bug333 (missed optimization)

Time bar (total: 9.9s)

analyze0.0ms (0%)

Algorithm
search
Search
ProbabilityValidUnknownPreconditionInfiniteDomainCan'tIter
0%0%50%50%0%0%0%0
100%50%0%50%0%0%0%1
Compiler

Compiled 17 to 11 computations (35.3% saved)

Precisions
Click to see histograms. Total time spent on operations: 0.0ms
ival-sub: 0.0ms (0% of total)
ival-add: 0.0ms (0% of total)
ival-and: 0.0ms (0% of total)
const: 0.0ms (0% of total)
ival-sqrt: 0.0ms (0% of total)
backward-pass: 0.0ms (0% of total)
ival-<=: 0.0ms (0% of total)

sample2.1s (20.9%)

Results
1.7s8068×1valid
12.0ms188×0valid
Precisions
Click to see histograms. Total time spent on operations: 1.4s
ival-sub: 498.0ms (36.7% of total)
ival-sqrt: 368.0ms (27.2% of total)
ival-add: 160.0ms (11.8% of total)
backward-pass: 147.0ms (10.8% of total)
ival-<=: 144.0ms (10.6% of total)
ival-and: 21.0ms (1.5% of total)
const: 17.0ms (1.3% of total)
Bogosity

preprocess36.0ms (0.4%)

Algorithm
egg-herbie
Rules
200×fnmadd-define
172×fmsub-define
168×fnmsub-define
166×sum3-define
156×sum3-define
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
01428
13127
26227
313227
426427
548027
667727
778127
878727
079
1149
2219
3349
4529
5979
61709
72719
83729
94809
105589
115649
05649
Stop Event
iter limit
saturated
saturated
Calls
Call 1
Inputs
(- (sqrt (+ 1 x)) (sqrt (- 1 x)))
Outputs
(- (sqrt (+ 1 x)) (sqrt (- 1 x)))
(-.f64 (sqrt.f64 (+.f64 #s(literal 1 binary64) x)) (sqrt.f64 (-.f64 #s(literal 1 binary64) x)))
Call 2
Inputs
(- (sqrt (+ 1 x)) (sqrt (- 1 x)))
(- (sqrt (+ 1 (neg x))) (sqrt (- 1 (neg x))))
(neg (- (sqrt (+ 1 (neg x))) (sqrt (- 1 (neg x)))))
Outputs
(- (sqrt (+ 1 x)) (sqrt (- 1 x)))
(- (sqrt (+ 1 (neg x))) (sqrt (- 1 (neg x))))
(- (sqrt (- 1 x)) (sqrt (+ 1 x)))
(neg (- (sqrt (+ 1 (neg x))) (sqrt (- 1 (neg x)))))
(- (sqrt (+ 1 x)) (sqrt (- 1 x)))
Symmetry

(negabs x)

explain147.0ms (1.5%)

FPErrors
Click to see full error table
Ground TruthOverpredictionsExampleUnderpredictionsExampleSubexpression
2550-0-(-.f64 (sqrt.f64 (+.f64 #s(literal 1 binary64) x)) (sqrt.f64 (-.f64 #s(literal 1 binary64) x)))
00-0-x
00-0-(sqrt.f64 (-.f64 #s(literal 1 binary64) x))
00-0-#s(literal 1 binary64)
00-0-(-.f64 #s(literal 1 binary64) x)
00-0-(sqrt.f64 (+.f64 #s(literal 1 binary64) x))
00-0-(+.f64 #s(literal 1 binary64) x)
Results
105.0ms504×1valid
1.0ms0valid
Compiler

Compiled 64 to 23 computations (64.1% saved)

Precisions
Click to see histograms. Total time spent on operations: 51.0ms
ival-sqrt: 20.0ms (38.9% of total)
ival-sub: 14.0ms (27.2% of total)
backward-pass: 9.0ms (17.5% of total)
ival-add: 7.0ms (13.6% of total)
const: 1.0ms (1.9% of total)

eval0.0ms (0%)

Compiler

Compiled 10 to 7 computations (30% saved)

prune1.0ms (0%)

Alt Table
Click to see full alt table
StatusAccuracyProgram
7.7%
(-.f64 (sqrt.f64 (+.f64 #s(literal 1 binary64) x)) (sqrt.f64 (-.f64 #s(literal 1 binary64) x)))
Compiler

Compiled 10 to 7 computations (30% saved)

simplify20.0ms (0.2%)

Algorithm
egg-herbie
Localize:

Found 4 expressions of interest:

NewMetricScoreProgram
cost-diff0
(sqrt.f64 (-.f64 #s(literal 1 binary64) x))
cost-diff0
(+.f64 #s(literal 1 binary64) x)
cost-diff0
(sqrt.f64 (+.f64 #s(literal 1 binary64) x))
cost-diff0
(-.f64 (sqrt.f64 (+.f64 #s(literal 1 binary64) x)) (sqrt.f64 (-.f64 #s(literal 1 binary64) x)))
Rules
166×sum3-define
124×fnmadd-define
92×fma-lowering-fma.f32
92×fmsub-define
92×fma-lowering-fma.f64
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
0725
11425
22125
33425
45225
59725
617025
727125
837225
948025
1055825
1156425
056425
Stop Event
iter limit
saturated
Calls
Call 1
Inputs
(- (sqrt (+ 1 x)) (sqrt (- 1 x)))
(sqrt (+ 1 x))
(+ 1 x)
1
x
(sqrt (- 1 x))
(- 1 x)
Outputs
(- (sqrt (+ 1 x)) (sqrt (- 1 x)))
(-.f64 (sqrt.f64 (+.f64 #s(literal 1 binary64) x)) (sqrt.f64 (-.f64 #s(literal 1 binary64) x)))
(sqrt (+ 1 x))
(sqrt.f64 (+.f64 #s(literal 1 binary64) x))
(+ 1 x)
(+.f64 #s(literal 1 binary64) x)
1
#s(literal 1 binary64)
x
(sqrt (- 1 x))
(sqrt.f64 (-.f64 #s(literal 1 binary64) x))
(- 1 x)
(-.f64 #s(literal 1 binary64) x)

localize76.0ms (0.8%)

Localize:

Found 4 expressions of interest:

NewMetricScoreProgram
accuracy100.0%
(+.f64 #s(literal 1 binary64) x)
accuracy100.0%
(sqrt.f64 (-.f64 #s(literal 1 binary64) x))
accuracy100.0%
(sqrt.f64 (+.f64 #s(literal 1 binary64) x))
accuracy7.7%
(-.f64 (sqrt.f64 (+.f64 #s(literal 1 binary64) x)) (sqrt.f64 (-.f64 #s(literal 1 binary64) x)))
Results
65.0ms252×1valid
0.0ms0valid
Compiler

Compiled 27 to 8 computations (70.4% saved)

Precisions
Click to see histograms. Total time spent on operations: 47.0ms
ival-add: 27.0ms (57.6% of total)
ival-sqrt: 8.0ms (17.1% of total)
ival-sub: 6.0ms (12.8% of total)
backward-pass: 4.0ms (8.5% of total)
const: 1.0ms (2.1% of total)

series5.0ms (0.1%)

Counts
4 → 48
Calls
Call 1
Inputs
#<alt (- (sqrt (+ 1 x)) (sqrt (- 1 x)))>
#<alt (sqrt (+ 1 x))>
#<alt (+ 1 x)>
#<alt (sqrt (- 1 x))>
Outputs
#<alt x>
#<alt (* x (+ 1 (* 1/8 (pow x 2))))>
#<alt (* x (+ 1 (* (pow x 2) (+ 1/8 (* 7/128 (pow x 2))))))>
#<alt (* x (+ 1 (* (pow x 2) (+ 1/8 (* (pow x 2) (+ 7/128 (* 33/1024 (pow x 2))))))))>
#<alt (* x (- (sqrt (/ 1 x)) (* (sqrt (/ 1 x)) (sqrt -1))))>
#<alt (* x (- (+ (sqrt (/ 1 x)) (* 1/2 (sqrt (/ 1 (pow x 3))))) (+ (* 1/2 (* (sqrt (/ 1 (pow x 3))) (/ 1 (sqrt -1)))) (* (sqrt (/ 1 x)) (sqrt -1)))))>
#<alt (* x (- (+ (sqrt (/ 1 x)) (+ (* -1/8 (sqrt (/ 1 (pow x 5)))) (* 1/2 (sqrt (/ 1 (pow x 3)))))) (+ (* -1/8 (* (sqrt (/ 1 (pow x 5))) (/ 1 (pow (sqrt -1) 3)))) (+ (* 1/2 (* (sqrt (/ 1 (pow x 3))) (/ 1 (sqrt -1)))) (* (sqrt (/ 1 x)) (sqrt -1))))))>
#<alt (* x (- (+ (sqrt (/ 1 x)) (+ (* -1/8 (sqrt (/ 1 (pow x 5)))) (+ (* 1/16 (sqrt (/ 1 (pow x 7)))) (* 1/2 (sqrt (/ 1 (pow x 3))))))) (+ (* -1/8 (* (sqrt (/ 1 (pow x 5))) (/ 1 (pow (sqrt -1) 3)))) (+ (* 1/16 (* (sqrt (/ 1 (pow x 7))) (/ 1 (pow (sqrt -1) 5)))) (+ (* 1/2 (* (sqrt (/ 1 (pow x 3))) (/ 1 (sqrt -1)))) (* (sqrt (/ 1 x)) (sqrt -1)))))))>
#<alt (* -1 (* x (- (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)) (* (sqrt (/ 1 x)) (sqrt -1)))))>
#<alt (* -1 (* x (- (+ (* 1/2 (sqrt (/ 1 (pow x 3)))) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))) (+ (* 1/2 (* (sqrt (/ 1 (pow x 3))) (sqrt -1))) (* (sqrt (/ 1 x)) (sqrt -1))))))>
#<alt (* -1 (* x (- (+ (* -1/8 (* (sqrt (/ 1 (pow x 5))) (/ 1 (pow (sqrt -1) 2)))) (+ (* 1/2 (sqrt (/ 1 (pow x 3)))) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)))) (+ (* -1/8 (* (sqrt (/ 1 (pow x 5))) (sqrt -1))) (+ (* 1/2 (* (sqrt (/ 1 (pow x 3))) (sqrt -1))) (* (sqrt (/ 1 x)) (sqrt -1)))))))>
#<alt (* -1 (* x (- (+ (* -1/8 (* (sqrt (/ 1 (pow x 5))) (/ 1 (pow (sqrt -1) 2)))) (+ (* 1/16 (* (sqrt (/ 1 (pow x 7))) (/ 1 (pow (sqrt -1) 4)))) (+ (* 1/2 (sqrt (/ 1 (pow x 3)))) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))))) (+ (* -1/8 (* (sqrt (/ 1 (pow x 5))) (sqrt -1))) (+ (* 1/16 (* (sqrt (/ 1 (pow x 7))) (sqrt -1))) (+ (* 1/2 (* (sqrt (/ 1 (pow x 3))) (sqrt -1))) (* (sqrt (/ 1 x)) (sqrt -1))))))))>
#<alt 1>
#<alt (+ 1 (* 1/2 x))>
#<alt (+ 1 (* x (+ 1/2 (* -1/8 x))))>
#<alt (+ 1 (* x (+ 1/2 (* x (- (* 1/16 x) 1/8)))))>
#<alt (sqrt x)>
#<alt (* x (+ (sqrt (/ 1 x)) (* 1/2 (sqrt (/ 1 (pow x 3))))))>
#<alt (* x (+ (sqrt (/ 1 x)) (+ (* -1/8 (sqrt (/ 1 (pow x 5)))) (* 1/2 (sqrt (/ 1 (pow x 3)))))))>
#<alt (* x (+ (sqrt (/ 1 x)) (+ (* -1/8 (sqrt (/ 1 (pow x 5)))) (+ (* 1/16 (sqrt (/ 1 (pow x 7)))) (* 1/2 (sqrt (/ 1 (pow x 3))))))))>
#<alt (* -1 (* (sqrt x) (pow (sqrt -1) 2)))>
#<alt (* -1 (* x (+ (* 1/2 (sqrt (/ 1 (pow x 3)))) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)))))>
#<alt (* -1 (* x (+ (* -1/8 (* (sqrt (/ 1 (pow x 5))) (/ 1 (pow (sqrt -1) 2)))) (+ (* 1/2 (sqrt (/ 1 (pow x 3)))) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))))))>
#<alt (* -1 (* x (+ (* -1/8 (* (sqrt (/ 1 (pow x 5))) (/ 1 (pow (sqrt -1) 2)))) (+ (* 1/16 (* (sqrt (/ 1 (pow x 7))) (/ 1 (pow (sqrt -1) 4)))) (+ (* 1/2 (sqrt (/ 1 (pow x 3)))) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)))))))>
#<alt 1>
#<alt (+ 1 x)>
#<alt (+ 1 x)>
#<alt (+ 1 x)>
#<alt x>
#<alt (* x (+ 1 (/ 1 x)))>
#<alt (* x (+ 1 (/ 1 x)))>
#<alt (* x (+ 1 (/ 1 x)))>
#<alt x>
#<alt (* x (+ 1 (/ 1 x)))>
#<alt (* x (+ 1 (/ 1 x)))>
#<alt (* x (+ 1 (/ 1 x)))>
#<alt 1>
#<alt (+ 1 (* -1/2 x))>
#<alt (+ 1 (* x (- (* -1/8 x) 1/2)))>
#<alt (+ 1 (* x (- (* x (- (* -1/16 x) 1/8)) 1/2)))>
#<alt (* (sqrt x) (sqrt -1))>
#<alt (* x (+ (* 1/2 (* (sqrt (/ 1 (pow x 3))) (/ 1 (sqrt -1)))) (* (sqrt (/ 1 x)) (sqrt -1))))>
#<alt (* x (+ (* -1/8 (* (sqrt (/ 1 (pow x 5))) (/ 1 (pow (sqrt -1) 3)))) (+ (* 1/2 (* (sqrt (/ 1 (pow x 3))) (/ 1 (sqrt -1)))) (* (sqrt (/ 1 x)) (sqrt -1)))))>
#<alt (* x (+ (* -1/8 (* (sqrt (/ 1 (pow x 5))) (/ 1 (pow (sqrt -1) 3)))) (+ (* 1/16 (* (sqrt (/ 1 (pow x 7))) (/ 1 (pow (sqrt -1) 5)))) (+ (* 1/2 (* (sqrt (/ 1 (pow x 3))) (/ 1 (sqrt -1)))) (* (sqrt (/ 1 x)) (sqrt -1))))))>
#<alt (* -1 (* (sqrt x) (sqrt -1)))>
#<alt (* -1 (* x (+ (* 1/2 (* (sqrt (/ 1 (pow x 3))) (sqrt -1))) (* (sqrt (/ 1 x)) (sqrt -1)))))>
#<alt (* -1 (* x (+ (* -1/8 (* (sqrt (/ 1 (pow x 5))) (sqrt -1))) (+ (* 1/2 (* (sqrt (/ 1 (pow x 3))) (sqrt -1))) (* (sqrt (/ 1 x)) (sqrt -1))))))>
#<alt (* -1 (* x (+ (* -1/8 (* (sqrt (/ 1 (pow x 5))) (sqrt -1))) (+ (* 1/16 (* (sqrt (/ 1 (pow x 7))) (sqrt -1))) (+ (* 1/2 (* (sqrt (/ 1 (pow x 3))) (sqrt -1))) (* (sqrt (/ 1 x)) (sqrt -1)))))))>
Calls

12 calls:

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

rewrite285.0ms (2.9%)

Algorithm
batch-egg-rewrite
Rules
3064×*-lowering-*.f32
3064×*-lowering-*.f64
2554×/-lowering-/.f32
2554×/-lowering-/.f64
1828×sum3-define
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
0720
14620
238920
3620920
0843520
Stop Event
iter limit
node limit
Counts
4 → 244
Calls
Call 1
Inputs
(- (sqrt (+ 1 x)) (sqrt (- 1 x)))
(sqrt (+ 1 x))
(+ 1 x)
(sqrt (- 1 x))
Outputs
(+.f64 (pow.f64 (+.f64 #s(literal 1 binary64) x) #s(literal 1/2 binary64)) (-.f64 #s(literal 0 binary64) (pow.f64 (-.f64 #s(literal 1 binary64) x) #s(literal 1/2 binary64))))
(+.f64 (-.f64 (pow.f64 (+.f64 #s(literal 1 binary64) x) #s(literal 1/2 binary64)) (pow.f64 (-.f64 #s(literal 1 binary64) x) #s(literal 1/2 binary64))) (fma.f64 (neg.f64 (pow.f64 (-.f64 #s(literal 1 binary64) x) #s(literal 1/4 binary64))) (pow.f64 (-.f64 #s(literal 1 binary64) x) #s(literal 1/4 binary64)) (pow.f64 (-.f64 #s(literal 1 binary64) x) #s(literal 1/2 binary64))))
(+.f64 (-.f64 #s(literal 0 binary64) (pow.f64 (-.f64 #s(literal 1 binary64) x) #s(literal 1/2 binary64))) (pow.f64 (+.f64 #s(literal 1 binary64) x) #s(literal 1/2 binary64)))
(+.f64 (/.f64 (pow.f64 (+.f64 #s(literal 1 binary64) x) #s(literal 3/2 binary64)) (+.f64 (sqrt.f64 (*.f64 (+.f64 #s(literal 1 binary64) x) (-.f64 #s(literal 1 binary64) x))) (+.f64 #s(literal 1 binary64) (+.f64 x (-.f64 #s(literal 1 binary64) x))))) (neg.f64 (/.f64 (pow.f64 (-.f64 #s(literal 1 binary64) x) #s(literal 3/2 binary64)) (+.f64 (sqrt.f64 (*.f64 (+.f64 #s(literal 1 binary64) x) (-.f64 #s(literal 1 binary64) x))) (+.f64 #s(literal 1 binary64) (+.f64 x (-.f64 #s(literal 1 binary64) x)))))))
(+.f64 (/.f64 (+.f64 #s(literal 1 binary64) x) (+.f64 (pow.f64 (+.f64 #s(literal 1 binary64) x) #s(literal 1/2 binary64)) (pow.f64 (-.f64 #s(literal 1 binary64) x) #s(literal 1/2 binary64)))) (neg.f64 (/.f64 (-.f64 #s(literal 1 binary64) x) (+.f64 (pow.f64 (+.f64 #s(literal 1 binary64) x) #s(literal 1/2 binary64)) (pow.f64 (-.f64 #s(literal 1 binary64) x) #s(literal 1/2 binary64))))))
(-.f64 (pow.f64 (+.f64 #s(literal 1 binary64) x) #s(literal 1/2 binary64)) (pow.f64 (-.f64 #s(literal 1 binary64) x) #s(literal 1/2 binary64)))
(-.f64 #s(literal 0 binary64) (-.f64 (pow.f64 (-.f64 #s(literal 1 binary64) x) #s(literal 1/2 binary64)) (pow.f64 (+.f64 #s(literal 1 binary64) x) #s(literal 1/2 binary64))))
(-.f64 (/.f64 (pow.f64 (+.f64 #s(literal 1 binary64) x) #s(literal 3/2 binary64)) (+.f64 (sqrt.f64 (*.f64 (+.f64 #s(literal 1 binary64) x) (-.f64 #s(literal 1 binary64) x))) (+.f64 #s(literal 1 binary64) (+.f64 x (-.f64 #s(literal 1 binary64) x))))) (/.f64 (pow.f64 (-.f64 #s(literal 1 binary64) x) #s(literal 3/2 binary64)) (+.f64 (sqrt.f64 (*.f64 (+.f64 #s(literal 1 binary64) x) (-.f64 #s(literal 1 binary64) x))) (+.f64 #s(literal 1 binary64) (+.f64 x (-.f64 #s(literal 1 binary64) x))))))
(-.f64 (/.f64 (+.f64 #s(literal 1 binary64) x) (+.f64 (pow.f64 (+.f64 #s(literal 1 binary64) x) #s(literal 1/2 binary64)) (pow.f64 (-.f64 #s(literal 1 binary64) x) #s(literal 1/2 binary64)))) (/.f64 (-.f64 #s(literal 1 binary64) x) (+.f64 (pow.f64 (+.f64 #s(literal 1 binary64) x) #s(literal 1/2 binary64)) (pow.f64 (-.f64 #s(literal 1 binary64) x) #s(literal 1/2 binary64)))))
(-.f64 (+.f64 (pow.f64 (+.f64 #s(literal 1 binary64) x) #s(literal 1/2 binary64)) #s(literal 0 binary64)) (pow.f64 (-.f64 #s(literal 1 binary64) x) #s(literal 1/2 binary64)))
(fma.f64 #s(literal -1 binary64) (pow.f64 (-.f64 #s(literal 1 binary64) x) #s(literal 1/2 binary64)) (pow.f64 (+.f64 #s(literal 1 binary64) x) #s(literal 1/2 binary64)))
(fma.f64 (pow.f64 (+.f64 #s(literal 1 binary64) x) #s(literal 1/4 binary64)) (pow.f64 (+.f64 #s(literal 1 binary64) x) #s(literal 1/4 binary64)) (-.f64 #s(literal 0 binary64) (pow.f64 (-.f64 #s(literal 1 binary64) x) #s(literal 1/2 binary64))))
(neg.f64 (/.f64 (-.f64 (pow.f64 (+.f64 #s(literal 1 binary64) x) #s(literal 3/2 binary64)) (pow.f64 (-.f64 #s(literal 1 binary64) x) #s(literal 3/2 binary64))) (-.f64 #s(literal 0 binary64) (+.f64 (sqrt.f64 (*.f64 (+.f64 #s(literal 1 binary64) x) (-.f64 #s(literal 1 binary64) x))) (+.f64 #s(literal 1 binary64) (+.f64 x (-.f64 #s(literal 1 binary64) x)))))))
(neg.f64 (/.f64 (+.f64 #s(literal 1 binary64) (-.f64 x (-.f64 #s(literal 1 binary64) x))) (-.f64 #s(literal 0 binary64) (+.f64 (pow.f64 (+.f64 #s(literal 1 binary64) x) #s(literal 1/2 binary64)) (pow.f64 (-.f64 #s(literal 1 binary64) x) #s(literal 1/2 binary64))))))
(neg.f64 (/.f64 (-.f64 #s(literal 0 binary64) (-.f64 (pow.f64 (+.f64 #s(literal 1 binary64) x) #s(literal 3/2 binary64)) (pow.f64 (-.f64 #s(literal 1 binary64) x) #s(literal 3/2 binary64)))) (+.f64 (sqrt.f64 (*.f64 (+.f64 #s(literal 1 binary64) x) (-.f64 #s(literal 1 binary64) x))) (+.f64 #s(literal 1 binary64) (+.f64 x (-.f64 #s(literal 1 binary64) x))))))
(neg.f64 (/.f64 (+.f64 (+.f64 (-.f64 #s(literal 0 binary64) x) #s(literal -1 binary64)) (-.f64 #s(literal 1 binary64) x)) (+.f64 (pow.f64 (+.f64 #s(literal 1 binary64) x) #s(literal 1/2 binary64)) (pow.f64 (-.f64 #s(literal 1 binary64) x) #s(literal 1/2 binary64)))))
(/.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (-.f64 (pow.f64 (+.f64 #s(literal 1 binary64) x) #s(literal 1/2 binary64)) (pow.f64 (-.f64 #s(literal 1 binary64) x) #s(literal 1/2 binary64)))))
(/.f64 #s(literal 1 binary64) (/.f64 (/.f64 #s(literal 1 binary64) (-.f64 (pow.f64 (+.f64 #s(literal 1 binary64) x) #s(literal 1/2 binary64)) (pow.f64 (-.f64 #s(literal 1 binary64) x) #s(literal 1/2 binary64)))) #s(literal 1 binary64)))
(/.f64 #s(literal 1 binary64) (/.f64 (+.f64 (+.f64 #s(literal 1 binary64) x) (-.f64 (-.f64 #s(literal 1 binary64) x) (neg.f64 (sqrt.f64 (*.f64 (+.f64 #s(literal 1 binary64) x) (-.f64 #s(literal 1 binary64) x)))))) (-.f64 (pow.f64 (+.f64 #s(literal 1 binary64) x) #s(literal 3/2 binary64)) (pow.f64 (-.f64 #s(literal 1 binary64) x) #s(literal 3/2 binary64)))))
(/.f64 (-.f64 (pow.f64 (+.f64 #s(literal 1 binary64) x) #s(literal 3/2 binary64)) (pow.f64 (-.f64 #s(literal 1 binary64) x) #s(literal 3/2 binary64))) (+.f64 (sqrt.f64 (*.f64 (+.f64 #s(literal 1 binary64) x) (-.f64 #s(literal 1 binary64) x))) (+.f64 #s(literal 1 binary64) (+.f64 x (-.f64 #s(literal 1 binary64) x)))))
(/.f64 (-.f64 (pow.f64 (+.f64 #s(literal 1 binary64) x) #s(literal 3/2 binary64)) (pow.f64 (-.f64 #s(literal 1 binary64) x) #s(literal 3/2 binary64))) (+.f64 (+.f64 #s(literal 1 binary64) x) (-.f64 (-.f64 #s(literal 1 binary64) x) (neg.f64 (sqrt.f64 (*.f64 (+.f64 #s(literal 1 binary64) x) (-.f64 #s(literal 1 binary64) x)))))))
(/.f64 (-.f64 (pow.f64 (+.f64 #s(literal 1 binary64) x) #s(literal 3/2 binary64)) (pow.f64 (-.f64 #s(literal 1 binary64) x) #s(literal 3/2 binary64))) (+.f64 (-.f64 #s(literal 1 binary64) x) (-.f64 (+.f64 #s(literal 1 binary64) x) (neg.f64 (sqrt.f64 (*.f64 (+.f64 #s(literal 1 binary64) x) (-.f64 #s(literal 1 binary64) x)))))))
(/.f64 (+.f64 #s(literal 1 binary64) (-.f64 x (-.f64 #s(literal 1 binary64) x))) (+.f64 (pow.f64 (+.f64 #s(literal 1 binary64) x) #s(literal 1/2 binary64)) (pow.f64 (-.f64 #s(literal 1 binary64) x) #s(literal 1/2 binary64))))
(/.f64 (-.f64 #s(literal 0 binary64) (-.f64 (pow.f64 (+.f64 #s(literal 1 binary64) x) #s(literal 3/2 binary64)) (pow.f64 (-.f64 #s(literal 1 binary64) x) #s(literal 3/2 binary64)))) (-.f64 #s(literal 0 binary64) (+.f64 (sqrt.f64 (*.f64 (+.f64 #s(literal 1 binary64) x) (-.f64 #s(literal 1 binary64) x))) (+.f64 #s(literal 1 binary64) (+.f64 x (-.f64 #s(literal 1 binary64) x))))))
(/.f64 (-.f64 #s(literal 0 binary64) (-.f64 (pow.f64 (+.f64 #s(literal 1 binary64) x) #s(literal 3/2 binary64)) (pow.f64 (-.f64 #s(literal 1 binary64) x) #s(literal 3/2 binary64)))) (neg.f64 (+.f64 (+.f64 #s(literal 1 binary64) x) (-.f64 (-.f64 #s(literal 1 binary64) x) (neg.f64 (sqrt.f64 (*.f64 (+.f64 #s(literal 1 binary64) x) (-.f64 #s(literal 1 binary64) x))))))))
(/.f64 (+.f64 (+.f64 (-.f64 #s(literal 0 binary64) x) #s(literal -1 binary64)) (-.f64 #s(literal 1 binary64) x)) (-.f64 #s(literal 0 binary64) (+.f64 (pow.f64 (+.f64 #s(literal 1 binary64) x) #s(literal 1/2 binary64)) (pow.f64 (-.f64 #s(literal 1 binary64) x) #s(literal 1/2 binary64)))))
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(/.f64 (sqrt.f64 (-.f64 #s(literal 0 binary64) (-.f64 #s(literal 1 binary64) (*.f64 x (*.f64 x x))))) (sqrt.f64 (-.f64 #s(literal 0 binary64) (+.f64 #s(literal 1 binary64) (*.f64 x (+.f64 #s(literal 1 binary64) x))))))
(/.f64 (sqrt.f64 (+.f64 #s(literal -1 binary64) (*.f64 x x))) (sqrt.f64 (+.f64 (-.f64 #s(literal 0 binary64) x) #s(literal -1 binary64))))
(/.f64 (neg.f64 (pow.f64 (-.f64 #s(literal 1 binary64) (*.f64 x (*.f64 x x))) #s(literal 1/2 binary64))) (neg.f64 (sqrt.f64 (+.f64 #s(literal 1 binary64) (*.f64 x (+.f64 #s(literal 1 binary64) x))))))
(/.f64 (neg.f64 (pow.f64 (-.f64 #s(literal 1 binary64) (*.f64 x x)) #s(literal 1/2 binary64))) (neg.f64 (pow.f64 (+.f64 #s(literal 1 binary64) x) #s(literal 1/2 binary64))))
(/.f64 (/.f64 (pow.f64 (-.f64 #s(literal 1 binary64) (*.f64 x x)) #s(literal 1/2 binary64)) (pow.f64 (+.f64 #s(literal 1 binary64) x) #s(literal 1/4 binary64))) (pow.f64 (+.f64 #s(literal 1 binary64) x) #s(literal 1/4 binary64)))
(pow.f64 (-.f64 #s(literal 1 binary64) x) #s(literal 1/2 binary64))
(pow.f64 (pow.f64 (-.f64 #s(literal 1 binary64) x) #s(literal 1/2 binary64)) #s(literal 1 binary64))
(pow.f64 (*.f64 (-.f64 #s(literal 1 binary64) x) (-.f64 #s(literal 1 binary64) x)) #s(literal 1/4 binary64))
(pow.f64 (pow.f64 (-.f64 #s(literal 1 binary64) x) #s(literal 1/4 binary64)) #s(literal 2 binary64))
(*.f64 #s(literal 1 binary64) (pow.f64 (-.f64 #s(literal 1 binary64) x) #s(literal 1/2 binary64)))
(*.f64 (pow.f64 (-.f64 #s(literal 1 binary64) (*.f64 x (*.f64 x x))) #s(literal 1/2 binary64)) (pow.f64 (/.f64 #s(literal 1 binary64) (+.f64 #s(literal 1 binary64) (*.f64 x (+.f64 #s(literal 1 binary64) x)))) #s(literal 1/2 binary64)))
(*.f64 (pow.f64 (-.f64 #s(literal 1 binary64) (*.f64 x (*.f64 x x))) #s(literal 1/2 binary64)) (sqrt.f64 (/.f64 #s(literal 1 binary64) (+.f64 #s(literal 1 binary64) (*.f64 x (+.f64 #s(literal 1 binary64) x))))))
(*.f64 (pow.f64 (-.f64 #s(literal 1 binary64) (*.f64 x (*.f64 x x))) #s(literal 1/2 binary64)) (/.f64 #s(literal 1 binary64) (sqrt.f64 (+.f64 #s(literal 1 binary64) (*.f64 x (+.f64 #s(literal 1 binary64) x))))))
(*.f64 (pow.f64 (-.f64 #s(literal 1 binary64) (*.f64 x x)) #s(literal 1/2 binary64)) (pow.f64 (/.f64 #s(literal 1 binary64) (+.f64 #s(literal 1 binary64) x)) #s(literal 1/2 binary64)))
(*.f64 (pow.f64 (-.f64 #s(literal 1 binary64) (*.f64 x x)) #s(literal 1/2 binary64)) (sqrt.f64 (/.f64 #s(literal 1 binary64) (+.f64 #s(literal 1 binary64) x))))
(*.f64 (pow.f64 (-.f64 #s(literal 1 binary64) (*.f64 x x)) #s(literal 1/2 binary64)) (/.f64 #s(literal 1 binary64) (pow.f64 (+.f64 #s(literal 1 binary64) x) #s(literal 1/2 binary64))))
(*.f64 (pow.f64 (-.f64 #s(literal 1 binary64) x) #s(literal 1/4 binary64)) (pow.f64 (-.f64 #s(literal 1 binary64) x) #s(literal 1/4 binary64)))
(*.f64 (pow.f64 #s(literal 1 binary64) #s(literal 1/2 binary64)) (pow.f64 (-.f64 #s(literal 1 binary64) x) #s(literal 1/2 binary64)))
(*.f64 (pow.f64 (/.f64 (-.f64 #s(literal 1 binary64) (*.f64 x x)) (+.f64 #s(literal 1 binary64) (*.f64 x (*.f64 x x)))) #s(literal 1/2 binary64)) (sqrt.f64 (+.f64 #s(literal 1 binary64) (*.f64 x (+.f64 x #s(literal -1 binary64))))))
(*.f64 (sqrt.f64 (pow.f64 (-.f64 #s(literal 1 binary64) x) #s(literal 1/2 binary64))) (sqrt.f64 (pow.f64 (-.f64 #s(literal 1 binary64) x) #s(literal 1/2 binary64))))
(*.f64 (sqrt.f64 (/.f64 (-.f64 #s(literal 1 binary64) (*.f64 x x)) (+.f64 #s(literal 1 binary64) (*.f64 x (*.f64 x x))))) (sqrt.f64 (+.f64 #s(literal 1 binary64) (*.f64 x (+.f64 x #s(literal -1 binary64))))))
(*.f64 (/.f64 (pow.f64 (-.f64 #s(literal 1 binary64) (*.f64 x x)) #s(literal 1/2 binary64)) (pow.f64 (-.f64 #s(literal 1 binary64) (*.f64 x x)) #s(literal 1/2 binary64))) (pow.f64 (-.f64 #s(literal 1 binary64) x) #s(literal 1/2 binary64)))
(*.f64 (/.f64 (pow.f64 (-.f64 #s(literal 1 binary64) (*.f64 x x)) #s(literal 1/2 binary64)) (sqrt.f64 (+.f64 #s(literal 1 binary64) (*.f64 x (*.f64 x x))))) (sqrt.f64 (+.f64 #s(literal 1 binary64) (*.f64 x (+.f64 x #s(literal -1 binary64))))))

