (* (sqrt (/ 1 (pow x 3))) (/ (pow (sqrt -1) 2) (sqrt 1/6)))) (* (sqrt (/ 1 x)) (* (pow (sqrt -1) 2) (sqrt 1/6))))))
(* (pow x 2) (+ (* -1 (/ (+ (* 1/32 (* (sqrt x) (/ (pow (sqrt -1) 2) (pow (sqrt 1/6) 3)))) (* 1/2 (* (sqrt x) (/ (pow (sqrt -1) 2) (sqrt 1/6))))) (pow x 3))) (+ (* -1/4 (* (sqrt (/ 1 (pow x 3))) (/ (pow (sqrt -1) 2) (sqrt 1/6)))) (* (sqrt (/ 1 x)) (* (pow (sqrt -1) 2) (sqrt 1/6))))))
x
(* x (+ 1 (* 1/2 x)))
(* x (+ 1 (* x (+ 1/2 (* 1/6 x)))))
(* x (+ 1 (* x (+ 1/2 (* 1/6 x)))))
(* 1/6 (pow x 3))
(* (pow x 3) (+ 1/6 (* 1/2 (/ 1 x))))
(* (pow x 3) (+ 1/6 (+ (* 1/2 (/ 1 x)) (/ 1 (pow x 2)))))
(* (pow x 3) (+ 1/6 (+ (* 1/2 (/ 1 x)) (/ 1 (pow x 2)))))
(* 1/6 (pow x 3))
(* (pow x 3) (+ 1/6 (* 1/2 (/ 1 x))))
(* -1 (* (pow x 3) (- (* -1 (/ (+ 1/2 (/ 1 x)) x)) 1/6)))
(* -1 (* (pow x 3) (- (* -1 (/ (+ 1/2 (/ 1 x)) x)) 1/6)))
1
(+ 1 (* 1/2 x))
(+ 1 (* x (+ 1/2 (* 1/6 x))))
(+ 1 (* x (+ 1/2 (* 1/6 x))))
(* 1/6 (pow x 2))
(* (pow x 2) (+ 1/6 (* 1/2 (/ 1 x))))
(* (pow x 2) (+ 1/6 (+ (* 1/2 (/ 1 x)) (/ 1 (pow x 2)))))
(* (pow x 2) (+ 1/6 (+ (* 1/2 (/ 1 x)) (/ 1 (pow x 2)))))
(* 1/6 (pow x 2))
(* (pow x 2) (+ 1/6 (* 1/2 (/ 1 x))))
(* (pow x 2) (+ 1/6 (+ (* 1/2 (/ 1 x)) (/ 1 (pow x 2)))))
(* (pow x 2) (+ 1/6 (+ (* 1/2 (/ 1 x)) (/ 1 (pow x 2)))))
(* 1/2 x)
(* x (+ 1/2 (* 1/6 x)))
(* x (+ 1/2 (* 1/6 x)))
(* x (+ 1/2 (* 1/6 x)))
(* 1/6 (pow x 2))
(* (pow x 2) (+ 1/6 (* 1/2 (/ 1 x))))
(* (pow x 2) (+ 1/6 (* 1/2 (/ 1 x))))
(* (pow x 2) (+ 1/6 (* 1/2 (/ 1 x))))
(* 1/6 (pow x 2))
(* (pow x 2) (+ 1/6 (* 1/2 (/ 1 x))))
(* (pow x 2) (+ 1/6 (* 1/2 (/ 1 x))))
(* (pow x 2) (+ 1/6 (* 1/2 (/ 1 x))))
Outputs
(* (sqrt (pow x 3)) (sqrt 1/6))
(*.f64 (sqrt.f64 (*.f64 x (*.f64 x x))) (sqrt.f64 #s(literal 1/6 binary64)))
(* (sqrt (pow x 3)) (sqrt 1/6))
(*.f64 (sqrt.f64 (*.f64 x (*.f64 x x))) (sqrt.f64 #s(literal 1/6 binary64)))
(* (sqrt (pow x 3)) (sqrt 1/6))
(*.f64 (sqrt.f64 (*.f64 x (*.f64 x x))) (sqrt.f64 #s(literal 1/6 binary64)))
(* (sqrt (pow x 3)) (sqrt 1/6))
(*.f64 (sqrt.f64 (*.f64 x (*.f64 x x))) (sqrt.f64 #s(literal 1/6 binary64)))
(* (sqrt (pow x 3)) (sqrt 1/6))
(*.f64 (sqrt.f64 (*.f64 x (*.f64 x x))) (sqrt.f64 #s(literal 1/6 binary64)))
(* (sqrt (pow x 3)) (sqrt 1/6))
(*.f64 (sqrt.f64 (*.f64 x (*.f64 x x))) (sqrt.f64 #s(literal 1/6 binary64)))
(* (sqrt (pow x 3)) (sqrt 1/6))
(*.f64 (sqrt.f64 (*.f64 x (*.f64 x x))) (sqrt.f64 #s(literal 1/6 binary64)))
(* (sqrt (pow x 3)) (sqrt 1/6))
(*.f64 (sqrt.f64 (*.f64 x (*.f64 x x))) (sqrt.f64 #s(literal 1/6 binary64)))
(* -1 (* (sqrt (pow x 3)) (* (sqrt -1) (sqrt -1/6))))
(*.f64 (*.f64 (sqrt.f64 (*.f64 x (*.f64 x x))) (sqrt.f64 #s(literal -1 binary64))) (-.f64 #s(literal 0 binary64) (sqrt.f64 #s(literal -1/6 binary64))))
(* -1 (* (sqrt (pow x 3)) (* (sqrt -1) (sqrt -1/6))))
(*.f64 (*.f64 (sqrt.f64 (*.f64 x (*.f64 x x))) (sqrt.f64 #s(literal -1 binary64))) (-.f64 #s(literal 0 binary64) (sqrt.f64 #s(literal -1/6 binary64))))
(* -1 (* (sqrt (pow x 3)) (* (sqrt -1) (sqrt -1/6))))
(*.f64 (*.f64 (sqrt.f64 (*.f64 x (*.f64 x x))) (sqrt.f64 #s(literal -1 binary64))) (-.f64 #s(literal 0 binary64) (sqrt.f64 #s(literal -1/6 binary64))))