simplify261.0ms (2.6%)

Algorithm
egg-herbie
Rules
4834×*-lowering-*.f32
4834×*-lowering-*.f64
4254×+-lowering-+.f64
4254×+-lowering-+.f32
1772×--lowering--.f32
Iterations

Useful iterations: 2 (0.0ms)

IterNodesCost
0161826
1528727
22050693
08755693
Stop Event
iter limit
node limit
Counts
48 → 48
Calls
Call 1
Inputs
x
(* x (+ 1 (* 1/8 (pow x 2))))
(* x (+ 1 (* (pow x 2) (+ 1/8 (* 7/128 (pow x 2))))))
(* x (+ 1 (* (pow x 2) (+ 1/8 (* (pow x 2) (+ 7/128 (* 33/1024 (pow x 2))))))))
(* x (- (sqrt (/ 1 x)) (* (sqrt (/ 1 x)) (sqrt -1))))
(* x (- (+ (sqrt (/ 1 x)) (* 1/2 (sqrt (/ 1 (pow x 3))))) (+ (* 1/2 (* (sqrt (/ 1 (pow x 3))) (/ 1 (sqrt -1)))) (* (sqrt (/ 1 x)) (sqrt -1)))))
(* x (- (+ (sqrt (/ 1 x)) (+ (* -1/8 (sqrt (/ 1 (pow x 5)))) (* 1/2 (sqrt (/ 1 (pow x 3)))))) (+ (* -1/8 (* (sqrt (/ 1 (pow x 5))) (/ 1 (pow (sqrt -1) 3)))) (+ (* 1/2 (* (sqrt (/ 1 (pow x 3))) (/ 1 (sqrt -1)))) (* (sqrt (/ 1 x)) (sqrt -1))))))
(* x (- (+ (sqrt (/ 1 x)) (+ (* -1/8 (sqrt (/ 1 (pow x 5)))) (+ (* 1/16 (sqrt (/ 1 (pow x 7)))) (* 1/2 (sqrt (/ 1 (pow x 3))))))) (+ (* -1/8 (* (sqrt (/ 1 (pow x 5))) (/ 1 (pow (sqrt -1) 3)))) (+ (* 1/16 (* (sqrt (/ 1 (pow x 7))) (/ 1 (pow (sqrt -1) 5)))) (+ (* 1/2 (* (sqrt (/ 1 (pow x 3))) (/ 1 (sqrt -1)))) (* (sqrt (/ 1 x)) (sqrt -1)))))))
(* -1 (* x (- (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)) (* (sqrt (/ 1 x)) (sqrt -1)))))
(* -1 (* x (- (+ (* 1/2 (sqrt (/ 1 (pow x 3)))) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))) (+ (* 1/2 (* (sqrt (/ 1 (pow x 3))) (sqrt -1))) (* (sqrt (/ 1 x)) (sqrt -1))))))
(* -1 (* x (- (+ (* -1/8 (* (sqrt (/ 1 (pow x 5))) (/ 1 (pow (sqrt -1) 2)))) (+ (* 1/2 (sqrt (/ 1 (pow x 3)))) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)))) (+ (* -1/8 (* (sqrt (/ 1 (pow x 5))) (sqrt -1))) (+ (* 1/2 (* (sqrt (/ 1 (pow x 3))) (sqrt -1))) (* (sqrt (/ 1 x)) (sqrt -1)))))))
(* -1 (* x (- (+ (* -1/8 (* (sqrt (/ 1 (pow x 5))) (/ 1 (pow (sqrt -1) 2)))) (+ (* 1/16 (* (sqrt (/ 1 (pow x 7))) (/ 1 (pow (sqrt -1) 4)))) (+ (* 1/2 (sqrt (/ 1 (pow x 3)))) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))))) (+ (* -1/8 (* (sqrt (/ 1 (pow x 5))) (sqrt -1))) (+ (* 1/16 (* (sqrt (/ 1 (pow x 7))) (sqrt -1))) (+ (* 1/2 (* (sqrt (/ 1 (pow x 3))) (sqrt -1))) (* (sqrt (/ 1 x)) (sqrt -1))))))))
1
(+ 1 (* 1/2 x))
(+ 1 (* x (+ 1/2 (* -1/8 x))))
(+ 1 (* x (+ 1/2 (* x (- (* 1/16 x) 1/8)))))
(sqrt x)
(* x (+ (sqrt (/ 1 x)) (* 1/2 (sqrt (/ 1 (pow x 3))))))
(* x (+ (sqrt (/ 1 x)) (+ (* -1/8 (sqrt (/ 1 (pow x 5)))) (* 1/2 (sqrt (/ 1 (pow x 3)))))))
(* x (+ (sqrt (/ 1 x)) (+ (* -1/8 (sqrt (/ 1 (pow x 5)))) (+ (* 1/16 (sqrt (/ 1 (pow x 7)))) (* 1/2 (sqrt (/ 1 (pow x 3))))))))
(* -1 (* (sqrt x) (pow (sqrt -1) 2)))
(* -1 (* x (+ (* 1/2 (sqrt (/ 1 (pow x 3)))) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)))))
(* -1 (* x (+ (* -1/8 (* (sqrt (/ 1 (pow x 5))) (/ 1 (pow (sqrt -1) 2)))) (+ (* 1/2 (sqrt (/ 1 (pow x 3)))) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))))))
(* -1 (* x (+ (* -1/8 (* (sqrt (/ 1 (pow x 5))) (/ 1 (pow (sqrt -1) 2)))) (+ (* 1/16 (* (sqrt (/ 1 (pow x 7))) (/ 1 (pow (sqrt -1) 4)))) (+ (* 1/2 (sqrt (/ 1 (pow x 3)))) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)))))))
1
(+ 1 x)
(+ 1 x)
(+ 1 x)
x
(* x (+ 1 (/ 1 x)))
(* x (+ 1 (/ 1 x)))
(* x (+ 1 (/ 1 x)))
x
(* x (+ 1 (/ 1 x)))
(* x (+ 1 (/ 1 x)))
(* x (+ 1 (/ 1 x)))
1
(+ 1 (* -1/2 x))
(+ 1 (* x (- (* -1/8 x) 1/2)))
(+ 1 (* x (- (* x (- (* -1/16 x) 1/8)) 1/2)))
(* (sqrt x) (sqrt -1))
(* x (+ (* 1/2 (* (sqrt (/ 1 (pow x 3))) (/ 1 (sqrt -1)))) (* (sqrt (/ 1 x)) (sqrt -1))))
(* x (+ (* -1/8 (* (sqrt (/ 1 (pow x 5))) (/ 1 (pow (sqrt -1) 3)))) (+ (* 1/2 (* (sqrt (/ 1 (pow x 3))) (/ 1 (sqrt -1)))) (* (sqrt (/ 1 x)) (sqrt -1)))))
(* x (+ (* -1/8 (* (sqrt (/ 1 (pow x 5))) (/ 1 (pow (sqrt -1) 3)))) (+ (* 1/16 (* (sqrt (/ 1 (pow x 7))) (/ 1 (pow (sqrt -1) 5)))) (+ (* 1/2 (* (sqrt (/ 1 (pow x 3))) (/ 1 (sqrt -1)))) (* (sqrt (/ 1 x)) (sqrt -1))))))
(* -1 (* (sqrt x) (sqrt -1)))
(* -1 (* x (+ (* 1/2 (* (sqrt (/ 1 (pow x 3))) (sqrt -1))) (* (sqrt (/ 1 x)) (sqrt -1)))))
(* -1 (* x (+ (* -1/8 (* (sqrt (/ 1 (pow x 5))) (sqrt -1))) (+ (* 1/2 (* (sqrt (/ 1 (pow x 3))) (sqrt -1))) (* (sqrt (/ 1 x)) (sqrt -1))))))
(* -1 (* x (+ (* -1/8 (* (sqrt (/ 1 (pow x 5))) (sqrt -1))) (+ (* 1/16 (* (sqrt (/ 1 (pow x 7))) (sqrt -1))) (+ (* 1/2 (* (sqrt (/ 1 (pow x 3))) (sqrt -1))) (* (sqrt (/ 1 x)) (sqrt -1)))))))
Outputs
x
(* x (+ 1 (* 1/8 (pow x 2))))
(*.f64 x (+.f64 #s(literal 1 binary64) (*.f64 #s(literal 1/8 binary64) (*.f64 x x))))
(* x (+ 1 (* (pow x 2) (+ 1/8 (* 7/128 (pow x 2))))))
(*.f64 x (+.f64 #s(literal 1 binary64) (*.f64 (*.f64 x x) (+.f64 #s(literal 1/8 binary64) (*.f64 (*.f64 x x) #s(literal 7/128 binary64))))))
(* x (+ 1 (* (pow x 2) (+ 1/8 (* (pow x 2) (+ 7/128 (* 33/1024 (pow x 2))))))))
(*.f64 x (+.f64 #s(literal 1 binary64) (*.f64 (*.f64 x x) (+.f64 #s(literal 1/8 binary64) (*.f64 x (*.f64 x (+.f64 #s(literal 7/128 binary64) (*.f64 (*.f64 x x) #s(literal 33/1024 binary64)))))))))
(* x (- (sqrt (/ 1 x)) (* (sqrt (/ 1 x)) (sqrt -1))))
(*.f64 x (*.f64 (+.f64 (-.f64 #s(literal 0 binary64) (sqrt.f64 #s(literal -1 binary64))) #s(literal 1 binary64)) (sqrt.f64 (/.f64 #s(literal 1 binary64) x))))
(* x (- (+ (sqrt (/ 1 x)) (* 1/2 (sqrt (/ 1 (pow x 3))))) (+ (* 1/2 (* (sqrt (/ 1 (pow x 3))) (/ 1 (sqrt -1)))) (* (sqrt (/ 1 x)) (sqrt -1)))))
(*.f64 x (+.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) (-.f64 (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (*.f64 x (*.f64 x x)))) (-.f64 #s(literal 1/2 binary64) (*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 #s(literal -1 binary64))) #s(literal 1/2 binary64)))) (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) (sqrt.f64 #s(literal -1 binary64))))))
(* x (- (+ (sqrt (/ 1 x)) (+ (* -1/8 (sqrt (/ 1 (pow x 5)))) (* 1/2 (sqrt (/ 1 (pow x 3)))))) (+ (* -1/8 (* (sqrt (/ 1 (pow x 5))) (/ 1 (pow (sqrt -1) 3)))) (+ (* 1/2 (* (sqrt (/ 1 (pow x 3))) (/ 1 (sqrt -1)))) (* (sqrt (/ 1 x)) (sqrt -1))))))
(*.f64 x (+.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) (-.f64 (+.f64 (*.f64 #s(literal -1/8 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 5 binary64))))) (-.f64 (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (*.f64 x (*.f64 x x)))) (-.f64 #s(literal 1/2 binary64) (*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 #s(literal -1 binary64))) #s(literal 1/2 binary64)))) (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) (sqrt.f64 #s(literal -1 binary64))))) (*.f64 #s(literal 1/8 binary64) (/.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 5 binary64)))) (sqrt.f64 #s(literal -1 binary64)))))))
(* x (- (+ (sqrt (/ 1 x)) (+ (* -1/8 (sqrt (/ 1 (pow x 5)))) (+ (* 1/16 (sqrt (/ 1 (pow x 7)))) (* 1/2 (sqrt (/ 1 (pow x 3))))))) (+ (* -1/8 (* (sqrt (/ 1 (pow x 5))) (/ 1 (pow (sqrt -1) 3)))) (+ (* 1/16 (* (sqrt (/ 1 (pow x 7))) (/ 1 (pow (sqrt -1) 5)))) (+ (* 1/2 (* (sqrt (/ 1 (pow x 3))) (/ 1 (sqrt -1)))) (* (sqrt (/ 1 x)) (sqrt -1)))))))
(*.f64 x (+.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) (+.f64 (*.f64 #s(literal -1/8 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 5 binary64))))) (+.f64 (*.f64 #s(literal 1/16 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 7 binary64))))) (-.f64 (-.f64 (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (*.f64 x (*.f64 x x)))) (-.f64 #s(literal 1/2 binary64) (*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 #s(literal -1 binary64))) #s(literal 1/2 binary64)))) (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) (sqrt.f64 #s(literal -1 binary64)))) (+.f64 (*.f64 #s(literal 1/8 binary64) (/.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 5 binary64)))) (sqrt.f64 #s(literal -1 binary64)))) (*.f64 #s(literal 1/16 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 5 binary64))))))))))
(* -1 (* x (- (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)) (* (sqrt (/ 1 x)) (sqrt -1)))))
(*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) (*.f64 (-.f64 #s(literal 0 binary64) x) (-.f64 #s(literal -1 binary64) (sqrt.f64 #s(literal -1 binary64)))))
(* -1 (* x (- (+ (* 1/2 (sqrt (/ 1 (pow x 3)))) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))) (+ (* 1/2 (* (sqrt (/ 1 (pow x 3))) (sqrt -1))) (* (sqrt (/ 1 x)) (sqrt -1))))))
(*.f64 (+.f64 (-.f64 #s(literal 0 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) x))) (-.f64 (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (*.f64 x (*.f64 x x)))) (-.f64 #s(literal 1/2 binary64) (*.f64 #s(literal 1/2 binary64) (sqrt.f64 #s(literal -1 binary64))))) (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) (sqrt.f64 #s(literal -1 binary64))))) (-.f64 #s(literal 0 binary64) x))
(* -1 (* x (- (+ (* -1/8 (* (sqrt (/ 1 (pow x 5))) (/ 1 (pow (sqrt -1) 2)))) (+ (* 1/2 (sqrt (/ 1 (pow x 3)))) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)))) (+ (* -1/8 (* (sqrt (/ 1 (pow x 5))) (sqrt -1))) (+ (* 1/2 (* (sqrt (/ 1 (pow x 3))) (sqrt -1))) (* (sqrt (/ 1 x)) (sqrt -1)))))))
(*.f64 (-.f64 (+.f64 (-.f64 (*.f64 #s(literal 1/2 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) (*.f64 x (*.f64 x x))))) (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 1/8 binary64) (*.f64 #s(literal -1/8 binary64) (sqrt.f64 #s(literal -1 binary64)))))) (*.f64 (sqrt.f64 #s(literal -1 binary64)) (+.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) (*.f64 #s(literal 1/2 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) (*.f64 x (*.f64 x x)))))))) (-.f64 #s(literal 0 binary64) x))
(* -1 (* x (- (+ (* -1/8 (* (sqrt (/ 1 (pow x 5))) (/ 1 (pow (sqrt -1) 2)))) (+ (* 1/16 (* (sqrt (/ 1 (pow x 7))) (/ 1 (pow (sqrt -1) 4)))) (+ (* 1/2 (sqrt (/ 1 (pow x 3)))) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))))) (+ (* -1/8 (* (sqrt (/ 1 (pow x 5))) (sqrt -1))) (+ (* 1/16 (* (sqrt (/ 1 (pow x 7))) (sqrt -1))) (+ (* 1/2 (* (sqrt (/ 1 (pow x 3))) (sqrt -1))) (* (sqrt (/ 1 x)) (sqrt -1))))))))
(*.f64 (+.f64 (+.f64 (*.f64 #s(literal 1/2 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) (*.f64 x (*.f64 x x))))) (-.f64 (*.f64 #s(literal 1/16 binary64) (/.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 7 binary64)))) (pow.f64 (sqrt.f64 #s(literal -1 binary64)) #s(literal 4 binary64)))) (sqrt.f64 (/.f64 #s(literal 1 binary64) x)))) (-.f64 (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 5 binary64)))) (-.f64 #s(literal 1/8 binary64) (*.f64 #s(literal -1/8 binary64) (sqrt.f64 #s(literal -1 binary64))))) (*.f64 (sqrt.f64 #s(literal -1 binary64)) (+.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) (+.f64 (*.f64 #s(literal 1/2 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) (*.f64 x (*.f64 x x))))) (*.f64 #s(literal 1/16 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 7 binary64)))))))))) (-.f64 #s(literal 0 binary64) 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 (* -1/8 x))))
(+.f64 #s(literal 1 binary64) (*.f64 x (+.f64 #s(literal 1/2 binary64) (*.f64 x #s(literal -1/8 binary64)))))
(+ 1 (* x (+ 1/2 (* x (- (* 1/16 x) 1/8)))))
(+.f64 #s(literal 1 binary64) (*.f64 x (+.f64 #s(literal 1/2 binary64) (*.f64 x (+.f64 #s(literal -1/8 binary64) (*.f64 x #s(literal 1/16 binary64)))))))
(sqrt x)
(sqrt.f64 x)
(* x (+ (sqrt (/ 1 x)) (* 1/2 (sqrt (/ 1 (pow x 3))))))
(*.f64 x (+.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) (*.f64 #s(literal 1/2 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) (*.f64 x (*.f64 x x)))))))
(* x (+ (sqrt (/ 1 x)) (+ (* -1/8 (sqrt (/ 1 (pow x 5)))) (* 1/2 (sqrt (/ 1 (pow x 3)))))))
(*.f64 x (+.f64 (*.f64 #s(literal 1/2 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) (*.f64 x (*.f64 x x))))) (+.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) (*.f64 #s(literal -1/8 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 5 binary64))))))))
(* x (+ (sqrt (/ 1 x)) (+ (* -1/8 (sqrt (/ 1 (pow x 5)))) (+ (* 1/16 (sqrt (/ 1 (pow x 7)))) (* 1/2 (sqrt (/ 1 (pow x 3))))))))
(*.f64 x (+.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) (+.f64 (*.f64 #s(literal -1/8 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 5 binary64))))) (+.f64 (*.f64 #s(literal 1/2 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) (*.f64 x (*.f64 x x))))) (*.f64 #s(literal 1/16 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 (+ (* 1/2 (sqrt (/ 1 (pow x 3)))) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)))))
(-.f64 #s(literal 0 binary64) (*.f64 x (-.f64 (*.f64 #s(literal 1/2 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) (*.f64 x (*.f64 x x))))) (sqrt.f64 (/.f64 #s(literal 1 binary64) x)))))
(* -1 (* x (+ (* -1/8 (* (sqrt (/ 1 (pow x 5))) (/ 1 (pow (sqrt -1) 2)))) (+ (* 1/2 (sqrt (/ 1 (pow x 3)))) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))))))
(-.f64 #s(literal 0 binary64) (*.f64 x (+.f64 (*.f64 #s(literal 1/2 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) (*.f64 x (*.f64 x x))))) (-.f64 (*.f64 #s(literal 1/8 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 5 binary64))))) (sqrt.f64 (/.f64 #s(literal 1 binary64) x))))))
(* -1 (* x (+ (* -1/8 (* (sqrt (/ 1 (pow x 5))) (/ 1 (pow (sqrt -1) 2)))) (+ (* 1/16 (* (sqrt (/ 1 (pow x 7))) (/ 1 (pow (sqrt -1) 4)))) (+ (* 1/2 (sqrt (/ 1 (pow x 3)))) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)))))))
(-.f64 #s(literal 0 binary64) (*.f64 x (+.f64 (-.f64 (*.f64 #s(literal 1/2 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) (*.f64 x (*.f64 x x))))) (sqrt.f64 (/.f64 #s(literal 1 binary64) x))) (+.f64 (*.f64 #s(literal 1/8 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 5 binary64))))) (*.f64 #s(literal 1/16 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))))))))
1
#s(literal 1 binary64)
(+ 1 x)
(+.f64 x #s(literal 1 binary64))
(+ 1 x)
(+.f64 x #s(literal 1 binary64))
(+ 1 x)
(+.f64 x #s(literal 1 binary64))
x
(* x (+ 1 (/ 1 x)))
(+.f64 x #s(literal 1 binary64))
(* x (+ 1 (/ 1 x)))
(+.f64 x #s(literal 1 binary64))
(* x (+ 1 (/ 1 x)))
(+.f64 x #s(literal 1 binary64))
x
(* x (+ 1 (/ 1 x)))
(+.f64 x #s(literal 1 binary64))
(* x (+ 1 (/ 1 x)))
(+.f64 x #s(literal 1 binary64))
(* x (+ 1 (/ 1 x)))
(+.f64 x #s(literal 1 binary64))
1
#s(literal 1 binary64)
(+ 1 (* -1/2 x))
(+.f64 #s(literal 1 binary64) (*.f64 x #s(literal -1/2 binary64)))
(+ 1 (* x (- (* -1/8 x) 1/2)))
(+.f64 #s(literal 1 binary64) (*.f64 x (+.f64 (*.f64 x #s(literal -1/8 binary64)) #s(literal -1/2 binary64))))
(+ 1 (* x (- (* x (- (* -1/16 x) 1/8)) 1/2)))
(+.f64 #s(literal 1 binary64) (*.f64 x (+.f64 #s(literal -1/2 binary64) (*.f64 x (+.f64 #s(literal -1/8 binary64) (*.f64 x #s(literal -1/16 binary64)))))))
(* (sqrt x) (sqrt -1))
(*.f64 (sqrt.f64 #s(literal -1 binary64)) (sqrt.f64 x))
(* x (+ (* 1/2 (* (sqrt (/ 1 (pow x 3))) (/ 1 (sqrt -1)))) (* (sqrt (/ 1 x)) (sqrt -1))))
(*.f64 x (+.f64 (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) (sqrt.f64 #s(literal -1 binary64))) (*.f64 #s(literal 1/2 binary64) (/.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (*.f64 x (*.f64 x x)))) (sqrt.f64 #s(literal -1 binary64))))))
(* x (+ (* -1/8 (* (sqrt (/ 1 (pow x 5))) (/ 1 (pow (sqrt -1) 3)))) (+ (* 1/2 (* (sqrt (/ 1 (pow x 3))) (/ 1 (sqrt -1)))) (* (sqrt (/ 1 x)) (sqrt -1)))))
(*.f64 x (+.f64 (+.f64 (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) (sqrt.f64 #s(literal -1 binary64))) (*.f64 #s(literal 1/2 binary64) (/.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (*.f64 x (*.f64 x x)))) (sqrt.f64 #s(literal -1 binary64))))) (*.f64 #s(literal 1/8 binary64) (/.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 5 binary64)))) (sqrt.f64 #s(literal -1 binary64))))))
(* x (+ (* -1/8 (* (sqrt (/ 1 (pow x 5))) (/ 1 (pow (sqrt -1) 3)))) (+ (* 1/16 (* (sqrt (/ 1 (pow x 7))) (/ 1 (pow (sqrt -1) 5)))) (+ (* 1/2 (* (sqrt (/ 1 (pow x 3))) (/ 1 (sqrt -1)))) (* (sqrt (/ 1 x)) (sqrt -1))))))
(*.f64 x (+.f64 (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) (sqrt.f64 #s(literal -1 binary64))) (+.f64 (*.f64 #s(literal 1/8 binary64) (/.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 5 binary64)))) (sqrt.f64 #s(literal -1 binary64)))) (+.f64 (*.f64 #s(literal 1/2 binary64) (/.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (*.f64 x (*.f64 x x)))) (sqrt.f64 #s(literal -1 binary64)))) (*.f64 #s(literal 1/16 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 5 binary64))))))))
(* -1 (* (sqrt x) (sqrt -1)))
(*.f64 (sqrt.f64 #s(literal -1 binary64)) (-.f64 #s(literal 0 binary64) (sqrt.f64 x)))
(* -1 (* x (+ (* 1/2 (* (sqrt (/ 1 (pow x 3))) (sqrt -1))) (* (sqrt (/ 1 x)) (sqrt -1)))))
(*.f64 x (*.f64 (-.f64 #s(literal 0 binary64) (sqrt.f64 #s(literal -1 binary64))) (+.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) (*.f64 #s(literal 1/2 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) (*.f64 x (*.f64 x x))))))))
(* -1 (* x (+ (* -1/8 (* (sqrt (/ 1 (pow x 5))) (sqrt -1))) (+ (* 1/2 (* (sqrt (/ 1 (pow x 3))) (sqrt -1))) (* (sqrt (/ 1 x)) (sqrt -1))))))
(-.f64 #s(literal 0 binary64) (*.f64 x (*.f64 (sqrt.f64 #s(literal -1 binary64)) (+.f64 (*.f64 #s(literal 1/2 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) (*.f64 x (*.f64 x x))))) (+.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) (*.f64 #s(literal -1/8 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 5 binary64))))))))))
(* -1 (* x (+ (* -1/8 (* (sqrt (/ 1 (pow x 5))) (sqrt -1))) (+ (* 1/16 (* (sqrt (/ 1 (pow x 7))) (sqrt -1))) (+ (* 1/2 (* (sqrt (/ 1 (pow x 3))) (sqrt -1))) (* (sqrt (/ 1 x)) (sqrt -1)))))))
(*.f64 (*.f64 (sqrt.f64 #s(literal -1 binary64)) (+.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) (+.f64 (*.f64 #s(literal -1/8 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 5 binary64))))) (+.f64 (*.f64 #s(literal 1/2 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) (*.f64 x (*.f64 x x))))) (*.f64 #s(literal 1/16 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 7 binary64))))))))) (-.f64 #s(literal 0 binary64) x))