(* -1 (* (sqrt (pow x 3)) (* (sqrt -1) (sqrt -1/6))))
(*.f64 (*.f64 (sqrt.f64 (*.f64 x (*.f64 x x))) (sqrt.f64 #s(literal -1 binary64))) (-.f64 #s(literal 0 binary64) (sqrt.f64 #s(literal -1/6 binary64))))
(* (sqrt x) (sqrt 1/6))
(*.f64 (sqrt.f64 #s(literal 1/6 binary64)) (sqrt.f64 x))
(* (sqrt x) (sqrt 1/6))
(*.f64 (sqrt.f64 #s(literal 1/6 binary64)) (sqrt.f64 x))
(* (sqrt x) (sqrt 1/6))
(*.f64 (sqrt.f64 #s(literal 1/6 binary64)) (sqrt.f64 x))
(* (sqrt x) (sqrt 1/6))
(*.f64 (sqrt.f64 #s(literal 1/6 binary64)) (sqrt.f64 x))
(* (sqrt x) (sqrt 1/6))
(*.f64 (sqrt.f64 #s(literal 1/6 binary64)) (sqrt.f64 x))
(* (sqrt x) (sqrt 1/6))
(*.f64 (sqrt.f64 #s(literal 1/6 binary64)) (sqrt.f64 x))
(* (sqrt x) (sqrt 1/6))
(*.f64 (sqrt.f64 #s(literal 1/6 binary64)) (sqrt.f64 x))
(* (sqrt x) (sqrt 1/6))
(*.f64 (sqrt.f64 #s(literal 1/6 binary64)) (sqrt.f64 x))
(* -1 (* (sqrt x) (* (sqrt -1) (sqrt -1/6))))
(*.f64 (*.f64 (sqrt.f64 #s(literal -1 binary64)) (sqrt.f64 #s(literal -1/6 binary64))) (-.f64 #s(literal 0 binary64) (sqrt.f64 x)))
(* -1 (* (sqrt x) (* (sqrt -1) (sqrt -1/6))))
(*.f64 (*.f64 (sqrt.f64 #s(literal -1 binary64)) (sqrt.f64 #s(literal -1/6 binary64))) (-.f64 #s(literal 0 binary64) (sqrt.f64 x)))
(* -1 (* (sqrt x) (* (sqrt -1) (sqrt -1/6))))
(*.f64 (*.f64 (sqrt.f64 #s(literal -1 binary64)) (sqrt.f64 #s(literal -1/6 binary64))) (-.f64 #s(literal 0 binary64) (sqrt.f64 x)))
(* -1 (* (sqrt x) (* (sqrt -1) (sqrt -1/6))))
(*.f64 (*.f64 (sqrt.f64 #s(literal -1 binary64)) (sqrt.f64 #s(literal -1/6 binary64))) (-.f64 #s(literal 0 binary64) (sqrt.f64 x)))
(* 1/6 x)
(*.f64 x #s(literal 1/6 binary64))
(* 1/6 x)
(*.f64 x #s(literal 1/6 binary64))
(* 1/6 x)
(*.f64 x #s(literal 1/6 binary64))
(* 1/6 x)
(*.f64 x #s(literal 1/6 binary64))
(* 1/6 x)
(*.f64 x #s(literal 1/6 binary64))
(* 1/6 x)
(*.f64 x #s(literal 1/6 binary64))
(* 1/6 x)
(*.f64 x #s(literal 1/6 binary64))
(* 1/6 x)
(*.f64 x #s(literal 1/6 binary64))
(* 1/6 x)
(*.f64 x #s(literal 1/6 binary64))
(* 1/6 x)
(*.f64 x #s(literal 1/6 binary64))
(* 1/6 x)
(*.f64 x #s(literal 1/6 binary64))
(* 1/6 x)
(*.f64 x #s(literal 1/6 binary64))
(sqrt 2)
(sqrt.f64 #s(literal 2 binary64))
(+ (sqrt 2) (* 1/2 (/ x (sqrt 2))))
(+.f64 (sqrt.f64 #s(literal 2 binary64)) (/.f64 (*.f64 x #s(literal 1/2 binary64)) (sqrt.f64 #s(literal 2 binary64))))
(+ (sqrt 2) (* x (+ (* 1/2 (/ (* x (- 1/2 (* 1/4 (/ 1 (pow (sqrt 2) 2))))) (sqrt 2))) (* 1/2 (/ 1 (sqrt 2))))))
(+.f64 (sqrt.f64 #s(literal 2 binary64)) (*.f64 x (+.f64 (/.f64 #s(literal 1/2 binary64) (sqrt.f64 #s(literal 2 binary64))) (*.f64 x (/.f64 #s(literal 3/16 binary64) (sqrt.f64 #s(literal 2 binary64)))))))
(+ (sqrt 2) (* x (+ (* x (+ (* 1/2 (/ (* x (- 1/4 (* 1/2 (/ (- 1/2 (* 1/4 (/ 1 (pow (sqrt 2) 2)))) (pow (sqrt 2) 2))))) (sqrt 2))) (* 1/2 (/ (- 1/2 (* 1/4 (/ 1 (pow (sqrt 2) 2)))) (sqrt 2))))) (* 1/2 (/ 1 (sqrt 2))))))
(+.f64 (sqrt.f64 #s(literal 2 binary64)) (*.f64 x (+.f64 (/.f64 #s(literal 1/2 binary64) (sqrt.f64 #s(literal 2 binary64))) (*.f64 x (+.f64 (/.f64 (*.f64 #s(literal 5/64 binary64) x) (sqrt.f64 #s(literal 2 binary64))) (/.f64 #s(literal 3/16 binary64) (sqrt.f64 #s(literal 2 binary64))))))))
(* (sqrt (/ 1 x)) (sqrt -4))
(*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) (sqrt.f64 #s(literal -4 binary64)))
(+ (* -4 (* (sqrt (/ 1 (pow x 3))) (/ 1 (sqrt -4)))) (* (sqrt (/ 1 x)) (sqrt -4)))
(+.f64 (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) (sqrt.f64 #s(literal -4 binary64))) (*.f64 (/.f64 #s(literal -4 binary64) (sqrt.f64 #s(literal -4 binary64))) (sqrt.f64 (/.f64 #s(literal 1 binary64) (*.f64 x (*.f64 x x))))))
(+ (* -8 (* (sqrt (/ 1 (pow x 5))) (/ 1 (sqrt -4)))) (+ (* -4 (* (sqrt (/ 1 (pow x 3))) (/ 1 (sqrt -4)))) (* (sqrt (/ 1 x)) (sqrt -4))))
(+.f64 (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) (sqrt.f64 #s(literal -4 binary64))) (*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 #s(literal -4 binary64))) (+.f64 (*.f64 #s(literal -8 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 5 binary64))))) (*.f64 #s(literal -4 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) (*.f64 x (*.f64 x x))))))))
(+ (* -8 (* (sqrt (/ 1 (pow x 5))) (/ 1 (sqrt -4)))) (+ (* -4 (* (sqrt (/ 1 (pow x 3))) (/ 1 (sqrt -4)))) (+ (* -1/2 (* (sqrt (/ 1 (pow x 7))) (/ (+ 32 (* 16 (/ x (pow (sqrt -4) 2)))) (sqrt -4)))) (* (sqrt (/ 1 x)) (sqrt -4)))))
(+.f64 (+.f64 (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) (sqrt.f64 #s(literal -4 binary64))) (*.f64 (/.f64 (+.f64 #s(literal 32 binary64) (/.f64 (*.f64 x #s(literal 16 binary64)) #s(literal -4 binary64))) (sqrt.f64 #s(literal -4 binary64))) (*.f64 #s(literal -1/2 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 7 binary64))))))) (*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 #s(literal -4 binary64))) (+.f64 (*.f64 #s(literal -8 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 5 binary64))))) (*.f64 #s(literal -4 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) (*.f64 x (*.f64 x x))))))))
(* 2 (* (sqrt (/ 1 x)) (sqrt -1)))
(*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) (*.f64 (sqrt.f64 #s(literal -1 binary64)) #s(literal 2 binary64)))
(+ (* -2 (* (sqrt (/ 1 (pow x 3))) (sqrt -1))) (* 2 (* (sqrt (/ 1 x)) (sqrt -1))))
(*.f64 (sqrt.f64 #s(literal -1 binary64)) (+.f64 (*.f64 #s(literal 2 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) x))) (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (*.f64 x (*.f64 x x)))) #s(literal -2 binary64))))
(+ (* -4 (* (sqrt (/ 1 (pow x 5))) (sqrt -1))) (+ (* -2 (* (sqrt (/ 1 (pow x 3))) (sqrt -1))) (* 2 (* (sqrt (/ 1 x)) (sqrt -1)))))
(*.f64 (sqrt.f64 #s(literal -1 binary64)) (+.f64 (*.f64 #s(literal 2 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) x))) (+.f64 (*.f64 #s(literal -4 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 5 binary64))))) (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (*.f64 x (*.f64 x x)))) #s(literal -2 binary64)))))
(+ (* -2 (* (sqrt (/ 1 (pow x 3))) (sqrt -1))) (+ (* -1 (/ (+ (* 1/4 (* (sqrt (/ 1 x)) (* (sqrt -1) (+ 32 (* -4 x))))) (* 4 (* (sqrt x) (sqrt -1)))) (pow x 3))) (* 2 (* (sqrt (/ 1 x)) (sqrt -1)))))