eval40.0ms (0.4%)

Compiler

Compiled 7942 to 1076 computations (86.5% saved)

prune42.0ms (0.4%)

Pruning

8 alts after pruning (7 fresh and 1 done)

PrunedKeptTotal
New2857292
Fresh000
Picked011
Done000
Total2858293
Accuracy
100.0%
Counts
293 → 8
Alt Table
Click to see full alt table
StatusAccuracyProgram
7.8%
(/.f64 (-.f64 (*.f64 (/.f64 (pow.f64 (+.f64 #s(literal 1 binary64) x) #s(literal 3/2 binary64)) (+.f64 (sqrt.f64 (*.f64 (+.f64 #s(literal 1 binary64) x) (-.f64 #s(literal 1 binary64) x))) (+.f64 #s(literal 1 binary64) (+.f64 x (-.f64 #s(literal 1 binary64) x))))) (/.f64 (pow.f64 (+.f64 #s(literal 1 binary64) x) #s(literal 3/2 binary64)) (+.f64 (sqrt.f64 (*.f64 (+.f64 #s(literal 1 binary64) x) (-.f64 #s(literal 1 binary64) x))) (+.f64 #s(literal 1 binary64) (+.f64 x (-.f64 #s(literal 1 binary64) x)))))) (*.f64 (/.f64 (pow.f64 (-.f64 #s(literal 1 binary64) x) #s(literal 3/2 binary64)) (+.f64 (sqrt.f64 (*.f64 (+.f64 #s(literal 1 binary64) x) (-.f64 #s(literal 1 binary64) x))) (+.f64 #s(literal 1 binary64) (+.f64 x (-.f64 #s(literal 1 binary64) x))))) (/.f64 (pow.f64 (-.f64 #s(literal 1 binary64) x) #s(literal 3/2 binary64)) (+.f64 (sqrt.f64 (*.f64 (+.f64 #s(literal 1 binary64) x) (-.f64 #s(literal 1 binary64) x))) (+.f64 #s(literal 1 binary64) (+.f64 x (-.f64 #s(literal 1 binary64) x))))))) (+.f64 (/.f64 (pow.f64 (+.f64 #s(literal 1 binary64) x) #s(literal 3/2 binary64)) (+.f64 (sqrt.f64 (*.f64 (+.f64 #s(literal 1 binary64) x) (-.f64 #s(literal 1 binary64) x))) (+.f64 #s(literal 1 binary64) (+.f64 x (-.f64 #s(literal 1 binary64) x))))) (/.f64 (pow.f64 (-.f64 #s(literal 1 binary64) x) #s(literal 3/2 binary64)) (+.f64 (sqrt.f64 (*.f64 (+.f64 #s(literal 1 binary64) x) (-.f64 #s(literal 1 binary64) x))) (+.f64 #s(literal 1 binary64) (+.f64 x (-.f64 #s(literal 1 binary64) x)))))))
7.8%
(/.f64 (+.f64 #s(literal 1 binary64) (-.f64 x (-.f64 #s(literal 1 binary64) x))) (+.f64 (pow.f64 (+.f64 #s(literal 1 binary64) x) #s(literal 1/2 binary64)) (pow.f64 (-.f64 #s(literal 1 binary64) x) #s(literal 1/2 binary64))))
7.7%
(-.f64 (sqrt.f64 (+.f64 #s(literal 1 binary64) x)) (sqrt.f64 (-.f64 #s(literal 1 binary64) x)))
7.8%
(*.f64 (/.f64 #s(literal 1 binary64) (+.f64 (pow.f64 (+.f64 #s(literal 1 binary64) x) #s(literal 1/2 binary64)) (pow.f64 (-.f64 #s(literal 1 binary64) x) #s(literal 1/2 binary64)))) (+.f64 #s(literal 1 binary64) (-.f64 x (-.f64 #s(literal 1 binary64) x))))
99.9%
(*.f64 x (+.f64 #s(literal 1 binary64) (*.f64 (*.f64 x x) (+.f64 #s(literal 1/8 binary64) (*.f64 (*.f64 x x) #s(literal 7/128 binary64))))))
99.9%
(*.f64 x (+.f64 #s(literal 1 binary64) (*.f64 (*.f64 x x) (+.f64 #s(literal 1/8 binary64) (*.f64 x (*.f64 x (+.f64 #s(literal 7/128 binary64) (*.f64 (*.f64 x x) #s(literal 33/1024 binary64)))))))))
99.8%
(*.f64 x (+.f64 #s(literal 1 binary64) (*.f64 #s(literal 1/8 binary64) (*.f64 x x))))
99.5%
x
Compiler

Compiled 470 to 155 computations (67% saved)

simplify193.0ms (1.9%)

Algorithm
egg-herbie
Localize:

Found 16 expressions of interest:

NewMetricScoreProgram
cost-diff0
(-.f64 #s(literal 1 binary64) x)
cost-diff0
(-.f64 x (-.f64 #s(literal 1 binary64) x))
cost-diff256
(+.f64 #s(literal 1 binary64) (-.f64 x (-.f64 #s(literal 1 binary64) x)))
cost-diff256
(/.f64 (+.f64 #s(literal 1 binary64) (-.f64 x (-.f64 #s(literal 1 binary64) x))) (+.f64 (pow.f64 (+.f64 #s(literal 1 binary64) x) #s(literal 1/2 binary64)) (pow.f64 (-.f64 #s(literal 1 binary64) x) #s(literal 1/2 binary64))))
cost-diff0
(*.f64 x x)
cost-diff0
(*.f64 (*.f64 x x) (+.f64 #s(literal 1/8 binary64) (*.f64 (*.f64 x x) #s(literal 7/128 binary64))))
cost-diff0
(+.f64 #s(literal 1 binary64) (*.f64 (*.f64 x x) (+.f64 #s(literal 1/8 binary64) (*.f64 (*.f64 x x) #s(literal 7/128 binary64)))))
cost-diff0
(*.f64 x (+.f64 #s(literal 1 binary64) (*.f64 (*.f64 x x) (+.f64 #s(literal 1/8 binary64) (*.f64 (*.f64 x x) #s(literal 7/128 binary64))))))
cost-diff0
(*.f64 x x)
cost-diff0
(*.f64 #s(literal 1/8 binary64) (*.f64 x x))
cost-diff0
(+.f64 #s(literal 1 binary64) (*.f64 #s(literal 1/8 binary64) (*.f64 x x)))
cost-diff0
(*.f64 x (+.f64 #s(literal 1 binary64) (*.f64 #s(literal 1/8 binary64) (*.f64 x x))))
cost-diff0
(*.f64 x x)
cost-diff0
(*.f64 (*.f64 x x) (+.f64 #s(literal 1/8 binary64) (*.f64 x (*.f64 x (+.f64 #s(literal 7/128 binary64) (*.f64 (*.f64 x x) #s(literal 33/1024 binary64)))))))
cost-diff0
(+.f64 #s(literal 1 binary64) (*.f64 (*.f64 x x) (+.f64 #s(literal 1/8 binary64) (*.f64 x (*.f64 x (+.f64 #s(literal 7/128 binary64) (*.f64 (*.f64 x x) #s(literal 33/1024 binary64))))))))
cost-diff0
(*.f64 x (+.f64 #s(literal 1 binary64) (*.f64 (*.f64 x x) (+.f64 #s(literal 1/8 binary64) (*.f64 x (*.f64 x (+.f64 #s(literal 7/128 binary64) (*.f64 (*.f64 x x) #s(literal 33/1024 binary64)))))))))
Rules
2812×*-lowering-*.f32
2812×*-lowering-*.f64
1866×+-lowering-+.f64
1866×+-lowering-+.f32
1746×--lowering--.f32
Iterations

Useful iterations: 2 (0.0ms)

IterNodesCost
031221
1102198
2321188
3954188
43542188
08272188
Stop Event
iter limit
node limit
Calls
Call 1
Inputs
(* x (+ 1 (* (* x x) (+ 1/8 (* x (* x (+ 7/128 (* (* x x) 33/1024))))))))
x
(+ 1 (* (* x x) (+ 1/8 (* x (* x (+ 7/128 (* (* x x) 33/1024)))))))
1
(* (* x x) (+ 1/8 (* x (* x (+ 7/128 (* (* x x) 33/1024))))))
(* x x)
(+ 1/8 (* x (* x (+ 7/128 (* (* x x) 33/1024)))))
1/8
(* x (* x (+ 7/128 (* (* x x) 33/1024))))
(* x (+ 7/128 (* (* x x) 33/1024)))
(+ 7/128 (* (* x x) 33/1024))
7/128
(* (* x x) 33/1024)
33/1024
x
(* x (+ 1 (* 1/8 (* x x))))
x
(+ 1 (* 1/8 (* x x)))
1
(* 1/8 (* x x))
1/8
(* x x)
(* x (+ 1 (* (* x x) (+ 1/8 (* (* x x) 7/128)))))
x
(+ 1 (* (* x x) (+ 1/8 (* (* x x) 7/128))))
1
(* (* x x) (+ 1/8 (* (* x x) 7/128)))
(* x x)
(+ 1/8 (* (* x x) 7/128))
1/8
(* (* x x) 7/128)
7/128
(/ (+ 1 (- x (- 1 x))) (+ (pow (+ 1 x) 1/2) (pow (- 1 x) 1/2)))
(+ 1 (- x (- 1 x)))
1
(- x (- 1 x))
x
(- 1 x)
(+ (pow (+ 1 x) 1/2) (pow (- 1 x) 1/2))
(pow (+ 1 x) 1/2)
(+ 1 x)
1/2
(pow (- 1 x) 1/2)
Outputs
(* x (+ 1 (* (* x x) (+ 1/8 (* x (* x (+ 7/128 (* (* x x) 33/1024))))))))
(*.f64 x (+.f64 #s(literal 1 binary64) (*.f64 x (*.f64 x (+.f64 #s(literal 1/8 binary64) (*.f64 x (*.f64 x (+.f64 #s(literal 7/128 binary64) (*.f64 x (*.f64 x #s(literal 33/1024 binary64)))))))))))
x
(+ 1 (* (* x x) (+ 1/8 (* x (* x (+ 7/128 (* (* x x) 33/1024)))))))
(+.f64 #s(literal 1 binary64) (*.f64 x (*.f64 x (+.f64 #s(literal 1/8 binary64) (*.f64 x (*.f64 x (+.f64 #s(literal 7/128 binary64) (*.f64 x (*.f64 x #s(literal 33/1024 binary64))))))))))
1
#s(literal 1 binary64)
(* (* x x) (+ 1/8 (* x (* x (+ 7/128 (* (* x x) 33/1024))))))
(*.f64 x (*.f64 x (+.f64 #s(literal 1/8 binary64) (*.f64 x (*.f64 x (+.f64 #s(literal 7/128 binary64) (*.f64 x (*.f64 x #s(literal 33/1024 binary64)))))))))
(* x x)
(*.f64 x x)
(+ 1/8 (* x (* x (+ 7/128 (* (* x x) 33/1024)))))
(+.f64 #s(literal 1/8 binary64) (*.f64 x (*.f64 x (+.f64 #s(literal 7/128 binary64) (*.f64 x (*.f64 x #s(literal 33/1024 binary64)))))))
1/8
#s(literal 1/8 binary64)
(* x (* x (+ 7/128 (* (* x x) 33/1024))))
(*.f64 x (*.f64 x (+.f64 #s(literal 7/128 binary64) (*.f64 x (*.f64 x #s(literal 33/1024 binary64))))))
(* x (+ 7/128 (* (* x x) 33/1024)))
(*.f64 x (+.f64 #s(literal 7/128 binary64) (*.f64 x (*.f64 x #s(literal 33/1024 binary64)))))
(+ 7/128 (* (* x x) 33/1024))
(+.f64 #s(literal 7/128 binary64) (*.f64 x (*.f64 x #s(literal 33/1024 binary64))))
7/128
#s(literal 7/128 binary64)
(* (* x x) 33/1024)
(*.f64 x (*.f64 x #s(literal 33/1024 binary64)))
33/1024
#s(literal 33/1024 binary64)
x
(* x (+ 1 (* 1/8 (* x x))))
(*.f64 x (+.f64 #s(literal 1 binary64) (*.f64 x (*.f64 x #s(literal 1/8 binary64)))))
x
(+ 1 (* 1/8 (* x x)))
(+.f64 #s(literal 1 binary64) (*.f64 x (*.f64 x #s(literal 1/8 binary64))))
1
#s(literal 1 binary64)
(* 1/8 (* x x))
(*.f64 x (*.f64 x #s(literal 1/8 binary64)))
1/8
#s(literal 1/8 binary64)
(* x x)
(*.f64 x x)
(* x (+ 1 (* (* x x) (+ 1/8 (* (* x x) 7/128)))))
(*.f64 x (+.f64 #s(literal 1 binary64) (*.f64 x (*.f64 x (+.f64 #s(literal 1/8 binary64) (*.f64 (*.f64 x x) #s(literal 7/128 binary64)))))))
x
(+ 1 (* (* x x) (+ 1/8 (* (* x x) 7/128))))
(+.f64 #s(literal 1 binary64) (*.f64 x (*.f64 x (+.f64 #s(literal 1/8 binary64) (*.f64 (*.f64 x x) #s(literal 7/128 binary64))))))
1
#s(literal 1 binary64)
(* (* x x) (+ 1/8 (* (* x x) 7/128)))
(*.f64 x (*.f64 x (+.f64 #s(literal 1/8 binary64) (*.f64 (*.f64 x x) #s(literal 7/128 binary64)))))
(* x x)
(*.f64 x x)
(+ 1/8 (* (* x x) 7/128))
(+.f64 #s(literal 1/8 binary64) (*.f64 (*.f64 x x) #s(literal 7/128 binary64)))
1/8
#s(literal 1/8 binary64)
(* (* x x) 7/128)
(*.f64 (*.f64 x x) #s(literal 7/128 binary64))
7/128
#s(literal 7/128 binary64)
(/ (+ 1 (- x (- 1 x))) (+ (pow (+ 1 x) 1/2) (pow (- 1 x) 1/2)))
(/.f64 (*.f64 x #s(literal 2 binary64)) (+.f64 (pow.f64 (+.f64 x #s(literal 1 binary64)) #s(literal 1/2 binary64)) (pow.f64 (-.f64 #s(literal 1 binary64) x) #s(literal 1/2 binary64))))
(+ 1 (- x (- 1 x)))
(*.f64 x #s(literal 2 binary64))
1
#s(literal 1 binary64)
(- x (- 1 x))
(+.f64 #s(literal -1 binary64) (*.f64 x #s(literal 2 binary64)))
x
(- 1 x)
(-.f64 #s(literal 1 binary64) x)
(+ (pow (+ 1 x) 1/2) (pow (- 1 x) 1/2))
(+.f64 (pow.f64 (+.f64 x #s(literal 1 binary64)) #s(literal 1/2 binary64)) (pow.f64 (-.f64 #s(literal 1 binary64) x) #s(literal 1/2 binary64)))
(pow (+ 1 x) 1/2)
(pow.f64 (+.f64 x #s(literal 1 binary64)) #s(literal 1/2 binary64))
(+ 1 x)
(+.f64 x #s(literal 1 binary64))
1/2
#s(literal 1/2 binary64)
(pow (- 1 x) 1/2)
(pow.f64 (-.f64 #s(literal 1 binary64) x) #s(literal 1/2 binary64))

localize491.0ms (4.9%)

Localize:

Found 16 expressions of interest:

NewMetricScoreProgram
accuracy100.0%
(pow.f64 (+.f64 #s(literal 1 binary64) x) #s(literal 1/2 binary64))
accuracy100.0%
(+.f64 (pow.f64 (+.f64 #s(literal 1 binary64) x) #s(literal 1/2 binary64)) (pow.f64 (-.f64 #s(literal 1 binary64) x) #s(literal 1/2 binary64)))
accuracy100.0%
(-.f64 x (-.f64 #s(literal 1 binary64) x))
accuracy7.9%
(+.f64 #s(literal 1 binary64) (-.f64 x (-.f64 #s(literal 1 binary64) x)))
accuracy100.0%
(*.f64 x x)
accuracy100.0%
(*.f64 (*.f64 x x) (+.f64 #s(literal 1/8 binary64) (*.f64 (*.f64 x x) #s(literal 7/128 binary64))))
accuracy100.0%
(*.f64 x (+.f64 #s(literal 1 binary64) (*.f64 (*.f64 x x) (+.f64 #s(literal 1/8 binary64) (*.f64 (*.f64 x x) #s(literal 7/128 binary64))))))
accuracy99.8%
(*.f64 (*.f64 x x) #s(literal 7/128 binary64))
accuracy100.0%
(+.f64 #s(literal 1 binary64) (*.f64 #s(literal 1/8 binary64) (*.f64 x x)))
accuracy100.0%
(*.f64 x x)
accuracy100.0%
(*.f64 #s(literal 1/8 binary64) (*.f64 x x))
accuracy100.0%
(*.f64 x (+.f64 #s(literal 1 binary64) (*.f64 #s(literal 1/8 binary64) (*.f64 x x))))
accuracy100.0%
(*.f64 (*.f64 x x) (+.f64 #s(literal 1/8 binary64) (*.f64 x (*.f64 x (+.f64 #s(literal 7/128 binary64) (*.f64 (*.f64 x x) #s(literal 33/1024 binary64)))))))
accuracy99.9%
(*.f64 x (+.f64 #s(literal 7/128 binary64) (*.f64 (*.f64 x x) #s(literal 33/1024 binary64))))
accuracy99.8%
(*.f64 x (*.f64 x (+.f64 #s(literal 7/128 binary64) (*.f64 (*.f64 x x) #s(literal 33/1024 binary64)))))
accuracy99.8%
(*.f64 (*.f64 x x) #s(literal 33/1024 binary64))
Results
330.0ms235×1valid
33.0ms3valid
11.0ms2valid
2.0ms0valid
Compiler