(-.f64 (*.f64 (sqrt.f64 #s(literal -1 binary64)) (+.f64 (*.f64 #s(literal 2 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) x))) (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (*.f64 x (*.f64 x x)))) #s(literal -2 binary64)))) (/.f64 (*.f64 (sqrt.f64 #s(literal -1 binary64)) (+.f64 (*.f64 (*.f64 #s(literal 1/4 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) x))) (+.f64 #s(literal 32 binary64) (*.f64 x #s(literal -4 binary64)))) (*.f64 (sqrt.f64 x) #s(literal 4 binary64)))) (*.f64 x (*.f64 x x))))
(sqrt 1/2)
(sqrt.f64 #s(literal 1/2 binary64))
(+ (sqrt 1/2) (* -1/8 (/ x (sqrt 1/2))))
(+.f64 (sqrt.f64 #s(literal 1/2 binary64)) (/.f64 (*.f64 x #s(literal -1/8 binary64)) (sqrt.f64 #s(literal 1/2 binary64))))
(+ (sqrt 1/2) (* x (- (* -1/128 (/ x (pow (sqrt 1/2) 3))) (* 1/8 (/ 1 (sqrt 1/2))))))
(+.f64 (sqrt.f64 #s(literal 1/2 binary64)) (*.f64 x (+.f64 (/.f64 (*.f64 #s(literal -1/64 binary64) x) (sqrt.f64 #s(literal 1/2 binary64))) (/.f64 #s(literal -1/8 binary64) (sqrt.f64 #s(literal 1/2 binary64))))))
(+ (sqrt 1/2) (* x (- (* x (- (* -1/1024 (/ x (pow (sqrt 1/2) 5))) (* 1/128 (/ 1 (pow (sqrt 1/2) 3))))) (* 1/8 (/ 1 (sqrt 1/2))))))
(+.f64 (sqrt.f64 #s(literal 1/2 binary64)) (*.f64 x (+.f64 (*.f64 x (+.f64 (/.f64 (*.f64 x #s(literal -1/1024 binary64)) (pow.f64 (sqrt.f64 #s(literal 1/2 binary64)) #s(literal 5 binary64))) (/.f64 #s(literal -1/64 binary64) (sqrt.f64 #s(literal 1/2 binary64))))) (/.f64 #s(literal -1/8 binary64) (sqrt.f64 #s(literal 1/2 binary64))))))
(* (sqrt x) (sqrt -1/4))
(*.f64 (sqrt.f64 x) (sqrt.f64 #s(literal -1/4 binary64)))
(* x (+ (* 1/4 (* (sqrt (/ 1 (pow x 3))) (/ 1 (sqrt -1/4)))) (* (sqrt (/ 1 x)) (sqrt -1/4))))
(*.f64 x (+.f64 (*.f64 #s(literal 1/4 binary64) (/.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (*.f64 x (*.f64 x x)))) (sqrt.f64 #s(literal -1/4 binary64)))) (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) (sqrt.f64 #s(literal -1/4 binary64)))))
(* x (+ (* -1/32 (* (sqrt (/ 1 (pow x 5))) (/ 1 (pow (sqrt -1/4) 3)))) (+ (* 1/4 (* (sqrt (/ 1 (pow x 3))) (/ 1 (sqrt -1/4)))) (* (sqrt (/ 1 x)) (sqrt -1/4)))))
(*.f64 x (+.f64 (*.f64 #s(literal 1/4 binary64) (/.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (*.f64 x (*.f64 x x)))) (sqrt.f64 #s(literal -1/4 binary64)))) (+.f64 (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) (sqrt.f64 #s(literal -1/4 binary64))) (*.f64 (/.f64 #s(literal 1/8 binary64) (sqrt.f64 #s(literal -1/4 binary64))) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 5 binary64))))))))
(* x (+ (* -1/32 (* (sqrt (/ 1 (pow x 5))) (/ 1 (pow (sqrt -1/4) 3)))) (+ (* 1/128 (* (sqrt (/ 1 (pow x 7))) (/ 1 (pow (sqrt -1/4) 5)))) (+ (* 1/4 (* (sqrt (/ 1 (pow x 3))) (/ 1 (sqrt -1/4)))) (* (sqrt (/ 1 x)) (sqrt -1/4))))))
(*.f64 x (+.f64 (+.f64 (*.f64 #s(literal 1/4 binary64) (/.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (*.f64 x (*.f64 x x)))) (sqrt.f64 #s(literal -1/4 binary64)))) (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) (sqrt.f64 #s(literal -1/4 binary64)))) (+.f64 (*.f64 (/.f64 #s(literal 1/8 binary64) (sqrt.f64 #s(literal -1/4 binary64))) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 5 binary64))))) (/.f64 (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 7 binary64)))) #s(literal 1/128 binary64)) (pow.f64 (sqrt.f64 #s(literal -1/4 binary64)) #s(literal 5 binary64))))))