Compiled 259 to 32 computations (87.6% saved)

Precisions
Click to see histograms. Total time spent on operations: 305.0ms
ival-pow: 197.0ms (64.5% of total)
ival-mult: 41.0ms (13.4% of total)
backward-pass: 31.0ms (10.2% of total)
ival-add: 25.0ms (8.2% of total)
ival-sub: 5.0ms (1.6% of total)
ival-div: 4.0ms (1.3% of total)
const: 2.0ms (0.7% of total)

series22.0ms (0.2%)

Counts
20 → 240
Calls
Call 1
Inputs
#<alt (* x (+ 1 (* (* x x) (+ 1/8 (* x (* x (+ 7/128 (* (* x x) 33/1024))))))))>
#<alt (+ 1 (* (* x x) (+ 1/8 (* x (* x (+ 7/128 (* (* x x) 33/1024)))))))>
#<alt (* (* x x) (+ 1/8 (* x (* x (+ 7/128 (* (* x x) 33/1024))))))>
#<alt (* x x)>
#<alt (* x (+ 1 (* 1/8 (* x x))))>
#<alt (+ 1 (* 1/8 (* x x)))>
#<alt (* 1/8 (* x x))>
#<alt (* x (+ 1 (* (* x x) (+ 1/8 (* (* x x) 7/128)))))>
#<alt (+ 1 (* (* x x) (+ 1/8 (* (* x x) 7/128))))>
#<alt (* (* x x) (+ 1/8 (* (* x x) 7/128)))>
#<alt (/ (+ 1 (- x (- 1 x))) (+ (pow (+ 1 x) 1/2) (pow (- 1 x) 1/2)))>
#<alt (+ 1 (- x (- 1 x)))>
#<alt (- x (- 1 x))>
#<alt (- 1 x)>
#<alt (* (* x x) 33/1024)>
#<alt (* x (* x (+ 7/128 (* (* x x) 33/1024))))>
#<alt (* x (+ 7/128 (* (* x x) 33/1024)))>
#<alt (* (* x x) 7/128)>
#<alt (+ (pow (+ 1 x) 1/2) (pow (- 1 x) 1/2))>
#<alt (pow (+ 1 x) 1/2)>
Outputs
#<alt x>
#<alt (* x (+ 1 (* 1/8 (pow x 2))))>
#<alt (* x (+ 1 (* (pow x 2) (+ 1/8 (* 7/128 (pow x 2))))))>
#<alt (* x (+ 1 (* (pow x 2) (+ 1/8 (* (pow x 2) (+ 7/128 (* 33/1024 (pow x 2))))))))>
#<alt (* 33/1024 (pow x 7))>
#<alt (* (pow x 7) (+ 33/1024 (* 7/128 (/ 1 (pow x 2)))))>
#<alt (* (pow x 7) (+ 33/1024 (+ (/ 1/8 (pow x 4)) (* 7/128 (/ 1 (pow x 2))))))>
#<alt (* (pow x 7) (+ 33/1024 (+ (/ 1/8 (pow x 4)) (+ (* 7/128 (/ 1 (pow x 2))) (/ 1 (pow x 6))))))>
#<alt (* 33/1024 (pow x 7))>
#<alt (* (pow x 7) (+ 33/1024 (* 7/128 (/ 1 (pow x 2)))))>
#<alt (* -1 (* (pow x 7) (- (* -1 (/ (+ 7/128 (* 1/8 (/ 1 (pow x 2)))) (pow x 2))) 33/1024)))>
#<alt (* -1 (* (pow x 7) (- (* -1 (/ (+ 1/8 (/ 1 (pow x 2))) (pow x 4))) (+ 33/1024 (* 7/128 (/ 1 (pow x 2)))))))>
#<alt 1>
#<alt (+ 1 (* 1/8 (pow x 2)))>
#<alt (+ 1 (* (pow x 2) (+ 1/8 (* 7/128 (pow x 2)))))>
#<alt (+ 1 (* (pow x 2) (+ 1/8 (* (pow x 2) (+ 7/128 (* 33/1024 (pow x 2)))))))>
#<alt (* 33/1024 (pow x 6))>
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#<alt (* (pow x 6) (+ 33/1024 (+ (/ 1/8 (pow x 4)) (* 7/128 (/ 1 (pow x 2))))))>
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#<alt (* (pow x 6) (+ 33/1024 (* 7/128 (/ 1 (pow x 2)))))>
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#<alt (* 1/8 (pow x 2))>
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#<alt (* 33/1024 (pow x 6))>
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#<alt (* (pow x 6) (+ 33/1024 (+ (/ 1/8 (pow x 4)) (* 7/128 (/ 1 (pow x 2))))))>
#<alt (* (pow x 6) (+ 33/1024 (+ (/ 1/8 (pow x 4)) (* 7/128 (/ 1 (pow x 2))))))>
#<alt (* 33/1024 (pow x 6))>
#<alt (* (pow x 6) (+ 33/1024 (* 7/128 (/ 1 (pow x 2)))))>
#<alt (* (pow x 6) (+ 33/1024 (+ (/ 1/8 (pow x 4)) (* 7/128 (/ 1 (pow x 2))))))>
#<alt (* (pow x 6) (+ 33/1024 (+ (/ 1/8 (pow x 4)) (* 7/128 (/ 1 (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 (pow x 2)>
#<alt x>
#<alt (* x (+ 1 (* 1/8 (pow x 2))))>
#<alt (* x (+ 1 (* 1/8 (pow x 2))))>
#<alt (* x (+ 1 (* 1/8 (pow x 2))))>
#<alt (* 1/8 (pow x 3))>
#<alt (* (pow x 3) (+ 1/8 (/ 1 (pow x 2))))>
#<alt (* (pow x 3) (+ 1/8 (/ 1 (pow x 2))))>
#<alt (* (pow x 3) (+ 1/8 (/ 1 (pow x 2))))>
#<alt (* 1/8 (pow x 3))>
#<alt (* (pow x 3) (+ 1/8 (/ 1 (pow x 2))))>
#<alt (* (pow x 3) (+ 1/8 (/ 1 (pow x 2))))>
#<alt (* (pow x 3) (+ 1/8 (/ 1 (pow x 2))))>
#<alt 1>
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#<alt (+ 1 (* 1/8 (pow x 2)))>
#<alt (+ 1 (* 1/8 (pow x 2)))>
#<alt (* 1/8 (pow x 2))>
#<alt (* (pow x 2) (+ 1/8 (/ 1 (pow x 2))))>
#<alt (* (pow x 2) (+ 1/8 (/ 1 (pow x 2))))>
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#<alt (* (pow x 2) (+ 1/8 (/ 1 (pow x 2))))>
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#<alt (* 1/8 (pow x 2))>
#<alt (* 1/8 (pow x 2))>
#<alt (* 1/8 (pow x 2))>
#<alt (* 1/8 (pow x 2))>
#<alt (* 1/8 (pow x 2))>
#<alt (* 1/8 (pow x 2))>
#<alt (* 1/8 (pow x 2))>
#<alt (* 1/8 (pow x 2))>
#<alt (* 1/8 (pow x 2))>
#<alt (* 1/8 (pow x 2))>
#<alt (* 1/8 (pow x 2))>
#<alt (* 1/8 (pow x 2))>
#<alt x>
#<alt (* x (+ 1 (* 1/8 (pow x 2))))>
#<alt (* x (+ 1 (* (pow x 2) (+ 1/8 (* 7/128 (pow x 2))))))>
#<alt (* x (+ 1 (* (pow x 2) (+ 1/8 (* 7/128 (pow x 2))))))>
#<alt (* 7/128 (pow x 5))>
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#<alt (* (pow x 5) (+ 7/128 (+ (* 1/8 (/ 1 (pow x 2))) (/ 1 (pow x 4)))))>
#<alt (* (pow x 5) (+ 7/128 (+ (* 1/8 (/ 1 (pow x 2))) (/ 1 (pow x 4)))))>
#<alt (* 7/128 (pow x 5))>
#<alt (* (pow x 5) (+ 7/128 (* 1/8 (/ 1 (pow x 2)))))>
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#<alt (* -1 (* (pow x 5) (- (* -1 (/ (+ 1/8 (/ 1 (pow x 2))) (pow x 2))) 7/128)))>
#<alt 1>
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#<alt (* 7/128 (pow x 4))>
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#<alt (* 7/128 (pow x 4))>
#<alt (* (pow x 4) (+ 7/128 (* 1/8 (/ 1 (pow x 2)))))>
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#<alt x>
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#<alt (* x (+ 1 (* (pow x 2) (+ 1/8 (* 7/128 (pow x 2))))))>
#<alt (* x (+ 1 (* (pow x 2) (+ 1/8 (* (pow x 2) (+ 7/128 (* 33/1024 (pow x 2))))))))>
#<alt (/ 2 (+ (sqrt (/ 1 x)) (* (sqrt (/ 1 x)) (sqrt -1))))>
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#<alt (- (+ (* -1 (/ (+ (* -2 (/ (pow (+ (* 1/2 (sqrt x)) (* 1/2 (* (sqrt x) (/ 1 (sqrt -1))))) 2) (pow (+ (sqrt (/ 1 x)) (* (sqrt (/ 1 x)) (sqrt -1))) 3))) (* 2 (/ (+ (* -1/8 (sqrt (pow x 3))) (* -1/8 (* (sqrt (pow x 3)) (/ 1 (pow (sqrt -1) 3))))) (pow (+ (sqrt (/ 1 x)) (* (sqrt (/ 1 x)) (sqrt -1))) 2)))) (pow x 4))) (* 2 (/ 1 (+ (sqrt (/ 1 x)) (* (sqrt (/ 1 x)) (sqrt -1)))))) (* 2 (/ (+ (* 1/2 (sqrt x)) (* 1/2 (* (sqrt x) (/ 1 (sqrt -1))))) (* (pow x 2) (pow (+ (sqrt (/ 1 x)) (* (sqrt (/ 1 x)) (sqrt -1))) 2)))))>
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#<alt (- (* -1 (/ (+ (* -2 (/ (+ (* -1/8 (* (sqrt (pow x 3)) (sqrt -1))) (* -1/8 (* (sqrt (pow x 3)) (/ 1 (pow (sqrt -1) 2))))) (pow (+ (* (sqrt (/ 1 x)) (sqrt -1)) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))) 2))) (* 2 (/ (pow (+ (* 1/2 (sqrt x)) (* 1/2 (* (sqrt x) (sqrt -1)))) 2) (pow (+ (* (sqrt (/ 1 x)) (sqrt -1)) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))) 3)))) (pow x 4))) (+ (* -2 (/ (+ (* 1/2 (sqrt x)) (* 1/2 (* (sqrt x) (sqrt -1)))) (* (pow x 2) (pow (+ (* (sqrt (/ 1 x)) (sqrt -1)) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))) 2)))) (* 2 (/ 1 (+ (* (sqrt (/ 1 x)) (sqrt -1)) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)))))))>
#<alt (- (* -1 (/ (+ (* -2 (/ (+ (* 1/16 (* (sqrt (pow x 5)) (sqrt -1))) (* 1/16 (* (sqrt (pow x 5)) (/ 1 (pow (sqrt -1) 4))))) (pow (+ (* (sqrt (/ 1 x)) (sqrt -1)) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))) 2))) (+ (* -1 (/ (* (+ (* -2 (/ (+ (* -1/8 (* (sqrt (pow x 3)) (sqrt -1))) (* -1/8 (* (sqrt (pow x 3)) (/ 1 (pow (sqrt -1) 2))))) (pow (+ (* (sqrt (/ 1 x)) (sqrt -1)) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))) 2))) (* 2 (/ (pow (+ (* 1/2 (sqrt x)) (* 1/2 (* (sqrt x) (sqrt -1)))) 2) (pow (+ (* (sqrt (/ 1 x)) (sqrt -1)) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))) 3)))) (+ (* 1/2 (sqrt x)) (* 1/2 (* (sqrt x) (sqrt -1))))) (+ (* (sqrt (/ 1 x)) (sqrt -1)) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))))) (* 2 (/ (* (+ (* -1/8 (* (sqrt (pow x 3)) (sqrt -1))) (* -1/8 (* (sqrt (pow x 3)) (/ 1 (pow (sqrt -1) 2))))) (+ (* 1/2 (sqrt x)) (* 1/2 (* (sqrt x) (sqrt -1))))) (pow (+ (* (sqrt (/ 1 x)) (sqrt -1)) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))) 3))))) (pow x 6))) (+ (* -2 (/ (+ (* -1/8 (* (sqrt (pow x 3)) (sqrt -1))) (* -1/8 (* (sqrt (pow x 3)) (/ 1 (pow (sqrt -1) 2))))) (* (pow x 4) (pow (+ (* (sqrt (/ 1 x)) (sqrt -1)) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))) 2)))) (+ (* -2 (/ (+ (* 1/2 (sqrt x)) (* 1/2 (* (sqrt x) (sqrt -1)))) (* (pow x 2) (pow (+ (* (sqrt (/ 1 x)) (sqrt -1)) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))) 2)))) (+ (* 2 (/ (pow (+ (* 1/2 (sqrt x)) (* 1/2 (* (sqrt x) (sqrt -1)))) 2) (* (pow x 4) (pow (+ (* (sqrt (/ 1 x)) (sqrt -1)) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))) 3)))) (* 2 (/ 1 (+ (* (sqrt (/ 1 x)) (sqrt -1)) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)))))))))>
#<alt (* 2 x)>
#<alt (* 2 x)>
#<alt (* 2 x)>
#<alt (* 2 x)>
#<alt (* 2 x)>
#<alt (* 2 x)>
#<alt (* 2 x)>
#<alt (* 2 x)>
#<alt (* 2 x)>
#<alt (* 2 x)>
#<alt (* 2 x)>
#<alt (* 2 x)>
#<alt -1>
#<alt (- (* 2 x) 1)>
#<alt (- (* 2 x) 1)>
#<alt (- (* 2 x) 1)>
#<alt (* 2 x)>
#<alt (* x (- 2 (/ 1 x)))>
#<alt (* x (- 2 (/ 1 x)))>
#<alt (* x (- 2 (/ 1 x)))>
#<alt (* 2 x)>
#<alt (* -1 (* x (- (/ 1 x) 2)))>
#<alt (* -1 (* x (- (/ 1 x) 2)))>
#<alt (* -1 (* x (- (/ 1 x) 2)))>
#<alt 1>
#<alt (+ 1 (* -1 x))>
#<alt (+ 1 (* -1 x))>
#<alt (+ 1 (* -1 x))>
#<alt (* -1 x)>
#<alt (* x (- (/ 1 x) 1))>
#<alt (* x (- (/ 1 x) 1))>
#<alt (* x (- (/ 1 x) 1))>
#<alt (* -1 x)>
#<alt (* -1 (* x (- 1 (/ 1 x))))>
#<alt (* -1 (* x (- 1 (/ 1 x))))>
#<alt (* -1 (* x (- 1 (/ 1 x))))>
#<alt (* 33/1024 (pow x 2))>
#<alt (* 33/1024 (pow x 2))>
#<alt (* 33/1024 (pow x 2))>
#<alt (* 33/1024 (pow x 2))>
#<alt (* 33/1024 (pow x 2))>
#<alt (* 33/1024 (pow x 2))>
#<alt (* 33/1024 (pow x 2))>
#<alt (* 33/1024 (pow x 2))>
#<alt (* 33/1024 (pow x 2))>
#<alt (* 33/1024 (pow x 2))>
#<alt (* 33/1024 (pow x 2))>
#<alt (* 33/1024 (pow x 2))>
#<alt (* 7/128 (pow x 2))>
#<alt (* (pow x 2) (+ 7/128 (* 33/1024 (pow x 2))))>
#<alt (* (pow x 2) (+ 7/128 (* 33/1024 (pow x 2))))>
#<alt (* (pow x 2) (+ 7/128 (* 33/1024 (pow x 2))))>
#<alt (* 33/1024 (pow x 4))>
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#<alt (* 33/1024 (pow x 4))>
#<alt (* (pow x 4) (+ 33/1024 (* 7/128 (/ 1 (pow x 2)))))>
#<alt (* (pow x 4) (+ 33/1024 (* 7/128 (/ 1 (pow x 2)))))>
#<alt (* (pow x 4) (+ 33/1024 (* 7/128 (/ 1 (pow x 2)))))>
#<alt (* 7/128 x)>
#<alt (* x (+ 7/128 (* 33/1024 (pow x 2))))>
#<alt (* x (+ 7/128 (* 33/1024 (pow x 2))))>
#<alt (* x (+ 7/128 (* 33/1024 (pow x 2))))>
#<alt (* 33/1024 (pow x 3))>
#<alt (* (pow x 3) (+ 33/1024 (* 7/128 (/ 1 (pow x 2)))))>
#<alt (* (pow x 3) (+ 33/1024 (* 7/128 (/ 1 (pow x 2)))))>
#<alt (* (pow x 3) (+ 33/1024 (* 7/128 (/ 1 (pow x 2)))))>
#<alt (* 33/1024 (pow x 3))>
#<alt (* (pow x 3) (+ 33/1024 (* 7/128 (/ 1 (pow x 2)))))>
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#<alt (* 7/128 (pow x 2))>
#<alt (* 7/128 (pow x 2))>
#<alt (* 7/128 (pow x 2))>
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#<alt (* 7/128 (pow x 2))>
#<alt (* 7/128 (pow x 2))>
#<alt (* 7/128 (pow x 2))>
#<alt (* 7/128 (pow x 2))>
#<alt (* 7/128 (pow x 2))>
#<alt (* 7/128 (pow x 2))>
#<alt (* 7/128 (pow x 2))>
#<alt 2>
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#<alt (+ 2 (* (pow x 2) (- (* -5/64 (pow x 2)) 1/4)))>
#<alt (+ 2 (* (pow x 2) (- (* (pow x 2) (- (* -21/512 (pow x 2)) 5/64)) 1/4)))>
#<alt (* x (+ (sqrt (/ 1 x)) (* (sqrt (/ 1 x)) (sqrt -1))))>
#<alt (* x (+ (sqrt (/ 1 x)) (+ (* 1/2 (sqrt (/ 1 (pow x 3)))) (+ (* 1/2 (* (sqrt (/ 1 (pow x 3))) (/ 1 (sqrt -1)))) (* (sqrt (/ 1 x)) (sqrt -1))))))>
#<alt (* x (+ (sqrt (/ 1 x)) (+ (* -1/8 (sqrt (/ 1 (pow x 5)))) (+ (* -1/8 (* (sqrt (/ 1 (pow x 5))) (/ 1 (pow (sqrt -1) 3)))) (+ (* 1/2 (sqrt (/ 1 (pow x 3)))) (+ (* 1/2 (* (sqrt (/ 1 (pow x 3))) (/ 1 (sqrt -1)))) (* (sqrt (/ 1 x)) (sqrt -1))))))))>
#<alt (* x (+ (sqrt (/ 1 x)) (+ (* -1/8 (sqrt (/ 1 (pow x 5)))) (+ (* -1/8 (* (sqrt (/ 1 (pow x 5))) (/ 1 (pow (sqrt -1) 3)))) (+ (* 1/16 (sqrt (/ 1 (pow x 7)))) (+ (* 1/16 (* (sqrt (/ 1 (pow x 7))) (/ 1 (pow (sqrt -1) 5)))) (+ (* 1/2 (sqrt (/ 1 (pow x 3)))) (+ (* 1/2 (* (sqrt (/ 1 (pow x 3))) (/ 1 (sqrt -1)))) (* (sqrt (/ 1 x)) (sqrt -1))))))))))>
#<alt (* -1 (* x (+ (* (sqrt (/ 1 x)) (sqrt -1)) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)))))>
#<alt (* -1 (* x (+ (* 1/2 (sqrt (/ 1 (pow x 3)))) (+ (* 1/2 (* (sqrt (/ 1 (pow x 3))) (sqrt -1))) (+ (* (sqrt (/ 1 x)) (sqrt -1)) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)))))))>
#<alt (* -1 (* x (+ (* -1/8 (* (sqrt (/ 1 (pow x 5))) (sqrt -1))) (+ (* -1/8 (* (sqrt (/ 1 (pow x 5))) (/ 1 (pow (sqrt -1) 2)))) (+ (* 1/2 (sqrt (/ 1 (pow x 3)))) (+ (* 1/2 (* (sqrt (/ 1 (pow x 3))) (sqrt -1))) (+ (* (sqrt (/ 1 x)) (sqrt -1)) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)))))))))>
#<alt (* -1 (* x (+ (* -1/8 (* (sqrt (/ 1 (pow x 5))) (sqrt -1))) (+ (* -1/8 (* (sqrt (/ 1 (pow x 5))) (/ 1 (pow (sqrt -1) 2)))) (+ (* 1/16 (* (sqrt (/ 1 (pow x 7))) (sqrt -1))) (+ (* 1/16 (* (sqrt (/ 1 (pow x 7))) (/ 1 (pow (sqrt -1) 4)))) (+ (* 1/2 (sqrt (/ 1 (pow x 3)))) (+ (* 1/2 (* (sqrt (/ 1 (pow x 3))) (sqrt -1))) (+ (* (sqrt (/ 1 x)) (sqrt -1)) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)))))))))))>
#<alt 1>
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#<alt (+ 1 (* x (+ 1/2 (* x (- (* 1/16 x) 1/8)))))>
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#<alt (* -1 (* (sqrt x) (pow (sqrt -1) 2)))>
#<alt (* -1 (* x (+ (* 1/2 (sqrt (/ 1 (pow x 3)))) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)))))>
#<alt (* -1 (* x (+ (* -1/8 (* (sqrt (/ 1 (pow x 5))) (/ 1 (pow (sqrt -1) 2)))) (+ (* 1/2 (sqrt (/ 1 (pow x 3)))) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))))))>
#<alt (* -1 (* x (+ (* -1/8 (* (sqrt (/ 1 (pow x 5))) (/ 1 (pow (sqrt -1) 2)))) (+ (* 1/16 (* (sqrt (/ 1 (pow x 7))) (/ 1 (pow (sqrt -1) 4)))) (+ (* 1/2 (sqrt (/ 1 (pow x 3)))) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)))))))>
Calls

60 calls:

TimeVariablePointExpression
4.0ms
x
@inf
(+ 1 (- x (- 1 x)))
3.0ms
x
@inf
(/ (+ 1 (- x (- 1 x))) (+ (pow (+ 1 x) 1/2) (pow (- 1 x) 1/2)))
2.0ms
x
@-inf
(/ (+ 1 (- x (- 1 x))) (+ (pow (+ 1 x) 1/2) (pow (- 1 x) 1/2)))
1.0ms
x
@-inf
(* x (+ 1 (* (* x x) (+ 1/8 (* (* x x) 7/128)))))
1.0ms
x
@0
(* x (+ 1 (* (* x x) (+ 1/8 (* x (* x (+ 7/128 (* (* x x) 33/1024))))))))

rewrite353.0ms (3.6%)

Algorithm
batch-egg-rewrite
Rules
3204×fma-lowering-fma.f32
3204×fma-lowering-fma.f64
2472×*-lowering-*.f32
2472×*-lowering-*.f64
1896×prod-diff
Iterations

Useful iterations: 2 (0.0ms)