(* -1/2 (* (sqrt x) (sqrt -1)))
(*.f64 (sqrt.f64 #s(literal -1 binary64)) (*.f64 (sqrt.f64 x) #s(literal -1/2 binary64)))
(* -1 (* x (+ (* 1/2 (* (sqrt (/ 1 x)) (sqrt -1))) (* 1/2 (* (sqrt (/ 1 (pow x 3))) (sqrt -1))))))
(*.f64 x (*.f64 #s(literal -1/2 binary64) (*.f64 (sqrt.f64 #s(literal -1 binary64)) (+.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) (sqrt.f64 (/.f64 #s(literal 1 binary64) (*.f64 x (*.f64 x x))))))))
(* -1 (* x (+ (* -1/4 (* (sqrt (/ 1 (pow x 5))) (sqrt -1))) (+ (* 1/2 (* (sqrt (/ 1 x)) (sqrt -1))) (* 1/2 (* (sqrt (/ 1 (pow x 3))) (sqrt -1)))))))
(*.f64 (*.f64 (sqrt.f64 #s(literal -1 binary64)) (+.f64 (*.f64 #s(literal 1/2 binary64) (+.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) (sqrt.f64 (/.f64 #s(literal 1 binary64) (*.f64 x (*.f64 x x)))))) (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 5 binary64)))) #s(literal -1/4 binary64)))) (-.f64 #s(literal 0 binary64) x))
(* -1 (* x (+ (* -1/4 (* (sqrt (/ 1 (pow x 5))) (sqrt -1))) (+ (* 1/4 (* (sqrt (/ 1 (pow x 7))) (sqrt -1))) (+ (* 1/2 (* (sqrt (/ 1 x)) (sqrt -1))) (* 1/2 (* (sqrt (/ 1 (pow x 3))) (sqrt -1))))))))
(-.f64 #s(literal 0 binary64) (*.f64 x (*.f64 (sqrt.f64 #s(literal -1 binary64)) (+.f64 (*.f64 #s(literal 1/2 binary64) (+.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) (sqrt.f64 (/.f64 #s(literal 1 binary64) (*.f64 x (*.f64 x x)))))) (+.f64 (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 5 binary64)))) #s(literal -1/4 binary64)) (*.f64 #s(literal 1/4 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 7 binary64))))))))))
1/2
#s(literal 1/2 binary64)
(+ 1/2 (* -1/4 x))
(+.f64 #s(literal 1/2 binary64) (*.f64 x #s(literal -1/4 binary64)))
(+ 1/2 (* -1/4 x))
(+.f64 #s(literal 1/2 binary64) (*.f64 x #s(literal -1/4 binary64)))
(+ 1/2 (* -1/4 x))
(+.f64 #s(literal 1/2 binary64) (*.f64 x #s(literal -1/4 binary64)))
(* -1/4 x)
(*.f64 x #s(literal -1/4 binary64))
(* x (- (* 1/2 (/ 1 x)) 1/4))
(+.f64 #s(literal 1/2 binary64) (*.f64 x #s(literal -1/4 binary64)))
(* x (- (* 1/2 (/ 1 x)) 1/4))
(+.f64 #s(literal 1/2 binary64) (*.f64 x #s(literal -1/4 binary64)))
(* x (- (* 1/2 (/ 1 x)) 1/4))
(+.f64 #s(literal 1/2 binary64) (*.f64 x #s(literal -1/4 binary64)))
(* -1/4 x)
(*.f64 x #s(literal -1/4 binary64))
(* -1 (* x (- 1/4 (* 1/2 (/ 1 x)))))
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(* (pow x 3) (+ 1/6 (* 1/2 (/ 1 x))))
(*.f64 x (*.f64 x (+.f64 (*.f64 x #s(literal 1/6 binary64)) #s(literal 1/2 binary64))))
(* (pow x 3) (+ 1/6 (+ (* 1/2 (/ 1 x)) (/ 1 (pow x 2)))))
(*.f64 x (+.f64 #s(literal 1 binary64) (*.f64 x (+.f64 (*.f64 x #s(literal 1/6 binary64)) #s(literal 1/2 binary64)))))
(* (pow x 3) (+ 1/6 (+ (* 1/2 (/ 1 x)) (/ 1 (pow x 2)))))
(*.f64 x (+.f64 #s(literal 1 binary64) (*.f64 x (+.f64 (*.f64 x #s(literal 1/6 binary64)) #s(literal 1/2 binary64)))))
(* 1/6 (pow x 3))
(*.f64 x (*.f64 #s(literal 1/6 binary64) (*.f64 x x)))
(* (pow x 3) (+ 1/6 (* 1/2 (/ 1 x))))