IterNodesCost
031171
1238145
22376140
08486140
Stop Event
iter limit
node limit
Counts
20 → 569
Calls
Call 1
Inputs
(* x (+ 1 (* (* x x) (+ 1/8 (* x (* x (+ 7/128 (* (* x x) 33/1024))))))))
(+ 1 (* (* x x) (+ 1/8 (* x (* x (+ 7/128 (* (* x x) 33/1024)))))))
(* (* x x) (+ 1/8 (* x (* x (+ 7/128 (* (* x x) 33/1024))))))
(* x x)
(* x (+ 1 (* 1/8 (* x x))))
(+ 1 (* 1/8 (* x x)))
(* 1/8 (* x x))
(* x (+ 1 (* (* x x) (+ 1/8 (* (* x x) 7/128)))))
(+ 1 (* (* x x) (+ 1/8 (* (* x x) 7/128))))
(* (* x x) (+ 1/8 (* (* x x) 7/128)))
(/ (+ 1 (- x (- 1 x))) (+ (pow (+ 1 x) 1/2) (pow (- 1 x) 1/2)))
(+ 1 (- x (- 1 x)))
(- x (- 1 x))
(- 1 x)
(* (* x x) 33/1024)
(* x (* x (+ 7/128 (* (* x x) 33/1024))))
(* x (+ 7/128 (* (* x x) 33/1024)))
(* (* x x) 7/128)
(+ (pow (+ 1 x) 1/2) (pow (- 1 x) 1/2))
(pow (+ 1 x) 1/2)
Outputs
(+.f64 x (*.f64 x (*.f64 (*.f64 x x) (+.f64 #s(literal 1/8 binary64) (*.f64 (*.f64 x x) (+.f64 #s(literal 7/128 binary64) (*.f64 (*.f64 x x) #s(literal 33/1024 binary64))))))))
(+.f64 (*.f64 x (*.f64 (*.f64 x x) (+.f64 #s(literal 1/8 binary64) (*.f64 (*.f64 x x) (+.f64 #s(literal 7/128 binary64) (*.f64 (*.f64 x x) #s(literal 33/1024 binary64))))))) x)
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(*.f64 (sqrt.f64 (+.f64 #s(literal 1 binary64) (*.f64 x (*.f64 x x)))) (pow.f64 (/.f64 #s(literal 1 binary64) (+.f64 #s(literal 1 binary64) (*.f64 x (+.f64 x #s(literal -1 binary64))))) #s(literal 1/2 binary64)))
(*.f64 (pow.f64 (pow.f64 (+.f64 x #s(literal 1 binary64)) #s(literal 1/4 binary64)) #s(literal 1/2 binary64)) (pow.f64 (pow.f64 (+.f64 x #s(literal 1 binary64)) #s(literal 3/4 binary64)) #s(literal 1/2 binary64)))
(*.f64 (pow.f64 (pow.f64 (+.f64 x #s(literal 1 binary64)) #s(literal 3/4 binary64)) #s(literal 1/2 binary64)) (pow.f64 (pow.f64 (+.f64 x #s(literal 1 binary64)) #s(literal 1/4 binary64)) #s(literal 1/2 binary64)))
(*.f64 (pow.f64 (/.f64 (-.f64 #s(literal 1 binary64) (*.f64 x x)) (-.f64 #s(literal 1 binary64) (*.f64 x (*.f64 x x)))) #s(literal 1/2 binary64)) (sqrt.f64 (+.f64 #s(literal 1 binary64) (*.f64 x (+.f64 x #s(literal 1 binary64))))))
(*.f64 (pow.f64 (/.f64 (-.f64 #s(literal 1 binary64) (*.f64 x x)) (-.f64 #s(literal 1 binary64) (*.f64 x x))) #s(literal 1/2 binary64)) (sqrt.f64 (+.f64 x #s(literal 1 binary64))))

simplify334.0ms (3.4%)

Algorithm
egg-herbie
Rules
5894×*-lowering-*.f32
5894×*-lowering-*.f64
2858×+-lowering-+.f64
2858×+-lowering-+.f32
2160×/-lowering-/.f32
Iterations

Useful iterations: 2 (0.0ms)

IterNodesCost
03393050
111382475
245272386
081302386
Stop Event
iter limit
node limit
Counts
240 → 240
Calls
Call 1
Inputs
x
(* x (+ 1 (* 1/8 (pow x 2))))
(* x (+ 1 (* (pow x 2) (+ 1/8 (* 7/128 (pow x 2))))))
(* x (+ 1 (* (pow x 2) (+ 1/8 (* (pow x 2) (+ 7/128 (* 33/1024 (pow x 2))))))))
(* 33/1024 (pow x 7))
(* (pow x 7) (+ 33/1024 (* 7/128 (/ 1 (pow x 2)))))
(* (pow x 7) (+ 33/1024 (+ (/ 1/8 (pow x 4)) (* 7/128 (/ 1 (pow x 2))))))
(* (pow x 7) (+ 33/1024 (+ (/ 1/8 (pow x 4)) (+ (* 7/128 (/ 1 (pow x 2))) (/ 1 (pow x 6))))))
(* 33/1024 (pow x 7))
(* (pow x 7) (+ 33/1024 (* 7/128 (/ 1 (pow x 2)))))
(* -1 (* (pow x 7) (- (* -1 (/ (+ 7/128 (* 1/8 (/ 1 (pow x 2)))) (pow x 2))) 33/1024)))
(* -1 (* (pow x 7) (- (* -1 (/ (+ 1/8 (/ 1 (pow x 2))) (pow x 4))) (+ 33/1024 (* 7/128 (/ 1 (pow x 2)))))))
1
(+ 1 (* 1/8 (pow x 2)))
(+ 1 (* (pow x 2) (+ 1/8 (* 7/128 (pow x 2)))))
(+ 1 (* (pow x 2) (+ 1/8 (* (pow x 2) (+ 7/128 (* 33/1024 (pow x 2)))))))
(* 33/1024 (pow x 6))
(* (pow x 6) (+ 33/1024 (* 7/128 (/ 1 (pow x 2)))))
(* (pow x 6) (+ 33/1024 (+ (/ 1/8 (pow x 4)) (* 7/128 (/ 1 (pow x 2))))))
(* (pow x 6) (+ 33/1024 (+ (/ 1/8 (pow x 4)) (+ (* 7/128 (/ 1 (pow x 2))) (/ 1 (pow x 6))))))
(* 33/1024 (pow x 6))
(* (pow x 6) (+ 33/1024 (* 7/128 (/ 1 (pow x 2)))))
(* (pow x 6) (+ 33/1024 (+ (/ 1/8 (pow x 4)) (* 7/128 (/ 1 (pow x 2))))))
(* (pow x 6) (+ 33/1024 (+ (/ 1/8 (pow x 4)) (+ (* 7/128 (/ 1 (pow x 2))) (/ 1 (pow x 6))))))
(* 1/8 (pow x 2))
(* (pow x 2) (+ 1/8 (* 7/128 (pow x 2))))
(* (pow x 2) (+ 1/8 (* (pow x 2) (+ 7/128 (* 33/1024 (pow x 2))))))
(* (pow x 2) (+ 1/8 (* (pow x 2) (+ 7/128 (* 33/1024 (pow x 2))))))
(* 33/1024 (pow x 6))
(* (pow x 6) (+ 33/1024 (* 7/128 (/ 1 (pow x 2)))))
(* (pow x 6) (+ 33/1024 (+ (/ 1/8 (pow x 4)) (* 7/128 (/ 1 (pow x 2))))))
(* (pow x 6) (+ 33/1024 (+ (/ 1/8 (pow x 4)) (* 7/128 (/ 1 (pow x 2))))))
(* 33/1024 (pow x 6))
(* (pow x 6) (+ 33/1024 (* 7/128 (/ 1 (pow x 2)))))
(* (pow x 6) (+ 33/1024 (+ (/ 1/8 (pow x 4)) (* 7/128 (/ 1 (pow x 2))))))
(* (pow x 6) (+ 33/1024 (+ (/ 1/8 (pow x 4)) (* 7/128 (/ 1 (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)
(pow x 2)
x
(* x (+ 1 (* 1/8 (pow x 2))))
(* x (+ 1 (* 1/8 (pow x 2))))
(* x (+ 1 (* 1/8 (pow x 2))))
(* 1/8 (pow x 3))
(* (pow x 3) (+ 1/8 (/ 1 (pow x 2))))
(* (pow x 3) (+ 1/8 (/ 1 (pow x 2))))
(* (pow x 3) (+ 1/8 (/ 1 (pow x 2))))
(* 1/8 (pow x 3))
(* (pow x 3) (+ 1/8 (/ 1 (pow x 2))))
(* (pow x 3) (+ 1/8 (/ 1 (pow x 2))))
(* (pow x 3) (+ 1/8 (/ 1 (pow x 2))))
1
(+ 1 (* 1/8 (pow x 2)))
(+ 1 (* 1/8 (pow x 2)))
(+ 1 (* 1/8 (pow x 2)))
(* 1/8 (pow x 2))
(* (pow x 2) (+ 1/8 (/ 1 (pow x 2))))
(* (pow x 2) (+ 1/8 (/ 1 (pow x 2))))
(* (pow x 2) (+ 1/8 (/ 1 (pow x 2))))
(* 1/8 (pow x 2))
(* (pow x 2) (+ 1/8 (/ 1 (pow x 2))))
(* (pow x 2) (+ 1/8 (/ 1 (pow x 2))))
(* (pow x 2) (+ 1/8 (/ 1 (pow x 2))))
(* 1/8 (pow x 2))
(* 1/8 (pow x 2))
(* 1/8 (pow x 2))
(* 1/8 (pow x 2))
(* 1/8 (pow x 2))
(* 1/8 (pow x 2))
(* 1/8 (pow x 2))
(* 1/8 (pow x 2))
(* 1/8 (pow x 2))
(* 1/8 (pow x 2))
(* 1/8 (pow x 2))
(* 1/8 (pow x 2))
x
(* x (+ 1 (* 1/8 (pow x 2))))
(* x (+ 1 (* (pow x 2) (+ 1/8 (* 7/128 (pow x 2))))))
(* x (+ 1 (* (pow x 2) (+ 1/8 (* 7/128 (pow x 2))))))
(* 7/128 (pow x 5))
(* (pow x 5) (+ 7/128 (* 1/8 (/ 1 (pow x 2)))))
(* (pow x 5) (+ 7/128 (+ (* 1/8 (/ 1 (pow x 2))) (/ 1 (pow x 4)))))
(* (pow x 5) (+ 7/128 (+ (* 1/8 (/ 1 (pow x 2))) (/ 1 (pow x 4)))))
(* 7/128 (pow x 5))
(* (pow x 5) (+ 7/128 (* 1/8 (/ 1 (pow x 2)))))
(* -1 (* (pow x 5) (- (* -1 (/ (+ 1/8 (/ 1 (pow x 2))) (pow x 2))) 7/128)))
(* -1 (* (pow x 5) (- (* -1 (/ (+ 1/8 (/ 1 (pow x 2))) (pow x 2))) 7/128)))
1
(+ 1 (* 1/8 (pow x 2)))
(+ 1 (* (pow x 2) (+ 1/8 (* 7/128 (pow x 2)))))
(+ 1 (* (pow x 2) (+ 1/8 (* 7/128 (pow x 2)))))
(* 7/128 (pow x 4))
(* (pow x 4) (+ 7/128 (* 1/8 (/ 1 (pow x 2)))))
(* (pow x 4) (+ 7/128 (+ (* 1/8 (/ 1 (pow x 2))) (/ 1 (pow x 4)))))
(* (pow x 4) (+ 7/128 (+ (* 1/8 (/ 1 (pow x 2))) (/ 1 (pow x 4)))))
(* 7/128 (pow x 4))
(* (pow x 4) (+ 7/128 (* 1/8 (/ 1 (pow x 2)))))
(* (pow x 4) (+ 7/128 (+ (* 1/8 (/ 1 (pow x 2))) (/ 1 (pow x 4)))))
(* (pow x 4) (+ 7/128 (+ (* 1/8 (/ 1 (pow x 2))) (/ 1 (pow x 4)))))
(* 1/8 (pow x 2))
(* (pow x 2) (+ 1/8 (* 7/128 (pow x 2))))
(* (pow x 2) (+ 1/8 (* 7/128 (pow x 2))))
(* (pow x 2) (+ 1/8 (* 7/128 (pow x 2))))
(* 7/128 (pow x 4))
(* (pow x 4) (+ 7/128 (* 1/8 (/ 1 (pow x 2)))))
(* (pow x 4) (+ 7/128 (* 1/8 (/ 1 (pow x 2)))))
(* (pow x 4) (+ 7/128 (* 1/8 (/ 1 (pow x 2)))))
(* 7/128 (pow x 4))
(* (pow x 4) (+ 7/128 (* 1/8 (/ 1 (pow x 2)))))
(* (pow x 4) (+ 7/128 (* 1/8 (/ 1 (pow x 2)))))
(* (pow x 4) (+ 7/128 (* 1/8 (/ 1 (pow x 2)))))
x
(* x (+ 1 (* 1/8 (pow x 2))))
(* x (+ 1 (* (pow x 2) (+ 1/8 (* 7/128 (pow x 2))))))
(* x (+ 1 (* (pow x 2) (+ 1/8 (* (pow x 2) (+ 7/128 (* 33/1024 (pow x 2))))))))
(/ 2 (+ (sqrt (/ 1 x)) (* (sqrt (/ 1 x)) (sqrt -1))))
(+ (* -2 (/ (+ (* 1/2 (sqrt x)) (* 1/2 (* (sqrt x) (/ 1 (sqrt -1))))) (* (pow x 2) (pow (+ (sqrt (/ 1 x)) (* (sqrt (/ 1 x)) (sqrt -1))) 2)))) (* 2 (/ 1 (+ (sqrt (/ 1 x)) (* (sqrt (/ 1 x)) (sqrt -1))))))
(- (+ (* -1 (/ (+ (* -2 (/ (pow (+ (* 1/2 (sqrt x)) (* 1/2 (* (sqrt x) (/ 1 (sqrt -1))))) 2) (pow (+ (sqrt (/ 1 x)) (* (sqrt (/ 1 x)) (sqrt -1))) 3))) (* 2 (/ (+ (* -1/8 (sqrt (pow x 3))) (* -1/8 (* (sqrt (pow x 3)) (/ 1 (pow (sqrt -1) 3))))) (pow (+ (sqrt (/ 1 x)) (* (sqrt (/ 1 x)) (sqrt -1))) 2)))) (pow x 4))) (* 2 (/ 1 (+ (sqrt (/ 1 x)) (* (sqrt (/ 1 x)) (sqrt -1)))))) (* 2 (/ (+ (* 1/2 (sqrt x)) (* 1/2 (* (sqrt x) (/ 1 (sqrt -1))))) (* (pow x 2) (pow (+ (sqrt (/ 1 x)) (* (sqrt (/ 1 x)) (sqrt -1))) 2)))))
(- (+ (* -1 (/ (+ (* -2 (/ (* (+ (* -1/8 (sqrt (pow x 3))) (* -1/8 (* (sqrt (pow x 3)) (/ 1 (pow (sqrt -1) 3))))) (+ (* 1/2 (sqrt x)) (* 1/2 (* (sqrt x) (/ 1 (sqrt -1)))))) (pow (+ (sqrt (/ 1 x)) (* (sqrt (/ 1 x)) (sqrt -1))) 3))) (+ (* -1 (/ (* (+ (* -2 (/ (pow (+ (* 1/2 (sqrt x)) (* 1/2 (* (sqrt x) (/ 1 (sqrt -1))))) 2) (pow (+ (sqrt (/ 1 x)) (* (sqrt (/ 1 x)) (sqrt -1))) 3))) (* 2 (/ (+ (* -1/8 (sqrt (pow x 3))) (* -1/8 (* (sqrt (pow x 3)) (/ 1 (pow (sqrt -1) 3))))) (pow (+ (sqrt (/ 1 x)) (* (sqrt (/ 1 x)) (sqrt -1))) 2)))) (+ (* 1/2 (sqrt x)) (* 1/2 (* (sqrt x) (/ 1 (sqrt -1)))))) (+ (sqrt (/ 1 x)) (* (sqrt (/ 1 x)) (sqrt -1))))) (* 2 (/ (+ (* 1/16 (sqrt (pow x 5))) (* 1/16 (* (sqrt (pow x 5)) (/ 1 (pow (sqrt -1) 5))))) (pow (+ (sqrt (/ 1 x)) (* (sqrt (/ 1 x)) (sqrt -1))) 2))))) (pow x 6))) (* 2 (/ 1 (+ (sqrt (/ 1 x)) (* (sqrt (/ 1 x)) (sqrt -1)))))) (+ (* -2 (/ (pow (+ (* 1/2 (sqrt x)) (* 1/2 (* (sqrt x) (/ 1 (sqrt -1))))) 2) (* (pow x 4) (pow (+ (sqrt (/ 1 x)) (* (sqrt (/ 1 x)) (sqrt -1))) 3)))) (+ (* 2 (/ (+ (* -1/8 (sqrt (pow x 3))) (* -1/8 (* (sqrt (pow x 3)) (/ 1 (pow (sqrt -1) 3))))) (* (pow x 4) (pow (+ (sqrt (/ 1 x)) (* (sqrt (/ 1 x)) (sqrt -1))) 2)))) (* 2 (/ (+ (* 1/2 (sqrt x)) (* 1/2 (* (sqrt x) (/ 1 (sqrt -1))))) (* (pow x 2) (pow (+ (sqrt (/ 1 x)) (* (sqrt (/ 1 x)) (sqrt -1))) 2)))))))
(/ -2 (+ (* (sqrt (/ 1 x)) (sqrt -1)) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))))
(- (* 2 (/ (+ (* 1/2 (sqrt x)) (* 1/2 (* (sqrt x) (sqrt -1)))) (* (pow x 2) (pow (+ (* (sqrt (/ 1 x)) (sqrt -1)) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))) 2)))) (* 2 (/ 1 (+ (* (sqrt (/ 1 x)) (sqrt -1)) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))))))
(- (* -1 (/ (+ (* -2 (/ (+ (* -1/8 (* (sqrt (pow x 3)) (sqrt -1))) (* -1/8 (* (sqrt (pow x 3)) (/ 1 (pow (sqrt -1) 2))))) (pow (+ (* (sqrt (/ 1 x)) (sqrt -1)) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))) 2))) (* 2 (/ (pow (+ (* 1/2 (sqrt x)) (* 1/2 (* (sqrt x) (sqrt -1)))) 2) (pow (+ (* (sqrt (/ 1 x)) (sqrt -1)) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))) 3)))) (pow x 4))) (+ (* -2 (/ (+ (* 1/2 (sqrt x)) (* 1/2 (* (sqrt x) (sqrt -1)))) (* (pow x 2) (pow (+ (* (sqrt (/ 1 x)) (sqrt -1)) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))) 2)))) (* 2 (/ 1 (+ (* (sqrt (/ 1 x)) (sqrt -1)) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)))))))
(- (* -1 (/ (+ (* -2 (/ (+ (* 1/16 (* (sqrt (pow x 5)) (sqrt -1))) (* 1/16 (* (sqrt (pow x 5)) (/ 1 (pow (sqrt -1) 4))))) (pow (+ (* (sqrt (/ 1 x)) (sqrt -1)) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))) 2))) (+ (* -1 (/ (* (+ (* -2 (/ (+ (* -1/8 (* (sqrt (pow x 3)) (sqrt -1))) (* -1/8 (* (sqrt (pow x 3)) (/ 1 (pow (sqrt -1) 2))))) (pow (+ (* (sqrt (/ 1 x)) (sqrt -1)) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))) 2))) (* 2 (/ (pow (+ (* 1/2 (sqrt x)) (* 1/2 (* (sqrt x) (sqrt -1)))) 2) (pow (+ (* (sqrt (/ 1 x)) (sqrt -1)) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))) 3)))) (+ (* 1/2 (sqrt x)) (* 1/2 (* (sqrt x) (sqrt -1))))) (+ (* (sqrt (/ 1 x)) (sqrt -1)) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))))) (* 2 (/ (* (+ (* -1/8 (* (sqrt (pow x 3)) (sqrt -1))) (* -1/8 (* (sqrt (pow x 3)) (/ 1 (pow (sqrt -1) 2))))) (+ (* 1/2 (sqrt x)) (* 1/2 (* (sqrt x) (sqrt -1))))) (pow (+ (* (sqrt (/ 1 x)) (sqrt -1)) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))) 3))))) (pow x 6))) (+ (* -2 (/ (+ (* -1/8 (* (sqrt (pow x 3)) (sqrt -1))) (* -1/8 (* (sqrt (pow x 3)) (/ 1 (pow (sqrt -1) 2))))) (* (pow x 4) (pow (+ (* (sqrt (/ 1 x)) (sqrt -1)) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))) 2)))) (+ (* -2 (/ (+ (* 1/2 (sqrt x)) (* 1/2 (* (sqrt x) (sqrt -1)))) (* (pow x 2) (pow (+ (* (sqrt (/ 1 x)) (sqrt -1)) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))) 2)))) (+ (* 2 (/ (pow (+ (* 1/2 (sqrt x)) (* 1/2 (* (sqrt x) (sqrt -1)))) 2) (* (pow x 4) (pow (+ (* (sqrt (/ 1 x)) (sqrt -1)) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))) 3)))) (* 2 (/ 1 (+ (* (sqrt (/ 1 x)) (sqrt -1)) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)))))))))
(* 2 x)
(* 2 x)
(* 2 x)
(* 2 x)
(* 2 x)
(* 2 x)
(* 2 x)
(* 2 x)
(* 2 x)
(* 2 x)
(* 2 x)
(* 2 x)
-1
(- (* 2 x) 1)
(- (* 2 x) 1)
(- (* 2 x) 1)
(* 2 x)
(* x (- 2 (/ 1 x)))
(* x (- 2 (/ 1 x)))
(* x (- 2 (/ 1 x)))
(* 2 x)
(* -1 (* x (- (/ 1 x) 2)))
(* -1 (* x (- (/ 1 x) 2)))
(* -1 (* x (- (/ 1 x) 2)))
1
(+ 1 (* -1 x))
(+ 1 (* -1 x))
(+ 1 (* -1 x))
(* -1 x)
(* x (- (/ 1 x) 1))
(* x (- (/ 1 x) 1))
(* x (- (/ 1 x) 1))
(* -1 x)
(* -1 (* x (- 1 (/ 1 x))))
(* -1 (* x (- 1 (/ 1 x))))
(* -1 (* x (- 1 (/ 1 x))))
(* 33/1024 (pow x 2))
(* 33/1024 (pow x 2))
(* 33/1024 (pow x 2))
(* 33/1024 (pow x 2))
(* 33/1024 (pow x 2))
(* 33/1024 (pow x 2))
(* 33/1024 (pow x 2))
(* 33/1024 (pow x 2))
(* 33/1024 (pow x 2))
(* 33/1024 (pow x 2))
(* 33/1024 (pow x 2))
(* 33/1024 (pow x 2))
(* 7/128 (pow x 2))
(* (pow x 2) (+ 7/128 (* 33/1024 (pow x 2))))
(* (pow x 2) (+ 7/128 (* 33/1024 (pow x 2))))
(* (pow x 2) (+ 7/128 (* 33/1024 (pow x 2))))
(* 33/1024 (pow x 4))
(* (pow x 4) (+ 33/1024 (* 7/128 (/ 1 (pow x 2)))))
(* (pow x 4) (+ 33/1024 (* 7/128 (/ 1 (pow x 2)))))
(* (pow x 4) (+ 33/1024 (* 7/128 (/ 1 (pow x 2)))))
(* 33/1024 (pow x 4))
(* (pow x 4) (+ 33/1024 (* 7/128 (/ 1 (pow x 2)))))
(* (pow x 4) (+ 33/1024 (* 7/128 (/ 1 (pow x 2)))))
(* (pow x 4) (+ 33/1024 (* 7/128 (/ 1 (pow x 2)))))
(* 7/128 x)
(* x (+ 7/128 (* 33/1024 (pow x 2))))
(* x (+ 7/128 (* 33/1024 (pow x 2))))
(* x (+ 7/128 (* 33/1024 (pow x 2))))
(* 33/1024 (pow x 3))
(* (pow x 3) (+ 33/1024 (* 7/128 (/ 1 (pow x 2)))))
(* (pow x 3) (+ 33/1024 (* 7/128 (/ 1 (pow x 2)))))
(* (pow x 3) (+ 33/1024 (* 7/128 (/ 1 (pow x 2)))))
(* 33/1024 (pow x 3))
(* (pow x 3) (+ 33/1024 (* 7/128 (/ 1 (pow x 2)))))
(* (pow x 3) (+ 33/1024 (* 7/128 (/ 1 (pow x 2)))))
(* (pow x 3) (+ 33/1024 (* 7/128 (/ 1 (pow x 2)))))
(* 7/128 (pow x 2))
(* 7/128 (pow x 2))
(* 7/128 (pow x 2))
(* 7/128 (pow x 2))
(* 7/128 (pow x 2))
(* 7/128 (pow x 2))
(* 7/128 (pow x 2))
(* 7/128 (pow x 2))
(* 7/128 (pow x 2))
(* 7/128 (pow x 2))
(* 7/128 (pow x 2))
(* 7/128 (pow x 2))
2
(+ 2 (* -1/4 (pow x 2)))
(+ 2 (* (pow x 2) (- (* -5/64 (pow x 2)) 1/4)))
(+ 2 (* (pow x 2) (- (* (pow x 2) (- (* -21/512 (pow x 2)) 5/64)) 1/4)))
(* x (+ (sqrt (/ 1 x)) (* (sqrt (/ 1 x)) (sqrt -1))))
(* x (+ (sqrt (/ 1 x)) (+ (* 1/2 (sqrt (/ 1 (pow x 3)))) (+ (* 1/2 (* (sqrt (/ 1 (pow x 3))) (/ 1 (sqrt -1)))) (* (sqrt (/ 1 x)) (sqrt -1))))))
(* x (+ (sqrt (/ 1 x)) (+ (* -1/8 (sqrt (/ 1 (pow x 5)))) (+ (* -1/8 (* (sqrt (/ 1 (pow x 5))) (/ 1 (pow (sqrt -1) 3)))) (+ (* 1/2 (sqrt (/ 1 (pow x 3)))) (+ (* 1/2 (* (sqrt (/ 1 (pow x 3))) (/ 1 (sqrt -1)))) (* (sqrt (/ 1 x)) (sqrt -1))))))))
(* x (+ (sqrt (/ 1 x)) (+ (* -1/8 (sqrt (/ 1 (pow x 5)))) (+ (* -1/8 (* (sqrt (/ 1 (pow x 5))) (/ 1 (pow (sqrt -1) 3)))) (+ (* 1/16 (sqrt (/ 1 (pow x 7)))) (+ (* 1/16 (* (sqrt (/ 1 (pow x 7))) (/ 1 (pow (sqrt -1) 5)))) (+ (* 1/2 (sqrt (/ 1 (pow x 3)))) (+ (* 1/2 (* (sqrt (/ 1 (pow x 3))) (/ 1 (sqrt -1)))) (* (sqrt (/ 1 x)) (sqrt -1))))))))))
(* -1 (* x (+ (* (sqrt (/ 1 x)) (sqrt -1)) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)))))
(* -1 (* x (+ (* 1/2 (sqrt (/ 1 (pow x 3)))) (+ (* 1/2 (* (sqrt (/ 1 (pow x 3))) (sqrt -1))) (+ (* (sqrt (/ 1 x)) (sqrt -1)) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)))))))
(* -1 (* x (+ (* -1/8 (* (sqrt (/ 1 (pow x 5))) (sqrt -1))) (+ (* -1/8 (* (sqrt (/ 1 (pow x 5))) (/ 1 (pow (sqrt -1) 2)))) (+ (* 1/2 (sqrt (/ 1 (pow x 3)))) (+ (* 1/2 (* (sqrt (/ 1 (pow x 3))) (sqrt -1))) (+ (* (sqrt (/ 1 x)) (sqrt -1)) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)))))))))
(* -1 (* x (+ (* -1/8 (* (sqrt (/ 1 (pow x 5))) (sqrt -1))) (+ (* -1/8 (* (sqrt (/ 1 (pow x 5))) (/ 1 (pow (sqrt -1) 2)))) (+ (* 1/16 (* (sqrt (/ 1 (pow x 7))) (sqrt -1))) (+ (* 1/16 (* (sqrt (/ 1 (pow x 7))) (/ 1 (pow (sqrt -1) 4)))) (+ (* 1/2 (sqrt (/ 1 (pow x 3)))) (+ (* 1/2 (* (sqrt (/ 1 (pow x 3))) (sqrt -1))) (+ (* (sqrt (/ 1 x)) (sqrt -1)) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)))))))))))
1
(+ 1 (* 1/2 x))
(+ 1 (* x (+ 1/2 (* -1/8 x))))
(+ 1 (* x (+ 1/2 (* x (- (* 1/16 x) 1/8)))))
(sqrt x)
(* x (+ (sqrt (/ 1 x)) (* 1/2 (sqrt (/ 1 (pow x 3))))))
(* x (+ (sqrt (/ 1 x)) (+ (* -1/8 (sqrt (/ 1 (pow x 5)))) (* 1/2 (sqrt (/ 1 (pow x 3)))))))
(* x (+ (sqrt (/ 1 x)) (+ (* -1/8 (sqrt (/ 1 (pow x 5)))) (+ (* 1/16 (sqrt (/ 1 (pow x 7)))) (* 1/2 (sqrt (/ 1 (pow x 3))))))))
(* -1 (* (sqrt x) (pow (sqrt -1) 2)))
(* -1 (* x (+ (* 1/2 (sqrt (/ 1 (pow x 3)))) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)))))
(* -1 (* x (+ (* -1/8 (* (sqrt (/ 1 (pow x 5))) (/ 1 (pow (sqrt -1) 2)))) (+ (* 1/2 (sqrt (/ 1 (pow x 3)))) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))))))
(* -1 (* x (+ (* -1/8 (* (sqrt (/ 1 (pow x 5))) (/ 1 (pow (sqrt -1) 2)))) (+ (* 1/16 (* (sqrt (/ 1 (pow x 7))) (/ 1 (pow (sqrt -1) 4)))) (+ (* 1/2 (sqrt (/ 1 (pow x 3)))) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)))))))
Outputs
x
(* x (+ 1 (* 1/8 (pow x 2))))
(*.f64 x (+.f64 #s(literal 1 binary64) (*.f64 #s(literal 1/8 binary64) (*.f64 x x))))
(* x (+ 1 (* (pow x 2) (+ 1/8 (* 7/128 (pow x 2))))))
(*.f64 x (+.f64 #s(literal 1 binary64) (*.f64 x (*.f64 x (+.f64 #s(literal 1/8 binary64) (*.f64 x (*.f64 x #s(literal 7/128 binary64))))))))
(* x (+ 1 (* (pow x 2) (+ 1/8 (* (pow x 2) (+ 7/128 (* 33/1024 (pow x 2))))))))
(*.f64 x (+.f64 #s(literal 1 binary64) (*.f64 x (*.f64 x (+.f64 #s(literal 1/8 binary64) (*.f64 (*.f64 x x) (+.f64 #s(literal 7/128 binary64) (*.f64 x (*.f64 x #s(literal 33/1024 binary64))))))))))
(* 33/1024 (pow x 7))
(*.f64 #s(literal 33/1024 binary64) (pow.f64 x #s(literal 7 binary64)))
(* (pow x 7) (+ 33/1024 (* 7/128 (/ 1 (pow x 2)))))
(*.f64 (pow.f64 x #s(literal 7 binary64)) (+.f64 #s(literal 33/1024 binary64) (/.f64 #s(literal 7/128 binary64) (*.f64 x x))))
(* (pow x 7) (+ 33/1024 (+ (/ 1/8 (pow x 4)) (* 7/128 (/ 1 (pow x 2))))))
(*.f64 (pow.f64 x #s(literal 7 binary64)) (+.f64 #s(literal 33/1024 binary64) (+.f64 (/.f64 #s(literal 7/128 binary64) (*.f64 x x)) (/.f64 #s(literal 1/8 binary64) (*.f64 (*.f64 x x) (*.f64 x x))))))
(* (pow x 7) (+ 33/1024 (+ (/ 1/8 (pow x 4)) (+ (* 7/128 (/ 1 (pow x 2))) (/ 1 (pow x 6))))))
(*.f64 (pow.f64 x #s(literal 7 binary64)) (+.f64 #s(literal 33/1024 binary64) (+.f64 (/.f64 #s(literal 1/8 binary64) (*.f64 (*.f64 x x) (*.f64 x x))) (+.f64 (/.f64 #s(literal 7/128 binary64) (*.f64 x x)) (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 6 binary64)))))))
(* 33/1024 (pow x 7))
(*.f64 #s(literal 33/1024 binary64) (pow.f64 x #s(literal 7 binary64)))
(* (pow x 7) (+ 33/1024 (* 7/128 (/ 1 (pow x 2)))))
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(*.f64 (+.f64 #s(literal 33/1024 binary64) (/.f64 #s(literal 7/128 binary64) (*.f64 x x))) (*.f64 (*.f64 x x) (*.f64 x x)))
(* (pow x 4) (+ 33/1024 (* 7/128 (/ 1 (pow x 2)))))
(*.f64 (+.f64 #s(literal 33/1024 binary64) (/.f64 #s(literal 7/128 binary64) (*.f64 x x))) (*.f64 (*.f64 x x) (*.f64 x x)))
(* 7/128 x)
(*.f64 x #s(literal 7/128 binary64))
(* x (+ 7/128 (* 33/1024 (pow x 2))))
(*.f64 x (+.f64 #s(literal 7/128 binary64) (*.f64 x (*.f64 x #s(literal 33/1024 binary64)))))
(* x (+ 7/128 (* 33/1024 (pow x 2))))
(*.f64 x (+.f64 #s(literal 7/128 binary64) (*.f64 x (*.f64 x #s(literal 33/1024 binary64)))))
(* x (+ 7/128 (* 33/1024 (pow x 2))))
(*.f64 x (+.f64 #s(literal 7/128 binary64) (*.f64 x (*.f64 x #s(literal 33/1024 binary64)))))
(* 33/1024 (pow x 3))
(*.f64 #s(literal 33/1024 binary64) (*.f64 x (*.f64 x x)))
(* (pow x 3) (+ 33/1024 (* 7/128 (/ 1 (pow x 2)))))
(*.f64 x (+.f64 #s(literal 7/128 binary64) (*.f64 x (*.f64 x #s(literal 33/1024 binary64)))))
(* (pow x 3) (+ 33/1024 (* 7/128 (/ 1 (pow x 2)))))
(*.f64 x (+.f64 #s(literal 7/128 binary64) (*.f64 x (*.f64 x #s(literal 33/1024 binary64)))))
(* (pow x 3) (+ 33/1024 (* 7/128 (/ 1 (pow x 2)))))
(*.f64 x (+.f64 #s(literal 7/128 binary64) (*.f64 x (*.f64 x #s(literal 33/1024 binary64)))))
(* 33/1024 (pow x 3))
(*.f64 #s(literal 33/1024 binary64) (*.f64 x (*.f64 x x)))
(* (pow x 3) (+ 33/1024 (* 7/128 (/ 1 (pow x 2)))))
(*.f64 x (+.f64 #s(literal 7/128 binary64) (*.f64 x (*.f64 x #s(literal 33/1024 binary64)))))
(* (pow x 3) (+ 33/1024 (* 7/128 (/ 1 (pow x 2)))))
(*.f64 x (+.f64 #s(literal 7/128 binary64) (*.f64 x (*.f64 x #s(literal 33/1024 binary64)))))
(* (pow x 3) (+ 33/1024 (* 7/128 (/ 1 (pow x 2)))))
(*.f64 x (+.f64 #s(literal 7/128 binary64) (*.f64 x (*.f64 x #s(literal 33/1024 binary64)))))
(* 7/128 (pow x 2))
(*.f64 x (*.f64 x #s(literal 7/128 binary64)))
(* 7/128 (pow x 2))
(*.f64 x (*.f64 x #s(literal 7/128 binary64)))
(* 7/128 (pow x 2))
(*.f64 x (*.f64 x #s(literal 7/128 binary64)))
(* 7/128 (pow x 2))
(*.f64 x (*.f64 x #s(literal 7/128 binary64)))
(* 7/128 (pow x 2))
(*.f64 x (*.f64 x #s(literal 7/128 binary64)))
(* 7/128 (pow x 2))
(*.f64 x (*.f64 x #s(literal 7/128 binary64)))
(* 7/128 (pow x 2))
(*.f64 x (*.f64 x #s(literal 7/128 binary64)))
(* 7/128 (pow x 2))
(*.f64 x (*.f64 x #s(literal 7/128 binary64)))
(* 7/128 (pow x 2))
(*.f64 x (*.f64 x #s(literal 7/128 binary64)))
(* 7/128 (pow x 2))
(*.f64 x (*.f64 x #s(literal 7/128 binary64)))
(* 7/128 (pow x 2))
(*.f64 x (*.f64 x #s(literal 7/128 binary64)))
(* 7/128 (pow x 2))
(*.f64 x (*.f64 x #s(literal 7/128 binary64)))
2
#s(literal 2 binary64)
(+ 2 (* -1/4 (pow x 2)))
(+.f64 #s(literal 2 binary64) (*.f64 (*.f64 x x) #s(literal -1/4 binary64)))
(+ 2 (* (pow x 2) (- (* -5/64 (pow x 2)) 1/4)))
(+.f64 #s(literal 2 binary64) (*.f64 x (*.f64 x (+.f64 #s(literal -1/4 binary64) (*.f64 (*.f64 x x) #s(literal -5/64 binary64))))))
(+ 2 (* (pow x 2) (- (* (pow x 2) (- (* -21/512 (pow x 2)) 5/64)) 1/4)))
(+.f64 #s(literal 2 binary64) (*.f64 (*.f64 x x) (+.f64 #s(literal -1/4 binary64) (*.f64 x (*.f64 x (+.f64 #s(literal -5/64 binary64) (*.f64 (*.f64 x x) #s(literal -21/512 binary64))))))))
(* x (+ (sqrt (/ 1 x)) (* (sqrt (/ 1 x)) (sqrt -1))))
(*.f64 x (*.f64 (+.f64 (sqrt.f64 #s(literal -1 binary64)) #s(literal 1 binary64)) (sqrt.f64 (/.f64 #s(literal 1 binary64) x))))
(* x (+ (sqrt (/ 1 x)) (+ (* 1/2 (sqrt (/ 1 (pow x 3)))) (+ (* 1/2 (* (sqrt (/ 1 (pow x 3))) (/ 1 (sqrt -1)))) (* (sqrt (/ 1 x)) (sqrt -1))))))
(*.f64 x (+.f64 (*.f64 #s(literal 1/2 binary64) (*.f64 (+.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 #s(literal -1 binary64))) #s(literal 1 binary64)) (sqrt.f64 (/.f64 #s(literal 1 binary64) (*.f64 x (*.f64 x x)))))) (*.f64 (+.f64 (sqrt.f64 #s(literal -1 binary64)) #s(literal 1 binary64)) (sqrt.f64 (/.f64 #s(literal 1 binary64) x)))))
(* x (+ (sqrt (/ 1 x)) (+ (* -1/8 (sqrt (/ 1 (pow x 5)))) (+ (* -1/8 (* (sqrt (/ 1 (pow x 5))) (/ 1 (pow (sqrt -1) 3)))) (+ (* 1/2 (sqrt (/ 1 (pow x 3)))) (+ (* 1/2 (* (sqrt (/ 1 (pow x 3))) (/ 1 (sqrt -1)))) (* (sqrt (/ 1 x)) (sqrt -1))))))))
(*.f64 x (+.f64 (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 5 binary64)))) (+.f64 (*.f64 #s(literal -1/8 binary64) (/.f64 #s(literal -1 binary64) (sqrt.f64 #s(literal -1 binary64)))) #s(literal -1/8 binary64))) (+.f64 (*.f64 #s(literal 1/2 binary64) (*.f64 (+.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 #s(literal -1 binary64))) #s(literal 1 binary64)) (sqrt.f64 (/.f64 #s(literal 1 binary64) (*.f64 x (*.f64 x x)))))) (*.f64 (+.f64 (sqrt.f64 #s(literal -1 binary64)) #s(literal 1 binary64)) (sqrt.f64 (/.f64 #s(literal 1 binary64) x))))))
(* x (+ (sqrt (/ 1 x)) (+ (* -1/8 (sqrt (/ 1 (pow x 5)))) (+ (* -1/8 (* (sqrt (/ 1 (pow x 5))) (/ 1 (pow (sqrt -1) 3)))) (+ (* 1/16 (sqrt (/ 1 (pow x 7)))) (+ (* 1/16 (* (sqrt (/ 1 (pow x 7))) (/ 1 (pow (sqrt -1) 5)))) (+ (* 1/2 (sqrt (/ 1 (pow x 3)))) (+ (* 1/2 (* (sqrt (/ 1 (pow x 3))) (/ 1 (sqrt -1)))) (* (sqrt (/ 1 x)) (sqrt -1))))))))))
(*.f64 x (+.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) (+.f64 (+.f64 (+.f64 (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) (sqrt.f64 #s(literal -1 binary64))) (*.f64 #s(literal 1/2 binary64) (*.f64 (+.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 #s(literal -1 binary64))) #s(literal 1 binary64)) (sqrt.f64 (/.f64 #s(literal 1 binary64) (*.f64 x (*.f64 x x))))))) (*.f64 #s(literal 1/16 binary64) (*.f64 (+.f64 (/.f64 #s(literal 1 binary64) (pow.f64 (sqrt.f64 #s(literal -1 binary64)) #s(literal 5 binary64))) #s(literal 1 binary64)) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 7 binary64))))))) (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 5 binary64)))) (+.f64 (*.f64 #s(literal -1/8 binary64) (/.f64 #s(literal -1 binary64) (sqrt.f64 #s(literal -1 binary64)))) #s(literal -1/8 binary64))))))
(* -1 (* x (+ (* (sqrt (/ 1 x)) (sqrt -1)) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)))))
(*.f64 (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) (-.f64 #s(literal 0 binary64) x)) (+.f64 #s(literal -1 binary64) (sqrt.f64 #s(literal -1 binary64))))
(* -1 (* x (+ (* 1/2 (sqrt (/ 1 (pow x 3)))) (+ (* 1/2 (* (sqrt (/ 1 (pow x 3))) (sqrt -1))) (+ (* (sqrt (/ 1 x)) (sqrt -1)) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)))))))
(*.f64 (-.f64 #s(literal 0 binary64) x) (+.f64 (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) (+.f64 #s(literal -1 binary64) (sqrt.f64 #s(literal -1 binary64)))) (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (*.f64 x (*.f64 x x)))) (+.f64 #s(literal 1/2 binary64) (*.f64 #s(literal 1/2 binary64) (sqrt.f64 #s(literal -1 binary64)))))))
(* -1 (* x (+ (* -1/8 (* (sqrt (/ 1 (pow x 5))) (sqrt -1))) (+ (* -1/8 (* (sqrt (/ 1 (pow x 5))) (/ 1 (pow (sqrt -1) 2)))) (+ (* 1/2 (sqrt (/ 1 (pow x 3)))) (+ (* 1/2 (* (sqrt (/ 1 (pow x 3))) (sqrt -1))) (+ (* (sqrt (/ 1 x)) (sqrt -1)) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)))))))))
(*.f64 (-.f64 #s(literal 0 binary64) x) (+.f64 (+.f64 (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) (+.f64 #s(literal -1 binary64) (sqrt.f64 #s(literal -1 binary64)))) (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (*.f64 x (*.f64 x x)))) (+.f64 #s(literal 1/2 binary64) (*.f64 #s(literal 1/2 binary64) (sqrt.f64 #s(literal -1 binary64)))))) (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 5 binary64)))) (+.f64 (*.f64 #s(literal -1/8 binary64) (sqrt.f64 #s(literal -1 binary64))) #s(literal 1/8 binary64)))))
(* -1 (* x (+ (* -1/8 (* (sqrt (/ 1 (pow x 5))) (sqrt -1))) (+ (* -1/8 (* (sqrt (/ 1 (pow x 5))) (/ 1 (pow (sqrt -1) 2)))) (+ (* 1/16 (* (sqrt (/ 1 (pow x 7))) (sqrt -1))) (+ (* 1/16 (* (sqrt (/ 1 (pow x 7))) (/ 1 (pow (sqrt -1) 4)))) (+ (* 1/2 (sqrt (/ 1 (pow x 3)))) (+ (* 1/2 (* (sqrt (/ 1 (pow x 3))) (sqrt -1))) (+ (* (sqrt (/ 1 x)) (sqrt -1)) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)))))))))))
(*.f64 (-.f64 #s(literal 0 binary64) x) (+.f64 (+.f64 (+.f64 (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) (+.f64 #s(literal -1 binary64) (sqrt.f64 #s(literal -1 binary64)))) (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (*.f64 x (*.f64 x x)))) (+.f64 #s(literal 1/2 binary64) (*.f64 #s(literal 1/2 binary64) (sqrt.f64 #s(literal -1 binary64)))))) (*.f64 (*.f64 #s(literal 1/16 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 7 binary64))))) (+.f64 (sqrt.f64 #s(literal -1 binary64)) (/.f64 #s(literal 1 binary64) (pow.f64 (sqrt.f64 #s(literal -1 binary64)) #s(literal 4 binary64)))))) (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 5 binary64)))) (+.f64 (*.f64 #s(literal -1/8 binary64) (sqrt.f64 #s(literal -1 binary64))) #s(literal 1/8 binary64)))))
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 (* -1/8 x))))
(+.f64 #s(literal 1 binary64) (*.f64 x (+.f64 #s(literal 1/2 binary64) (*.f64 x #s(literal -1/8 binary64)))))
(+ 1 (* x (+ 1/2 (* x (- (* 1/16 x) 1/8)))))
(+.f64 #s(literal 1 binary64) (*.f64 x (+.f64 #s(literal 1/2 binary64) (*.f64 x (+.f64 #s(literal -1/8 binary64) (*.f64 x #s(literal 1/16 binary64)))))))
(sqrt x)
(sqrt.f64 x)
(* x (+ (sqrt (/ 1 x)) (* 1/2 (sqrt (/ 1 (pow x 3))))))
(*.f64 x (+.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) (*.f64 #s(literal 1/2 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) (*.f64 x (*.f64 x x)))))))
(* x (+ (sqrt (/ 1 x)) (+ (* -1/8 (sqrt (/ 1 (pow x 5)))) (* 1/2 (sqrt (/ 1 (pow x 3)))))))
(*.f64 x (+.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) (+.f64 (*.f64 #s(literal 1/2 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) (*.f64 x (*.f64 x x))))) (*.f64 #s(literal -1/8 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 5 binary64))))))))
(* x (+ (sqrt (/ 1 x)) (+ (* -1/8 (sqrt (/ 1 (pow x 5)))) (+ (* 1/16 (sqrt (/ 1 (pow x 7)))) (* 1/2 (sqrt (/ 1 (pow x 3))))))))
(*.f64 x (+.f64 (+.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) (+.f64 (*.f64 #s(literal 1/2 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) (*.f64 x (*.f64 x x))))) (*.f64 #s(literal -1/8 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 5 binary64))))))) (*.f64 #s(literal 1/16 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 (+ (* 1/2 (sqrt (/ 1 (pow x 3)))) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)))))
(-.f64 #s(literal 0 binary64) (*.f64 x (+.f64 (neg.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x))) (*.f64 #s(literal 1/2 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) (*.f64 x (*.f64 x x))))))))
(* -1 (* x (+ (* -1/8 (* (sqrt (/ 1 (pow x 5))) (/ 1 (pow (sqrt -1) 2)))) (+ (* 1/2 (sqrt (/ 1 (pow x 3)))) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))))))
(-.f64 #s(literal 0 binary64) (*.f64 x (+.f64 (neg.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x))) (+.f64 (*.f64 #s(literal 1/2 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) (*.f64 x (*.f64 x x))))) (*.f64 #s(literal 1/8 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 5 binary64)))))))))
(* -1 (* x (+ (* -1/8 (* (sqrt (/ 1 (pow x 5))) (/ 1 (pow (sqrt -1) 2)))) (+ (* 1/16 (* (sqrt (/ 1 (pow x 7))) (/ 1 (pow (sqrt -1) 4)))) (+ (* 1/2 (sqrt (/ 1 (pow x 3)))) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)))))))
(*.f64 (-.f64 #s(literal 0 binary64) x) (+.f64 (*.f64 #s(literal 1/8 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 5 binary64))))) (+.f64 (*.f64 #s(literal 1/2 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) (*.f64 x (*.f64 x x))))) (+.f64 (neg.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x))) (/.f64 (*.f64 #s(literal 1/16 binary64) (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)))))))