(*.f64 x (*.f64 x (+.f64 (*.f64 x #s(literal 1/6 binary64)) #s(literal 1/2 binary64))))
(* -1 (* (pow x 3) (- (* -1 (/ (+ 1/2 (/ 1 x)) x)) 1/6)))
(*.f64 (+.f64 #s(literal -1/6 binary64) (/.f64 (+.f64 #s(literal -1/2 binary64) (/.f64 #s(literal -1 binary64) x)) x)) (-.f64 #s(literal 0 binary64) (*.f64 x (*.f64 x x))))
(* -1 (* (pow x 3) (- (* -1 (/ (+ 1/2 (/ 1 x)) x)) 1/6)))
(*.f64 (+.f64 #s(literal -1/6 binary64) (/.f64 (+.f64 #s(literal -1/2 binary64) (/.f64 #s(literal -1 binary64) x)) x)) (-.f64 #s(literal 0 binary64) (*.f64 x (*.f64 x x))))
1
#s(literal 1 binary64)
(+ 1 (* 1/2 x))
(+.f64 #s(literal 1 binary64) (*.f64 x #s(literal 1/2 binary64)))
(+ 1 (* x (+ 1/2 (* 1/6 x))))
(+.f64 #s(literal 1 binary64) (*.f64 x (+.f64 (*.f64 x #s(literal 1/6 binary64)) #s(literal 1/2 binary64))))
(+ 1 (* x (+ 1/2 (* 1/6 x))))
(+.f64 #s(literal 1 binary64) (*.f64 x (+.f64 (*.f64 x #s(literal 1/6 binary64)) #s(literal 1/2 binary64))))
(* 1/6 (pow x 2))
(*.f64 #s(literal 1/6 binary64) (*.f64 x x))
(* (pow x 2) (+ 1/6 (* 1/2 (/ 1 x))))
(*.f64 x (+.f64 (*.f64 x #s(literal 1/6 binary64)) #s(literal 1/2 binary64)))
(* (pow x 2) (+ 1/6 (+ (* 1/2 (/ 1 x)) (/ 1 (pow x 2)))))
(+.f64 #s(literal 1 binary64) (*.f64 x (+.f64 (*.f64 x #s(literal 1/6 binary64)) #s(literal 1/2 binary64))))
(* (pow x 2) (+ 1/6 (+ (* 1/2 (/ 1 x)) (/ 1 (pow x 2)))))
(+.f64 #s(literal 1 binary64) (*.f64 x (+.f64 (*.f64 x #s(literal 1/6 binary64)) #s(literal 1/2 binary64))))
(* 1/6 (pow x 2))
(*.f64 #s(literal 1/6 binary64) (*.f64 x x))
(* (pow x 2) (+ 1/6 (* 1/2 (/ 1 x))))
(*.f64 x (+.f64 (*.f64 x #s(literal 1/6 binary64)) #s(literal 1/2 binary64)))
(* (pow x 2) (+ 1/6 (+ (* 1/2 (/ 1 x)) (/ 1 (pow x 2)))))
(+.f64 #s(literal 1 binary64) (*.f64 x (+.f64 (*.f64 x #s(literal 1/6 binary64)) #s(literal 1/2 binary64))))
(* (pow x 2) (+ 1/6 (+ (* 1/2 (/ 1 x)) (/ 1 (pow x 2)))))
(+.f64 #s(literal 1 binary64) (*.f64 x (+.f64 (*.f64 x #s(literal 1/6 binary64)) #s(literal 1/2 binary64))))
(* 1/2 x)
(*.f64 x #s(literal 1/2 binary64))
(* x (+ 1/2 (* 1/6 x)))
(*.f64 x (+.f64 (*.f64 x #s(literal 1/6 binary64)) #s(literal 1/2 binary64)))
(* x (+ 1/2 (* 1/6 x)))
(*.f64 x (+.f64 (*.f64 x #s(literal 1/6 binary64)) #s(literal 1/2 binary64)))
(* x (+ 1/2 (* 1/6 x)))
(*.f64 x (+.f64 (*.f64 x #s(literal 1/6 binary64)) #s(literal 1/2 binary64)))
(* 1/6 (pow x 2))
(*.f64 #s(literal 1/6 binary64) (*.f64 x x))
(* (pow x 2) (+ 1/6 (* 1/2 (/ 1 x))))
(*.f64 x (+.f64 (*.f64 x #s(literal 1/6 binary64)) #s(literal 1/2 binary64)))
(* (pow x 2) (+ 1/6 (* 1/2 (/ 1 x))))
(*.f64 x (+.f64 (*.f64 x #s(literal 1/6 binary64)) #s(literal 1/2 binary64)))
(* (pow x 2) (+ 1/6 (* 1/2 (/ 1 x))))
(*.f64 x (+.f64 (*.f64 x #s(literal 1/6 binary64)) #s(literal 1/2 binary64)))
(* 1/6 (pow x 2))
(*.f64 #s(literal 1/6 binary64) (*.f64 x x))
(* (pow x 2) (+ 1/6 (* 1/2 (/ 1 x))))
(*.f64 x (+.f64 (*.f64 x #s(literal 1/6 binary64)) #s(literal 1/2 binary64)))
(* (pow x 2) (+ 1/6 (* 1/2 (/ 1 x))))
(*.f64 x (+.f64 (*.f64 x #s(literal 1/6 binary64)) #s(literal 1/2 binary64)))
(* (pow x 2) (+ 1/6 (* 1/2 (/ 1 x))))
(*.f64 x (+.f64 (*.f64 x #s(literal 1/6 binary64)) #s(literal 1/2 binary64)))