eval135.0ms (1.4%)

Compiler

Compiled 25896 to 2592 computations (90% saved)

prune92.0ms (0.9%)

Pruning

8 alts after pruning (4 fresh and 4 done)

PrunedKeptTotal
New9384942
Fresh202
Picked235
Done011
Total9428950
Accuracy
100.0%
Counts
950 → 8
Alt Table
Click to see full alt table
StatusAccuracyProgram
7.8%
(/.f64 (+.f64 #s(literal 1 binary64) (-.f64 x (-.f64 #s(literal 1 binary64) x))) (+.f64 #s(literal 2 binary64) (*.f64 (*.f64 x x) (+.f64 #s(literal -1/4 binary64) (*.f64 x (*.f64 x (+.f64 #s(literal -5/64 binary64) (*.f64 (*.f64 x x) #s(literal -21/512 binary64)))))))))
100.0%
(/.f64 (*.f64 x #s(literal 2 binary64)) (+.f64 (pow.f64 (+.f64 #s(literal 1 binary64) x) #s(literal 1/2 binary64)) (pow.f64 (-.f64 #s(literal 1 binary64) x) #s(literal 1/2 binary64))))
7.7%
(-.f64 (sqrt.f64 (+.f64 #s(literal 1 binary64) x)) (sqrt.f64 (-.f64 #s(literal 1 binary64) x)))
99.9%
(+.f64 (*.f64 (+.f64 #s(literal 1/8 binary64) (*.f64 (*.f64 x x) #s(literal 7/128 binary64))) (*.f64 x (*.f64 x x))) x)
99.9%
(*.f64 x (+.f64 (+.f64 #s(literal 1 binary64) (*.f64 (*.f64 x x) #s(literal 1/8 binary64))) (*.f64 (*.f64 x x) (*.f64 (*.f64 x x) (+.f64 #s(literal 7/128 binary64) (*.f64 (*.f64 x x) #s(literal 33/1024 binary64)))))))
99.9%
(*.f64 x (+.f64 #s(literal 1 binary64) (*.f64 (*.f64 x x) (+.f64 #s(literal 1/8 binary64) (*.f64 x (*.f64 x (+.f64 #s(literal 7/128 binary64) (*.f64 (*.f64 x x) #s(literal 33/1024 binary64)))))))))
99.8%
(*.f64 x (+.f64 #s(literal 1 binary64) (*.f64 #s(literal 1/8 binary64) (*.f64 x x))))
99.5%
x
Compiler

Compiled 130 to 81 computations (37.7% saved)

simplify197.0ms (2%)

Algorithm
egg-herbie
Localize:

Found 16 expressions of interest:

NewMetricScoreProgram
cost-diff0
(-.f64 #s(literal 1 binary64) x)
cost-diff0
(-.f64 x (-.f64 #s(literal 1 binary64) x))
cost-diff256
(+.f64 #s(literal 1 binary64) (-.f64 x (-.f64 #s(literal 1 binary64) x)))
cost-diff256
(/.f64 (+.f64 #s(literal 1 binary64) (-.f64 x (-.f64 #s(literal 1 binary64) x))) (+.f64 #s(literal 2 binary64) (*.f64 (*.f64 x x) (+.f64 #s(literal -1/4 binary64) (*.f64 x (*.f64 x (+.f64 #s(literal -5/64 binary64) (*.f64 (*.f64 x x) #s(literal -21/512 binary64)))))))))
cost-diff0
(pow.f64 (+.f64 #s(literal 1 binary64) x) #s(literal 1/2 binary64))
cost-diff0
(+.f64 (pow.f64 (+.f64 #s(literal 1 binary64) x) #s(literal 1/2 binary64)) (pow.f64 (-.f64 #s(literal 1 binary64) x) #s(literal 1/2 binary64)))
cost-diff0
(*.f64 x #s(literal 2 binary64))
cost-diff0
(/.f64 (*.f64 x #s(literal 2 binary64)) (+.f64 (pow.f64 (+.f64 #s(literal 1 binary64) x) #s(literal 1/2 binary64)) (pow.f64 (-.f64 #s(literal 1 binary64) x) #s(literal 1/2 binary64))))
cost-diff0
(*.f64 (*.f64 x x) #s(literal 7/128 binary64))
cost-diff0
(+.f64 #s(literal 1/8 binary64) (*.f64 (*.f64 x x) #s(literal 7/128 binary64)))
cost-diff0
(*.f64 (+.f64 #s(literal 1/8 binary64) (*.f64 (*.f64 x x) #s(literal 7/128 binary64))) (*.f64 x (*.f64 x x)))
cost-diff0
(+.f64 (*.f64 (+.f64 #s(literal 1/8 binary64) (*.f64 (*.f64 x x) #s(literal 7/128 binary64))) (*.f64 x (*.f64 x x))) x)
cost-diff0
(*.f64 (*.f64 x x) #s(literal 1/8 binary64))
cost-diff0
(+.f64 #s(literal 1 binary64) (*.f64 (*.f64 x x) #s(literal 1/8 binary64)))
cost-diff256
(+.f64 (+.f64 #s(literal 1 binary64) (*.f64 (*.f64 x x) #s(literal 1/8 binary64))) (*.f64 (*.f64 x x) (*.f64 (*.f64 x x) (+.f64 #s(literal 7/128 binary64) (*.f64 (*.f64 x x) #s(literal 33/1024 binary64))))))
cost-diff256
(*.f64 x (+.f64 (+.f64 #s(literal 1 binary64) (*.f64 (*.f64 x x) #s(literal 1/8 binary64))) (*.f64 (*.f64 x x) (*.f64 (*.f64 x x) (+.f64 #s(literal 7/128 binary64) (*.f64 (*.f64 x x) #s(literal 33/1024 binary64)))))))
Rules
2652×+-lowering-+.f64
2652×+-lowering-+.f32
2314×*-lowering-*.f32
2314×*-lowering-*.f64
1506×fnmadd-define
Iterations

Useful iterations: 3 (0.0ms)

IterNodesCost
041279
1127248
2396244
31262241
45568241
08456241
Stop Event
iter limit
node limit
Calls
Call 1
Inputs
(* x (+ (+ 1 (* (* x x) 1/8)) (* (* x x) (* (* x x) (+ 7/128 (* (* x x) 33/1024))))))
x
(+ (+ 1 (* (* x x) 1/8)) (* (* x x) (* (* x x) (+ 7/128 (* (* x x) 33/1024)))))
(+ 1 (* (* x x) 1/8))
1
(* (* x x) 1/8)
(* x x)
1/8
(* (* x x) (* (* x x) (+ 7/128 (* (* x x) 33/1024))))
(* (* x x) (+ 7/128 (* (* x x) 33/1024)))
(+ 7/128 (* (* x x) 33/1024))
7/128
(* (* x x) 33/1024)
33/1024
(+ (* (+ 1/8 (* (* x x) 7/128)) (* x (* x x))) x)
(* (+ 1/8 (* (* x x) 7/128)) (* x (* x x)))
(+ 1/8 (* (* x x) 7/128))
1/8
(* (* x x) 7/128)
(* x x)
x
7/128
(* x (* x x))
(/ (* x 2) (+ (pow (+ 1 x) 1/2) (pow (- 1 x) 1/2)))
(* x 2)
x
2
(+ (pow (+ 1 x) 1/2) (pow (- 1 x) 1/2))
(pow (+ 1 x) 1/2)
(+ 1 x)
1
1/2
(pow (- 1 x) 1/2)
(- 1 x)
(/ (+ 1 (- x (- 1 x))) (+ 2 (* (* x x) (+ -1/4 (* x (* x (+ -5/64 (* (* x x) -21/512))))))))
(+ 1 (- x (- 1 x)))
1
(- x (- 1 x))
x
(- 1 x)
(+ 2 (* (* x x) (+ -1/4 (* x (* x (+ -5/64 (* (* x x) -21/512)))))))
2
(* (* x x) (+ -1/4 (* x (* x (+ -5/64 (* (* x x) -21/512))))))
(* x x)
(+ -1/4 (* x (* x (+ -5/64 (* (* x x) -21/512)))))
-1/4
(* x (* x (+ -5/64 (* (* x x) -21/512))))
(* x (+ -5/64 (* (* x x) -21/512)))
(+ -5/64 (* (* x x) -21/512))
-5/64
(* (* x x) -21/512)
-21/512
Outputs
(* x (+ (+ 1 (* (* x x) 1/8)) (* (* x x) (* (* x x) (+ 7/128 (* (* x x) 33/1024))))))
(*.f64 x (+.f64 #s(literal 1 binary64) (*.f64 (*.f64 x x) (+.f64 #s(literal 1/8 binary64) (*.f64 x (*.f64 x (+.f64 #s(literal 7/128 binary64) (*.f64 (*.f64 x x) #s(literal 33/1024 binary64)))))))))
x
(+ (+ 1 (* (* x x) 1/8)) (* (* x x) (* (* x x) (+ 7/128 (* (* x x) 33/1024)))))
(+.f64 #s(literal 1 binary64) (*.f64 (*.f64 x x) (+.f64 #s(literal 1/8 binary64) (*.f64 x (*.f64 x (+.f64 #s(literal 7/128 binary64) (*.f64 (*.f64 x x) #s(literal 33/1024 binary64))))))))
(+ 1 (* (* x x) 1/8))
(+.f64 #s(literal 1 binary64) (*.f64 x (*.f64 x #s(literal 1/8 binary64))))
1
#s(literal 1 binary64)
(* (* x x) 1/8)
(*.f64 x (*.f64 x #s(literal 1/8 binary64)))
(* x x)
(*.f64 x x)
1/8
#s(literal 1/8 binary64)
(* (* x x) (* (* x x) (+ 7/128 (* (* x x) 33/1024))))
(*.f64 (+.f64 #s(literal 7/128 binary64) (*.f64 (*.f64 x x) #s(literal 33/1024 binary64))) (*.f64 x (*.f64 x (*.f64 x x))))
(* (* x x) (+ 7/128 (* (* x x) 33/1024)))
(*.f64 x (*.f64 x (+.f64 #s(literal 7/128 binary64) (*.f64 (*.f64 x x) #s(literal 33/1024 binary64)))))
(+ 7/128 (* (* x x) 33/1024))
(+.f64 #s(literal 7/128 binary64) (*.f64 (*.f64 x x) #s(literal 33/1024 binary64)))
7/128
#s(literal 7/128 binary64)
(* (* x x) 33/1024)
(*.f64 (*.f64 x x) #s(literal 33/1024 binary64))
33/1024
#s(literal 33/1024 binary64)
(+ (* (+ 1/8 (* (* x x) 7/128)) (* x (* x x))) x)
(*.f64 x (+.f64 #s(literal 1 binary64) (*.f64 x (*.f64 x (+.f64 #s(literal 1/8 binary64) (*.f64 (*.f64 x x) #s(literal 7/128 binary64)))))))
(* (+ 1/8 (* (* x x) 7/128)) (* x (* x x)))
(*.f64 (*.f64 x x) (*.f64 x (+.f64 #s(literal 1/8 binary64) (*.f64 (*.f64 x x) #s(literal 7/128 binary64)))))
(+ 1/8 (* (* x x) 7/128))
(+.f64 #s(literal 1/8 binary64) (*.f64 (*.f64 x x) #s(literal 7/128 binary64)))
1/8
#s(literal 1/8 binary64)
(* (* x x) 7/128)
(*.f64 (*.f64 x x) #s(literal 7/128 binary64))
(* x x)
(*.f64 x x)
x
7/128
#s(literal 7/128 binary64)
(* x (* x x))
(*.f64 x (*.f64 x x))
(/ (* x 2) (+ (pow (+ 1 x) 1/2) (pow (- 1 x) 1/2)))
(/.f64 (*.f64 x #s(literal 2 binary64)) (+.f64 (pow.f64 (+.f64 x #s(literal 1 binary64)) #s(literal 1/2 binary64)) (pow.f64 (-.f64 #s(literal 1 binary64) x) #s(literal 1/2 binary64))))
(* x 2)
(*.f64 x #s(literal 2 binary64))
x
2
#s(literal 2 binary64)
(+ (pow (+ 1 x) 1/2) (pow (- 1 x) 1/2))
(+.f64 (pow.f64 (+.f64 x #s(literal 1 binary64)) #s(literal 1/2 binary64)) (pow.f64 (-.f64 #s(literal 1 binary64) x) #s(literal 1/2 binary64)))
(pow (+ 1 x) 1/2)
(pow.f64 (+.f64 x #s(literal 1 binary64)) #s(literal 1/2 binary64))
(+ 1 x)
(+.f64 x #s(literal 1 binary64))
1
#s(literal 1 binary64)
1/2
#s(literal 1/2 binary64)
(pow (- 1 x) 1/2)
(pow.f64 (-.f64 #s(literal 1 binary64) x) #s(literal 1/2 binary64))
(- 1 x)
(-.f64 #s(literal 1 binary64) x)
(/ (+ 1 (- x (- 1 x))) (+ 2 (* (* x x) (+ -1/4 (* x (* x (+ -5/64 (* (* x x) -21/512))))))))
(/.f64 (*.f64 x #s(literal 2 binary64)) (+.f64 #s(literal 2 binary64) (*.f64 x (*.f64 x (+.f64 #s(literal -1/4 binary64) (*.f64 x (*.f64 x (+.f64 #s(literal -5/64 binary64) (*.f64 (*.f64 x x) #s(literal -21/512 binary64))))))))))
(+ 1 (- x (- 1 x)))
(*.f64 x #s(literal 2 binary64))
1
#s(literal 1 binary64)
(- x (- 1 x))
(+.f64 #s(literal -1 binary64) (*.f64 x #s(literal 2 binary64)))
x
(- 1 x)
(-.f64 #s(literal 1 binary64) x)
(+ 2 (* (* x x) (+ -1/4 (* x (* x (+ -5/64 (* (* x x) -21/512)))))))
(+.f64 #s(literal 2 binary64) (*.f64 x (*.f64 x (+.f64 #s(literal -1/4 binary64) (*.f64 x (*.f64 x (+.f64 #s(literal -5/64 binary64) (*.f64 (*.f64 x x) #s(literal -21/512 binary64)))))))))
2
#s(literal 2 binary64)
(* (* x x) (+ -1/4 (* x (* x (+ -5/64 (* (* x x) -21/512))))))
(*.f64 x (*.f64 x (+.f64 #s(literal -1/4 binary64) (*.f64 x (*.f64 x (+.f64 #s(literal -5/64 binary64) (*.f64 (*.f64 x x) #s(literal -21/512 binary64))))))))
(* x x)
(*.f64 x x)
(+ -1/4 (* x (* x (+ -5/64 (* (* x x) -21/512)))))
(+.f64 #s(literal -1/4 binary64) (*.f64 x (*.f64 x (+.f64 #s(literal -5/64 binary64) (*.f64 (*.f64 x x) #s(literal -21/512 binary64))))))
-1/4
#s(literal -1/4 binary64)
(* x (* x (+ -5/64 (* (* x x) -21/512))))
(*.f64 x (*.f64 x (+.f64 #s(literal -5/64 binary64) (*.f64 (*.f64 x x) #s(literal -21/512 binary64)))))
(* x (+ -5/64 (* (* x x) -21/512)))
(*.f64 x (+.f64 #s(literal -5/64 binary64) (*.f64 (*.f64 x x) #s(literal -21/512 binary64))))
(+ -5/64 (* (* x x) -21/512))
(+.f64 #s(literal -5/64 binary64) (*.f64 (*.f64 x x) #s(literal -21/512 binary64)))
-5/64
#s(literal -5/64 binary64)
(* (* x x) -21/512)
(*.f64 (*.f64 x x) #s(literal -21/512 binary64))
-21/512
#s(literal -21/512 binary64)

localize537.0ms (5.4%)

Localize:

Found 16 expressions of interest:

NewMetricScoreProgram
accuracy99.8%
(*.f64 x (+.f64 #s(literal -5/64 binary64) (*.f64 (*.f64 x x) #s(literal -21/512 binary64))))
accuracy99.8%
(*.f64 x (*.f64 x (+.f64 #s(literal -5/64 binary64) (*.f64 (*.f64 x x) #s(literal -21/512 binary64)))))
accuracy99.8%
(*.f64 (*.f64 x x) #s(literal -21/512 binary64))
accuracy7.9%
(+.f64 #s(literal 1 binary64) (-.f64 x (-.f64 #s(literal 1 binary64) x)))
accuracy100.0%
(*.f64 x #s(literal 2 binary64))
accuracy100.0%
(pow.f64 (-.f64 #s(literal 1 binary64) x) #s(literal 1/2 binary64))
accuracy100.0%
(pow.f64 (+.f64 #s(literal 1 binary64) x) #s(literal 1/2 binary64))
accuracy100.0%
(+.f64 (pow.f64 (+.f64 #s(literal 1 binary64) x) #s(literal 1/2 binary64)) (pow.f64 (-.f64 #s(literal 1 binary64) x) #s(literal 1/2 binary64)))
accuracy100.0%
(*.f64 x x)
accuracy100.0%
(*.f64 (+.f64 #s(literal 1/8 binary64) (*.f64 (*.f64 x x) #s(literal 7/128 binary64))) (*.f64 x (*.f64 x x)))
accuracy99.9%
(*.f64 x (*.f64 x x))
accuracy99.8%
(*.f64 (*.f64 x x) #s(literal 7/128 binary64))
accuracy100.0%
(*.f64 x (+.f64 (+.f64 #s(literal 1 binary64) (*.f64 (*.f64 x x) #s(literal 1/8 binary64))) (*.f64 (*.f64 x x) (*.f64 (*.f64 x x) (+.f64 #s(literal 7/128 binary64) (*.f64 (*.f64 x x) #s(literal 33/1024 binary64)))))))
accuracy99.9%
(*.f64 (*.f64 x x) (*.f64 (*.f64 x x) (+.f64 #s(literal 7/128 binary64) (*.f64 (*.f64 x x) #s(literal 33/1024 binary64)))))
accuracy99.8%
(*.f64 (*.f64 x x) (+.f64 #s(literal 7/128 binary64) (*.f64 (*.f64 x x) #s(literal 33/1024 binary64))))
accuracy99.8%
(*.f64 (*.f64 x x) #s(literal 33/1024 binary64))
Results
358.0ms231×1valid
82.0ms15×3valid
8.0ms2valid
2.0ms0valid
Compiler

Compiled 340 to 42 computations (87.6% saved)

Precisions
Click to see histograms. Total time spent on operations: 340.0ms
ival-pow: 215.0ms (63.2% of total)
ival-mult: 53.0ms (15.6% of total)
ival-add: 31.0ms (9.1% of total)
backward-pass: 23.0ms (6.8% of total)
ival-div: 8.0ms (2.4% of total)
ival-sub: 7.0ms (2.1% of total)
const: 3.0ms (0.9% of total)

series13.0ms (0.1%)