eval92.0ms (1.3%)

Compiler

Compiled 17364 to 2345 computations (86.5% saved)

prune110.0ms (1.5%)

Pruning

14 alts after pruning (4 fresh and 10 done)

PrunedKeptTotal
New7572759
Fresh022
Picked145
Done167
Total75914773
Accuracy
100.0%
Counts
773 → 14
Alt Table
Click to see full alt table
StatusAccuracyProgram
66.2%
(pow.f64 (+.f64 #s(literal 1/2 binary64) (*.f64 x #s(literal -1/4 binary64))) #s(literal -1/2 binary64))
0.2%
(/.f64 #s(literal 1 binary64) (sqrt.f64 (/.f64 (+.f64 #s(literal 6 binary64) (/.f64 #s(literal -18 binary64) x)) (*.f64 x (*.f64 x x)))))
63.0%
(/.f64 #s(literal 1 binary64) (sqrt.f64 (+.f64 #s(literal 1/2 binary64) (*.f64 x (+.f64 #s(literal -1/4 binary64) (*.f64 (*.f64 x x) #s(literal 1/48 binary64)))))))
65.3%
(/.f64 #s(literal 1 binary64) (sqrt.f64 (+.f64 #s(literal 1/2 binary64) (*.f64 x #s(literal -1/4 binary64)))))
69.3%
(/.f64 #s(literal 1 binary64) (sqrt.f64 #s(literal 1/2 binary64)))
2.6%
(*.f64 (sqrt.f64 (+.f64 #s(literal 1/2 binary64) (*.f64 x #s(literal 1/6 binary64)))) x)
1.6%
(*.f64 (sqrt.f64 (*.f64 x #s(literal 1/6 binary64))) x)
2.9%
(*.f64 x (sqrt.f64 #s(literal 1/2 binary64)))
63.5%
(sqrt.f64 (+.f64 #s(literal 2 binary64) x))
100.0%
(sqrt.f64 (+.f64 #s(literal 1 binary64) (exp.f64 x)))
2.3%
(sqrt.f64 (*.f64 x (+.f64 #s(literal 1 binary64) (*.f64 x (+.f64 #s(literal 1/2 binary64) (*.f64 x #s(literal 1/6 binary64)))))))
3.3%
(sqrt.f64 (*.f64 x (*.f64 x (+.f64 #s(literal 1/2 binary64) (*.f64 x #s(literal 1/6 binary64))))))
2.3%
(sqrt.f64 x)
70.2%
(sqrt.f64 #s(literal 2 binary64))
Compiler

Compiled 286 to 161 computations (43.7% saved)

regimes32.0ms (0.4%)

Counts
20 → 1
Calls
Call 1
Inputs
(sqrt.f64 #s(literal 2 binary64))
(sqrt.f64 x)
(sqrt.f64 (+.f64 #s(literal 2 binary64) x))
(*.f64 x (sqrt.f64 #s(literal 1/2 binary64)))
(/.f64 #s(literal 1 binary64) (sqrt.f64 #s(literal 1/2 binary64)))
(*.f64 (sqrt.f64 (*.f64 x #s(literal 1/6 binary64))) x)
(pow.f64 (+.f64 #s(literal 1/2 binary64) (*.f64 x #s(literal -1/4 binary64))) #s(literal -1/2 binary64))
(sqrt.f64 (*.f64 (*.f64 x (*.f64 x x)) #s(literal 1/6 binary64)))
(*.f64 (sqrt.f64 (+.f64 #s(literal 1/2 binary64) (*.f64 x #s(literal 1/6 binary64)))) x)
(/.f64 #s(literal 1 binary64) (sqrt.f64 (+.f64 #s(literal 1/2 binary64) (*.f64 x #s(literal -1/4 binary64)))))
(*.f64 (pow.f64 (+.f64 #s(literal 1/2 binary64) (*.f64 x #s(literal 1/6 binary64))) #s(literal 1/2 binary64)) x)
(sqrt.f64 (*.f64 x (*.f64 x (+.f64 #s(literal 1/2 binary64) (*.f64 x #s(literal 1/6 binary64))))))
(sqrt.f64 (+.f64 #s(literal 2 binary64) (*.f64 x (+.f64 #s(literal 1 binary64) (*.f64 #s(literal 1/2 binary64) x)))))
(sqrt.f64 (*.f64 x (+.f64 #s(literal 1 binary64) (*.f64 x (+.f64 #s(literal 1/2 binary64) (*.f64 x #s(literal 1/6 binary64)))))))
(sqrt.f64 (+.f64 #s(literal 2 binary64) (*.f64 x (+.f64 #s(literal 1 binary64) (*.f64 x (+.f64 #s(literal 1/2 binary64) (*.f64 x #s(literal 1/6 binary64))))))))
(/.f64 #s(literal 1 binary64) (sqrt.f64 (+.f64 #s(literal 1/2 binary64) (*.f64 x (+.f64 #s(literal -1/4 binary64) (*.f64 (*.f64 x x) #s(literal 1/48 binary64)))))))
(/.f64 #s(literal 1 binary64) (sqrt.f64 (/.f64 (+.f64 #s(literal 6 binary64) (/.f64 #s(literal -18 binary64) x)) (*.f64 x (*.f64 x x)))))
(/.f64 #s(literal 1 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) (+.f64 #s(literal 2 binary64) (*.f64 x (+.f64 #s(literal 1 binary64) (*.f64 x (+.f64 #s(literal 1/2 binary64) (*.f64 x #s(literal 1/6 binary64))))))))))
(sqrt.f64 (+.f64 #s(literal 1 binary64) (exp.f64 x)))
(sqrt.f64 (/.f64 (-.f64 (exp.f64 (*.f64 #s(literal 2 binary64) x)) #s(literal 1 binary64)) (-.f64 (exp.f64 x) #s(literal 1 binary64))))
Outputs
(sqrt.f64 (+.f64 #s(literal 1 binary64) (exp.f64 x)))
Calls

3 calls:

19.0ms
(sqrt.f64 (/.f64 (-.f64 (exp.f64 (*.f64 #s(literal 2 binary64) x)) #s(literal 1 binary64)) (-.f64 (exp.f64 x) #s(literal 1 binary64))))
6.0ms
x
5.0ms
(/.f64 (-.f64 (exp.f64 (*.f64 #s(literal 2 binary64) x)) #s(literal 1 binary64)) (-.f64 (exp.f64 x) #s(literal 1 binary64)))
Results
AccuracySegmentsBranch
100.0%1x
100.0%1(sqrt.f64 (/.f64 (-.f64 (exp.f64 (*.f64 #s(literal 2 binary64) x)) #s(literal 1 binary64)) (-.f64 (exp.f64 x) #s(literal 1 binary64))))
100.0%1(/.f64 (-.f64 (exp.f64 (*.f64 #s(literal 2 binary64) x)) #s(literal 1 binary64)) (-.f64 (exp.f64 x) #s(literal 1 binary64)))
Compiler

Compiled 27 to 20 computations (25.9% saved)

regimes6.0ms (0.1%)

Accuracy

Total -44.9b remaining (-235.9%)

Threshold costs -44.9b (-235.9%)

Counts
18 → 1
Calls
Call 1
Inputs
(sqrt.f64 #s(literal 2 binary64))
(sqrt.f64 x)
(sqrt.f64 (+.f64 #s(literal 2 binary64) x))
(*.f64 x (sqrt.f64 #s(literal 1/2 binary64)))
(/.f64 #s(literal 1 binary64) (sqrt.f64 #s(literal 1/2 binary64)))
(*.f64 (sqrt.f64 (*.f64 x #s(literal 1/6 binary64))) x)
(pow.f64 (+.f64 #s(literal 1/2 binary64) (*.f64 x #s(literal -1/4 binary64))) #s(literal -1/2 binary64))
(sqrt.f64 (*.f64 (*.f64 x (*.f64 x x)) #s(literal 1/6 binary64)))
(*.f64 (sqrt.f64 (+.f64 #s(literal 1/2 binary64) (*.f64 x #s(literal 1/6 binary64)))) x)
(/.f64 #s(literal 1 binary64) (sqrt.f64 (+.f64 #s(literal 1/2 binary64) (*.f64 x #s(literal -1/4 binary64)))))
(*.f64 (pow.f64 (+.f64 #s(literal 1/2 binary64) (*.f64 x #s(literal 1/6 binary64))) #s(literal 1/2 binary64)) x)
(sqrt.f64 (*.f64 x (*.f64 x (+.f64 #s(literal 1/2 binary64) (*.f64 x #s(literal 1/6 binary64))))))
(sqrt.f64 (+.f64 #s(literal 2 binary64) (*.f64 x (+.f64 #s(literal 1 binary64) (*.f64 #s(literal 1/2 binary64) x)))))
(sqrt.f64 (*.f64 x (+.f64 #s(literal 1 binary64) (*.f64 x (+.f64 #s(literal 1/2 binary64) (*.f64 x #s(literal 1/6 binary64)))))))
(sqrt.f64 (+.f64 #s(literal 2 binary64) (*.f64 x (+.f64 #s(literal 1 binary64) (*.f64 x (+.f64 #s(literal 1/2 binary64) (*.f64 x #s(literal 1/6 binary64))))))))
(/.f64 #s(literal 1 binary64) (sqrt.f64 (+.f64 #s(literal 1/2 binary64) (*.f64 x (+.f64 #s(literal -1/4 binary64) (*.f64 (*.f64 x x) #s(literal 1/48 binary64)))))))
(/.f64 #s(literal 1 binary64) (sqrt.f64 (/.f64 (+.f64 #s(literal 6 binary64) (/.f64 #s(literal -18 binary64) x)) (*.f64 x (*.f64 x x)))))
(/.f64 #s(literal 1 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) (+.f64 #s(literal 2 binary64) (*.f64 x (+.f64 #s(literal 1 binary64) (*.f64 x (+.f64 #s(literal 1/2 binary64) (*.f64 x #s(literal 1/6 binary64))))))))))
Outputs
(sqrt.f64 #s(literal 2 binary64))
Calls

1 calls:

5.0ms
x
Results
AccuracySegmentsBranch
70.2%1x
Compiler

Compiled 2 to 1 computations (50% saved)

simplify8.0ms (0.1%)

Algorithm
egg-herbie
Rules
+-commutative_binary64
1-exp_binary64
1-exp_binary32
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
077
1117
Stop Event
saturated
Calls
Call 1
Inputs
(sqrt.f64 (+.f64 #s(literal 1 binary64) (exp.f64 x)))
(sqrt.f64 #s(literal 2 binary64))
Outputs
(sqrt.f64 (+.f64 #s(literal 1 binary64) (exp.f64 x)))
(sqrt.f64 #s(literal 2 binary64))

soundness503.0ms (6.9%)

Rules
3346×*-lowering-*.f32
3346×*-lowering-*.f64
2108×*-lowering-*.f32
2108×*-lowering-*.f64
1870×+-lowering-+.f64
Iterations

Useful iterations: 5 (0.0ms)

IterNodesCost
052221
1162175
2539174
31189171
42839170
56888170
08224170
0108
1248
2318
3458
4767
51415
63015
78525
849845
082455
Stop Event
fuel
iter limit
node limit
iter limit
node limit
Compiler

Compiled 23 to 20 computations (13% saved)

preprocess25.0ms (0.3%)

Compiler

Compiled 42 to 34 computations (19% saved)

end0.0ms (0%)

Profiling

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