Counts
25 → 300
Calls
Call 1
Inputs
#<alt (* x (+ (+ 1 (* (* x x) 1/8)) (* (* x x) (* (* x x) (+ 7/128 (* (* x x) 33/1024))))))>
#<alt (+ (+ 1 (* (* x x) 1/8)) (* (* x x) (* (* x x) (+ 7/128 (* (* x x) 33/1024)))))>
#<alt (+ 1 (* (* x x) 1/8))>
#<alt (* (* x x) 1/8)>
#<alt (+ (* (+ 1/8 (* (* x x) 7/128)) (* x (* x x))) x)>
#<alt (* (+ 1/8 (* (* x x) 7/128)) (* x (* x x)))>
#<alt (+ 1/8 (* (* x x) 7/128))>
#<alt (* (* x x) 7/128)>
#<alt (/ (* x 2) (+ (pow (+ 1 x) 1/2) (pow (- 1 x) 1/2)))>
#<alt (* x 2)>
#<alt (+ (pow (+ 1 x) 1/2) (pow (- 1 x) 1/2))>
#<alt (pow (+ 1 x) 1/2)>
#<alt (/ (+ 1 (- x (- 1 x))) (+ 2 (* (* x x) (+ -1/4 (* x (* x (+ -5/64 (* (* x x) -21/512))))))))>
#<alt (+ 1 (- x (- 1 x)))>
#<alt (- x (- 1 x))>
#<alt (- 1 x)>
#<alt (* (* x x) 33/1024)>
#<alt (* (* x x) (+ 7/128 (* (* x x) 33/1024)))>
#<alt (* (* x x) (* (* x x) (+ 7/128 (* (* x x) 33/1024))))>
#<alt (* x (* x x))>
#<alt (* x x)>
#<alt (pow (- 1 x) 1/2)>
#<alt (* (* x x) -21/512)>
#<alt (* x (* x (+ -5/64 (* (* x x) -21/512))))>
#<alt (* x (+ -5/64 (* (* x x) -21/512)))>
Outputs
#<alt x>
#<alt (* x (+ 1 (* 1/8 (pow x 2))))>
#<alt (* x (+ 1 (* (pow x 2) (+ 1/8 (* 7/128 (pow x 2))))))>
#<alt (* x (+ 1 (* (pow x 2) (+ 1/8 (* (pow x 2) (+ 7/128 (* 33/1024 (pow x 2))))))))>
#<alt (* 33/1024 (pow x 7))>
#<alt (* (pow x 7) (+ 33/1024 (* 7/128 (/ 1 (pow x 2)))))>
#<alt (* (pow x 7) (+ 33/1024 (+ (/ 1/8 (pow x 4)) (* 7/128 (/ 1 (pow x 2))))))>
#<alt (* (pow x 7) (+ 33/1024 (+ (/ 1/8 (pow x 4)) (+ (* 7/128 (/ 1 (pow x 2))) (/ 1 (pow x 6))))))>
#<alt (* 33/1024 (pow x 7))>
#<alt (* (pow x 7) (+ 33/1024 (* 7/128 (/ 1 (pow x 2)))))>
#<alt (* -1 (* (pow x 7) (- (* -1 (/ (+ 7/128 (* 1/8 (/ 1 (pow x 2)))) (pow x 2))) 33/1024)))>
#<alt (* -1 (* (pow x 7) (- (* -1 (/ (+ 1/8 (/ 1 (pow x 2))) (pow x 4))) (+ 33/1024 (* 7/128 (/ 1 (pow x 2)))))))>
#<alt 1>
#<alt (+ 1 (* 1/8 (pow x 2)))>
#<alt (+ 1 (* (pow x 2) (+ 1/8 (* 7/128 (pow x 2)))))>
#<alt (+ 1 (* (pow x 2) (+ 1/8 (* (pow x 2) (+ 7/128 (* 33/1024 (pow x 2)))))))>
#<alt (* 33/1024 (pow x 6))>
#<alt (* (pow x 6) (+ 33/1024 (* 7/128 (/ 1 (pow x 2)))))>
#<alt (* (pow x 6) (+ 33/1024 (+ (/ 1/8 (pow x 4)) (* 7/128 (/ 1 (pow x 2))))))>
#<alt (* (pow x 6) (+ 33/1024 (+ (/ 1/8 (pow x 4)) (+ (* 7/128 (/ 1 (pow x 2))) (/ 1 (pow x 6))))))>
#<alt (* 33/1024 (pow x 6))>
#<alt (* (pow x 6) (+ 33/1024 (* 7/128 (/ 1 (pow x 2)))))>
#<alt (* (pow x 6) (+ 33/1024 (+ (/ 1/8 (pow x 4)) (* 7/128 (/ 1 (pow x 2))))))>
#<alt (* (pow x 6) (+ 33/1024 (+ (/ 1/8 (pow x 4)) (+ (* 7/128 (/ 1 (pow x 2))) (/ 1 (pow x 6))))))>
#<alt 1>
#<alt (+ 1 (* 1/8 (pow x 2)))>
#<alt (+ 1 (* 1/8 (pow x 2)))>
#<alt (+ 1 (* 1/8 (pow x 2)))>
#<alt (* 1/8 (pow x 2))>
#<alt (* (pow x 2) (+ 1/8 (/ 1 (pow x 2))))>
#<alt (* (pow x 2) (+ 1/8 (/ 1 (pow x 2))))>
#<alt (* (pow x 2) (+ 1/8 (/ 1 (pow x 2))))>
#<alt (* 1/8 (pow x 2))>
#<alt (* (pow x 2) (+ 1/8 (/ 1 (pow x 2))))>
#<alt (* (pow x 2) (+ 1/8 (/ 1 (pow x 2))))>
#<alt (* (pow x 2) (+ 1/8 (/ 1 (pow x 2))))>
#<alt (* 1/8 (pow x 2))>
#<alt (* 1/8 (pow x 2))>
#<alt (* 1/8 (pow x 2))>
#<alt (* 1/8 (pow x 2))>
#<alt (* 1/8 (pow x 2))>
#<alt (* 1/8 (pow x 2))>
#<alt (* 1/8 (pow x 2))>
#<alt (* 1/8 (pow x 2))>
#<alt (* 1/8 (pow x 2))>
#<alt (* 1/8 (pow x 2))>
#<alt (* 1/8 (pow x 2))>
#<alt (* 1/8 (pow x 2))>
#<alt x>
#<alt (* x (+ 1 (* 1/8 (pow x 2))))>
#<alt (* x (+ 1 (* (pow x 2) (+ 1/8 (* 7/128 (pow x 2))))))>
#<alt (* x (+ 1 (* (pow x 2) (+ 1/8 (* 7/128 (pow x 2))))))>
#<alt (* 7/128 (pow x 5))>
#<alt (* (pow x 5) (+ 7/128 (* 1/8 (/ 1 (pow x 2)))))>
#<alt (* (pow x 5) (+ 7/128 (+ (* 1/8 (/ 1 (pow x 2))) (/ 1 (pow x 4)))))>
#<alt (* (pow x 5) (+ 7/128 (+ (* 1/8 (/ 1 (pow x 2))) (/ 1 (pow x 4)))))>
#<alt (* 7/128 (pow x 5))>
#<alt (* (pow x 5) (+ 7/128 (* 1/8 (/ 1 (pow x 2)))))>
#<alt (* -1 (* (pow x 5) (- (* -1 (/ (+ 1/8 (/ 1 (pow x 2))) (pow x 2))) 7/128)))>
#<alt (* -1 (* (pow x 5) (- (* -1 (/ (+ 1/8 (/ 1 (pow x 2))) (pow x 2))) 7/128)))>
#<alt (* 1/8 (pow x 3))>
#<alt (* (pow x 3) (+ 1/8 (* 7/128 (pow x 2))))>
#<alt (* (pow x 3) (+ 1/8 (* 7/128 (pow x 2))))>
#<alt (* (pow x 3) (+ 1/8 (* 7/128 (pow x 2))))>
#<alt (* 7/128 (pow x 5))>
#<alt (* (pow x 5) (+ 7/128 (* 1/8 (/ 1 (pow x 2)))))>
#<alt (* (pow x 5) (+ 7/128 (* 1/8 (/ 1 (pow x 2)))))>
#<alt (* (pow x 5) (+ 7/128 (* 1/8 (/ 1 (pow x 2)))))>
#<alt (* 7/128 (pow x 5))>
#<alt (* (pow x 5) (+ 7/128 (* 1/8 (/ 1 (pow x 2)))))>
#<alt (* (pow x 5) (+ 7/128 (* 1/8 (/ 1 (pow x 2)))))>
#<alt (* (pow x 5) (+ 7/128 (* 1/8 (/ 1 (pow x 2)))))>
#<alt 1/8>
#<alt (+ 1/8 (* 7/128 (pow x 2)))>
#<alt (+ 1/8 (* 7/128 (pow x 2)))>
#<alt (+ 1/8 (* 7/128 (pow x 2)))>
#<alt (* 7/128 (pow x 2))>
#<alt (* (pow x 2) (+ 7/128 (* 1/8 (/ 1 (pow x 2)))))>
#<alt (* (pow x 2) (+ 7/128 (* 1/8 (/ 1 (pow x 2)))))>
#<alt (* (pow x 2) (+ 7/128 (* 1/8 (/ 1 (pow x 2)))))>
#<alt (* 7/128 (pow x 2))>
#<alt (* (pow x 2) (+ 7/128 (* 1/8 (/ 1 (pow x 2)))))>
#<alt (* (pow x 2) (+ 7/128 (* 1/8 (/ 1 (pow x 2)))))>
#<alt (* (pow x 2) (+ 7/128 (* 1/8 (/ 1 (pow x 2)))))>
#<alt (* 7/128 (pow x 2))>
#<alt (* 7/128 (pow x 2))>
#<alt (* 7/128 (pow x 2))>
#<alt (* 7/128 (pow x 2))>
#<alt (* 7/128 (pow x 2))>
#<alt (* 7/128 (pow x 2))>
#<alt (* 7/128 (pow x 2))>
#<alt (* 7/128 (pow x 2))>
#<alt (* 7/128 (pow x 2))>
#<alt (* 7/128 (pow x 2))>
#<alt (* 7/128 (pow x 2))>
#<alt (* 7/128 (pow x 2))>
#<alt x>
#<alt (* x (+ 1 (* 1/8 (pow x 2))))>
#<alt (* x (+ 1 (* (pow x 2) (+ 1/8 (* 7/128 (pow x 2))))))>
#<alt (* x (+ 1 (* (pow x 2) (+ 1/8 (* (pow x 2) (+ 7/128 (* 33/1024 (pow x 2))))))))>
#<alt (/ 2 (+ (sqrt (/ 1 x)) (* (sqrt (/ 1 x)) (sqrt -1))))>
#<alt (+ (* -2 (/ (+ (* 1/2 (sqrt x)) (* 1/2 (* (sqrt x) (/ 1 (sqrt -1))))) (* (pow x 2) (pow (+ (sqrt (/ 1 x)) (* (sqrt (/ 1 x)) (sqrt -1))) 2)))) (* 2 (/ 1 (+ (sqrt (/ 1 x)) (* (sqrt (/ 1 x)) (sqrt -1))))))>
#<alt (- (+ (* -1 (/ (+ (* -2 (/ (pow (+ (* 1/2 (sqrt x)) (* 1/2 (* (sqrt x) (/ 1 (sqrt -1))))) 2) (pow (+ (sqrt (/ 1 x)) (* (sqrt (/ 1 x)) (sqrt -1))) 3))) (* 2 (/ (+ (* -1/8 (sqrt (pow x 3))) (* -1/8 (* (sqrt (pow x 3)) (/ 1 (pow (sqrt -1) 3))))) (pow (+ (sqrt (/ 1 x)) (* (sqrt (/ 1 x)) (sqrt -1))) 2)))) (pow x 4))) (* 2 (/ 1 (+ (sqrt (/ 1 x)) (* (sqrt (/ 1 x)) (sqrt -1)))))) (* 2 (/ (+ (* 1/2 (sqrt x)) (* 1/2 (* (sqrt x) (/ 1 (sqrt -1))))) (* (pow x 2) (pow (+ (sqrt (/ 1 x)) (* (sqrt (/ 1 x)) (sqrt -1))) 2)))))>
#<alt (- (+ (* -1 (/ (+ (* -2 (/ (* (+ (* -1/8 (sqrt (pow x 3))) (* -1/8 (* (sqrt (pow x 3)) (/ 1 (pow (sqrt -1) 3))))) (+ (* 1/2 (sqrt x)) (* 1/2 (* (sqrt x) (/ 1 (sqrt -1)))))) (pow (+ (sqrt (/ 1 x)) (* (sqrt (/ 1 x)) (sqrt -1))) 3))) (+ (* -1 (/ (* (+ (* -2 (/ (pow (+ (* 1/2 (sqrt x)) (* 1/2 (* (sqrt x) (/ 1 (sqrt -1))))) 2) (pow (+ (sqrt (/ 1 x)) (* (sqrt (/ 1 x)) (sqrt -1))) 3))) (* 2 (/ (+ (* -1/8 (sqrt (pow x 3))) (* -1/8 (* (sqrt (pow x 3)) (/ 1 (pow (sqrt -1) 3))))) (pow (+ (sqrt (/ 1 x)) (* (sqrt (/ 1 x)) (sqrt -1))) 2)))) (+ (* 1/2 (sqrt x)) (* 1/2 (* (sqrt x) (/ 1 (sqrt -1)))))) (+ (sqrt (/ 1 x)) (* (sqrt (/ 1 x)) (sqrt -1))))) (* 2 (/ (+ (* 1/16 (sqrt (pow x 5))) (* 1/16 (* (sqrt (pow x 5)) (/ 1 (pow (sqrt -1) 5))))) (pow (+ (sqrt (/ 1 x)) (* (sqrt (/ 1 x)) (sqrt -1))) 2))))) (pow x 6))) (* 2 (/ 1 (+ (sqrt (/ 1 x)) (* (sqrt (/ 1 x)) (sqrt -1)))))) (+ (* -2 (/ (pow (+ (* 1/2 (sqrt x)) (* 1/2 (* (sqrt x) (/ 1 (sqrt -1))))) 2) (* (pow x 4) (pow (+ (sqrt (/ 1 x)) (* (sqrt (/ 1 x)) (sqrt -1))) 3)))) (+ (* 2 (/ (+ (* -1/8 (sqrt (pow x 3))) (* -1/8 (* (sqrt (pow x 3)) (/ 1 (pow (sqrt -1) 3))))) (* (pow x 4) (pow (+ (sqrt (/ 1 x)) (* (sqrt (/ 1 x)) (sqrt -1))) 2)))) (* 2 (/ (+ (* 1/2 (sqrt x)) (* 1/2 (* (sqrt x) (/ 1 (sqrt -1))))) (* (pow x 2) (pow (+ (sqrt (/ 1 x)) (* (sqrt (/ 1 x)) (sqrt -1))) 2)))))))>
#<alt (/ -2 (+ (* (sqrt (/ 1 x)) (sqrt -1)) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))))>
#<alt (- (* 2 (/ (+ (* 1/2 (sqrt x)) (* 1/2 (* (sqrt x) (sqrt -1)))) (* (pow x 2) (pow (+ (* (sqrt (/ 1 x)) (sqrt -1)) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))) 2)))) (* 2 (/ 1 (+ (* (sqrt (/ 1 x)) (sqrt -1)) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))))))>
#<alt (- (* -1 (/ (+ (* -2 (/ (+ (* -1/8 (* (sqrt (pow x 3)) (sqrt -1))) (* -1/8 (* (sqrt (pow x 3)) (/ 1 (pow (sqrt -1) 2))))) (pow (+ (* (sqrt (/ 1 x)) (sqrt -1)) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))) 2))) (* 2 (/ (pow (+ (* 1/2 (sqrt x)) (* 1/2 (* (sqrt x) (sqrt -1)))) 2) (pow (+ (* (sqrt (/ 1 x)) (sqrt -1)) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))) 3)))) (pow x 4))) (+ (* -2 (/ (+ (* 1/2 (sqrt x)) (* 1/2 (* (sqrt x) (sqrt -1)))) (* (pow x 2) (pow (+ (* (sqrt (/ 1 x)) (sqrt -1)) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))) 2)))) (* 2 (/ 1 (+ (* (sqrt (/ 1 x)) (sqrt -1)) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)))))))>
#<alt (- (* -1 (/ (+ (* -2 (/ (+ (* 1/16 (* (sqrt (pow x 5)) (sqrt -1))) (* 1/16 (* (sqrt (pow x 5)) (/ 1 (pow (sqrt -1) 4))))) (pow (+ (* (sqrt (/ 1 x)) (sqrt -1)) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))) 2))) (+ (* -1 (/ (* (+ (* -2 (/ (+ (* -1/8 (* (sqrt (pow x 3)) (sqrt -1))) (* -1/8 (* (sqrt (pow x 3)) (/ 1 (pow (sqrt -1) 2))))) (pow (+ (* (sqrt (/ 1 x)) (sqrt -1)) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))) 2))) (* 2 (/ (pow (+ (* 1/2 (sqrt x)) (* 1/2 (* (sqrt x) (sqrt -1)))) 2) (pow (+ (* (sqrt (/ 1 x)) (sqrt -1)) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))) 3)))) (+ (* 1/2 (sqrt x)) (* 1/2 (* (sqrt x) (sqrt -1))))) (+ (* (sqrt (/ 1 x)) (sqrt -1)) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))))) (* 2 (/ (* (+ (* -1/8 (* (sqrt (pow x 3)) (sqrt -1))) (* -1/8 (* (sqrt (pow x 3)) (/ 1 (pow (sqrt -1) 2))))) (+ (* 1/2 (sqrt x)) (* 1/2 (* (sqrt x) (sqrt -1))))) (pow (+ (* (sqrt (/ 1 x)) (sqrt -1)) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))) 3))))) (pow x 6))) (+ (* -2 (/ (+ (* -1/8 (* (sqrt (pow x 3)) (sqrt -1))) (* -1/8 (* (sqrt (pow x 3)) (/ 1 (pow (sqrt -1) 2))))) (* (pow x 4) (pow (+ (* (sqrt (/ 1 x)) (sqrt -1)) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))) 2)))) (+ (* -2 (/ (+ (* 1/2 (sqrt x)) (* 1/2 (* (sqrt x) (sqrt -1)))) (* (pow x 2) (pow (+ (* (sqrt (/ 1 x)) (sqrt -1)) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))) 2)))) (+ (* 2 (/ (pow (+ (* 1/2 (sqrt x)) (* 1/2 (* (sqrt x) (sqrt -1)))) 2) (* (pow x 4) (pow (+ (* (sqrt (/ 1 x)) (sqrt -1)) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))) 3)))) (* 2 (/ 1 (+ (* (sqrt (/ 1 x)) (sqrt -1)) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)))))))))>
#<alt (* 2 x)>
#<alt (* 2 x)>
#<alt (* 2 x)>
#<alt (* 2 x)>
#<alt (* 2 x)>
#<alt (* 2 x)>
#<alt (* 2 x)>
#<alt (* 2 x)>
#<alt (* 2 x)>
#<alt (* 2 x)>
#<alt (* 2 x)>
#<alt (* 2 x)>
#<alt 2>
#<alt (+ 2 (* -1/4 (pow x 2)))>
#<alt (+ 2 (* (pow x 2) (- (* -5/64 (pow x 2)) 1/4)))>
#<alt (+ 2 (* (pow x 2) (- (* (pow x 2) (- (* -21/512 (pow x 2)) 5/64)) 1/4)))>
#<alt (* x (+ (sqrt (/ 1 x)) (* (sqrt (/ 1 x)) (sqrt -1))))>
#<alt (* x (+ (sqrt (/ 1 x)) (+ (* 1/2 (sqrt (/ 1 (pow x 3)))) (+ (* 1/2 (* (sqrt (/ 1 (pow x 3))) (/ 1 (sqrt -1)))) (* (sqrt (/ 1 x)) (sqrt -1))))))>
#<alt (* x (+ (sqrt (/ 1 x)) (+ (* -1/8 (sqrt (/ 1 (pow x 5)))) (+ (* -1/8 (* (sqrt (/ 1 (pow x 5))) (/ 1 (pow (sqrt -1) 3)))) (+ (* 1/2 (sqrt (/ 1 (pow x 3)))) (+ (* 1/2 (* (sqrt (/ 1 (pow x 3))) (/ 1 (sqrt -1)))) (* (sqrt (/ 1 x)) (sqrt -1))))))))>
#<alt (* x (+ (sqrt (/ 1 x)) (+ (* -1/8 (sqrt (/ 1 (pow x 5)))) (+ (* -1/8 (* (sqrt (/ 1 (pow x 5))) (/ 1 (pow (sqrt -1) 3)))) (+ (* 1/16 (sqrt (/ 1 (pow x 7)))) (+ (* 1/16 (* (sqrt (/ 1 (pow x 7))) (/ 1 (pow (sqrt -1) 5)))) (+ (* 1/2 (sqrt (/ 1 (pow x 3)))) (+ (* 1/2 (* (sqrt (/ 1 (pow x 3))) (/ 1 (sqrt -1)))) (* (sqrt (/ 1 x)) (sqrt -1))))))))))>
#<alt (* -1 (* x (+ (* (sqrt (/ 1 x)) (sqrt -1)) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)))))>
#<alt (* -1 (* x (+ (* 1/2 (sqrt (/ 1 (pow x 3)))) (+ (* 1/2 (* (sqrt (/ 1 (pow x 3))) (sqrt -1))) (+ (* (sqrt (/ 1 x)) (sqrt -1)) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)))))))>
#<alt (* -1 (* x (+ (* -1/8 (* (sqrt (/ 1 (pow x 5))) (sqrt -1))) (+ (* -1/8 (* (sqrt (/ 1 (pow x 5))) (/ 1 (pow (sqrt -1) 2)))) (+ (* 1/2 (sqrt (/ 1 (pow x 3)))) (+ (* 1/2 (* (sqrt (/ 1 (pow x 3))) (sqrt -1))) (+ (* (sqrt (/ 1 x)) (sqrt -1)) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)))))))))>
#<alt (* -1 (* x (+ (* -1/8 (* (sqrt (/ 1 (pow x 5))) (sqrt -1))) (+ (* -1/8 (* (sqrt (/ 1 (pow x 5))) (/ 1 (pow (sqrt -1) 2)))) (+ (* 1/16 (* (sqrt (/ 1 (pow x 7))) (sqrt -1))) (+ (* 1/16 (* (sqrt (/ 1 (pow x 7))) (/ 1 (pow (sqrt -1) 4)))) (+ (* 1/2 (sqrt (/ 1 (pow x 3)))) (+ (* 1/2 (* (sqrt (/ 1 (pow x 3))) (sqrt -1))) (+ (* (sqrt (/ 1 x)) (sqrt -1)) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)))))))))))>
#<alt 1>
#<alt (+ 1 (* 1/2 x))>
#<alt (+ 1 (* x (+ 1/2 (* -1/8 x))))>
#<alt (+ 1 (* x (+ 1/2 (* x (- (* 1/16 x) 1/8)))))>
#<alt (sqrt x)>
#<alt (* x (+ (sqrt (/ 1 x)) (* 1/2 (sqrt (/ 1 (pow x 3))))))>
#<alt (* x (+ (sqrt (/ 1 x)) (+ (* -1/8 (sqrt (/ 1 (pow x 5)))) (* 1/2 (sqrt (/ 1 (pow x 3)))))))>
#<alt (* x (+ (sqrt (/ 1 x)) (+ (* -1/8 (sqrt (/ 1 (pow x 5)))) (+ (* 1/16 (sqrt (/ 1 (pow x 7)))) (* 1/2 (sqrt (/ 1 (pow x 3))))))))>
#<alt (* -1 (* (sqrt x) (pow (sqrt -1) 2)))>
#<alt (* -1 (* x (+ (* 1/2 (sqrt (/ 1 (pow x 3)))) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)))))>
#<alt (* -1 (* x (+ (* -1/8 (* (sqrt (/ 1 (pow x 5))) (/ 1 (pow (sqrt -1) 2)))) (+ (* 1/2 (sqrt (/ 1 (pow x 3)))) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))))))>
#<alt (* -1 (* x (+ (* -1/8 (* (sqrt (/ 1 (pow x 5))) (/ 1 (pow (sqrt -1) 2)))) (+ (* 1/16 (* (sqrt (/ 1 (pow x 7))) (/ 1 (pow (sqrt -1) 4)))) (+ (* 1/2 (sqrt (/ 1 (pow x 3)))) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)))))))>
#<alt x>
#<alt (* x (+ 1 (* 1/8 (pow x 2))))>
#<alt (* x (+ 1 (* (pow x 2) (+ 1/8 (* 7/128 (pow x 2))))))>
#<alt (* x (+ 1 (* (pow x 2) (+ 1/8 (* (pow x 2) (+ 7/128 (* 33/1024 (pow x 2))))))))>
#<alt (/ -1024/21 (pow x 5))>
#<alt (/ (- (* 40960/441 (/ 1 (pow x 2))) 1024/21) (pow x 5))>
#<alt (/ (- (+ (* 40960/441 (/ 1 (pow x 2))) (/ 1114112/9261 (pow x 4))) 1024/21) (pow x 5))>
#<alt (/ (- (+ (* 40960/441 (/ 1 (pow x 2))) (/ 1114112/9261 (pow x 4))) (+ 1024/21 (* 617086976/194481 (/ 1 (pow x 6))))) (pow x 5))>
#<alt (/ -1024/21 (pow x 5))>
#<alt (* -1 (/ (- 1024/21 (* 40960/441 (/ 1 (pow x 2)))) (pow x 5)))>
#<alt (* -1 (/ (+ 1024/21 (* -1 (/ (+ 40960/441 (* 1114112/9261 (/ 1 (pow x 2)))) (pow x 2)))) (pow x 5)))>
#<alt (* -1 (/ (- (+ 1024/21 (* 617086976/194481 (/ 1 (pow x 6)))) (+ (* 40960/441 (/ 1 (pow x 2))) (/ 1114112/9261 (pow x 4)))) (pow x 5)))>
#<alt (* 2 x)>
#<alt (* 2 x)>
#<alt (* 2 x)>
#<alt (* 2 x)>
#<alt (* 2 x)>
#<alt (* 2 x)>
#<alt (* 2 x)>
#<alt (* 2 x)>
#<alt (* 2 x)>
#<alt (* 2 x)>
#<alt (* 2 x)>
#<alt (* 2 x)>
#<alt -1>
#<alt (- (* 2 x) 1)>
#<alt (- (* 2 x) 1)>
#<alt (- (* 2 x) 1)>
#<alt (* 2 x)>
#<alt (* x (- 2 (/ 1 x)))>
#<alt (* x (- 2 (/ 1 x)))>
#<alt (* x (- 2 (/ 1 x)))>
#<alt (* 2 x)>
#<alt (* -1 (* x (- (/ 1 x) 2)))>
#<alt (* -1 (* x (- (/ 1 x) 2)))>
#<alt (* -1 (* x (- (/ 1 x) 2)))>
#<alt 1>
#<alt (+ 1 (* -1 x))>
#<alt (+ 1 (* -1 x))>
#<alt (+ 1 (* -1 x))>
#<alt (* -1 x)>
#<alt (* x (- (/ 1 x) 1))>
#<alt (* x (- (/ 1 x) 1))>
#<alt (* x (- (/ 1 x) 1))>
#<alt (* -1 x)>
#<alt (* -1 (* x (- 1 (/ 1 x))))>
#<alt (* -1 (* x (- 1 (/ 1 x))))>
#<alt (* -1 (* x (- 1 (/ 1 x))))>
#<alt (* 33/1024 (pow x 2))>
#<alt (* 33/1024 (pow x 2))>
#<alt (* 33/1024 (pow x 2))>
#<alt (* 33/1024 (pow x 2))>
#<alt (* 33/1024 (pow x 2))>
#<alt (* 33/1024 (pow x 2))>
#<alt (* 33/1024 (pow x 2))>
#<alt (* 33/1024 (pow x 2))>
#<alt (* 33/1024 (pow x 2))>
#<alt (* 33/1024 (pow x 2))>
#<alt (* 33/1024 (pow x 2))>
#<alt (* 33/1024 (pow x 2))>
#<alt (* 7/128 (pow x 2))>
#<alt (* (pow x 2) (+ 7/128 (* 33/1024 (pow x 2))))>
#<alt (* (pow x 2) (+ 7/128 (* 33/1024 (pow x 2))))>
#<alt (* (pow x 2) (+ 7/128 (* 33/1024 (pow x 2))))>
#<alt (* 33/1024 (pow x 4))>
#<alt (* (pow x 4) (+ 33/1024 (* 7/128 (/ 1 (pow x 2)))))>
#<alt (* (pow x 4) (+ 33/1024 (* 7/128 (/ 1 (pow x 2)))))>
#<alt (* (pow x 4) (+ 33/1024 (* 7/128 (/ 1 (pow x 2)))))>
#<alt (* 33/1024 (pow x 4))>
#<alt (* (pow x 4) (+ 33/1024 (* 7/128 (/ 1 (pow x 2)))))>
#<alt (* (pow x 4) (+ 33/1024 (* 7/128 (/ 1 (pow x 2)))))>
#<alt (* (pow x 4) (+ 33/1024 (* 7/128 (/ 1 (pow x 2)))))>
#<alt (* 7/128 (pow x 4))>
#<alt (* (pow x 4) (+ 7/128 (* 33/1024 (pow x 2))))>
#<alt (* (pow x 4) (+ 7/128 (* 33/1024 (pow x 2))))>
#<alt (* (pow x 4) (+ 7/128 (* 33/1024 (pow x 2))))>
#<alt (* 33/1024 (pow x 6))>
#<alt (* (pow x 6) (+ 33/1024 (* 7/128 (/ 1 (pow x 2)))))>
#<alt (* (pow x 6) (+ 33/1024 (* 7/128 (/ 1 (pow x 2)))))>
#<alt (* (pow x 6) (+ 33/1024 (* 7/128 (/ 1 (pow x 2)))))>
#<alt (* 33/1024 (pow x 6))>
#<alt (* (pow x 6) (+ 33/1024 (* 7/128 (/ 1 (pow x 2)))))>
#<alt (* (pow x 6) (+ 33/1024 (* 7/128 (/ 1 (pow x 2)))))>
#<alt (* (pow x 6) (+ 33/1024 (* 7/128 (/ 1 (pow x 2)))))>
#<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 1>
#<alt (+ 1 (* -1/2 x))>
#<alt (+ 1 (* x (- (* -1/8 x) 1/2)))>
#<alt (+ 1 (* x (- (* x (- (* -1/16 x) 1/8)) 1/2)))>
#<alt (* (sqrt x) (sqrt -1))>
#<alt (* x (+ (* 1/2 (* (sqrt (/ 1 (pow x 3))) (/ 1 (sqrt -1)))) (* (sqrt (/ 1 x)) (sqrt -1))))>
#<alt (* x (+ (* -1/8 (* (sqrt (/ 1 (pow x 5))) (/ 1 (pow (sqrt -1) 3)))) (+ (* 1/2 (* (sqrt (/ 1 (pow x 3))) (/ 1 (sqrt -1)))) (* (sqrt (/ 1 x)) (sqrt -1)))))>
#<alt (* x (+ (* -1/8 (* (sqrt (/ 1 (pow x 5))) (/ 1 (pow (sqrt -1) 3)))) (+ (* 1/16 (* (sqrt (/ 1 (pow x 7))) (/ 1 (pow (sqrt -1) 5)))) (+ (* 1/2 (* (sqrt (/ 1 (pow x 3))) (/ 1 (sqrt -1)))) (* (sqrt (/ 1 x)) (sqrt -1))))))>
#<alt (* -1 (* (sqrt x) (sqrt -1)))>
#<alt (* -1 (* x (+ (* 1/2 (* (sqrt (/ 1 (pow x 3))) (sqrt -1))) (* (sqrt (/ 1 x)) (sqrt -1)))))>
#<alt (* -1 (* x (+ (* -1/8 (* (sqrt (/ 1 (pow x 5))) (sqrt -1))) (+ (* 1/2 (* (sqrt (/ 1 (pow x 3))) (sqrt -1))) (* (sqrt (/ 1 x)) (sqrt -1))))))>
#<alt (* -1 (* x (+ (* -1/8 (* (sqrt (/ 1 (pow x 5))) (sqrt -1))) (+ (* 1/16 (* (sqrt (/ 1 (pow x 7))) (sqrt -1))) (+ (* 1/2 (* (sqrt (/ 1 (pow x 3))) (sqrt -1))) (* (sqrt (/ 1 x)) (sqrt -1)))))))>
#<alt (* -21/512 (pow x 2))>
#<alt (* -21/512 (pow x 2))>
#<alt (* -21/512 (pow x 2))>
#<alt (* -21/512 (pow x 2))>
#<alt (* -21/512 (pow x 2))>
#<alt (* -21/512 (pow x 2))>
#<alt (* -21/512 (pow x 2))>
#<alt (* -21/512 (pow x 2))>
#<alt (* -21/512 (pow x 2))>
#<alt (* -21/512 (pow x 2))>
#<alt (* -21/512 (pow x 2))>
#<alt (* -21/512 (pow x 2))>
#<alt (* -5/64 (pow x 2))>
#<alt (* (pow x 2) (- (* -21/512 (pow x 2)) 5/64))>
#<alt (* (pow x 2) (- (* -21/512 (pow x 2)) 5/64))>
#<alt (* (pow x 2) (- (* -21/512 (pow x 2)) 5/64))>
#<alt (* -21/512 (pow x 4))>
#<alt (* -1 (* (pow x 4) (+ 21/512 (* 5/64 (/ 1 (pow x 2))))))>
#<alt (* -1 (* (pow x 4) (+ 21/512 (* 5/64 (/ 1 (pow x 2))))))>
#<alt (* -1 (* (pow x 4) (+ 21/512 (* 5/64 (/ 1 (pow x 2))))))>
#<alt (* -21/512 (pow x 4))>
#<alt (* -1 (* (pow x 4) (+ 21/512 (* 5/64 (/ 1 (pow x 2))))))>
#<alt (* -1 (* (pow x 4) (+ 21/512 (* 5/64 (/ 1 (pow x 2))))))>
#<alt (* -1 (* (pow x 4) (+ 21/512 (* 5/64 (/ 1 (pow x 2))))))>
#<alt (* -5/64 x)>
#<alt (* x (- (* -21/512 (pow x 2)) 5/64))>
#<alt (* x (- (* -21/512 (pow x 2)) 5/64))>
#<alt (* x (- (* -21/512 (pow x 2)) 5/64))>
#<alt (* -21/512 (pow x 3))>
#<alt (* -1 (* (pow x 3) (+ 21/512 (* 5/64 (/ 1 (pow x 2))))))>
#<alt (* -1 (* (pow x 3) (+ 21/512 (* 5/64 (/ 1 (pow x 2))))))>
#<alt (* -1 (* (pow x 3) (+ 21/512 (* 5/64 (/ 1 (pow x 2))))))>
#<alt (* -21/512 (pow x 3))>
#<alt (* -1 (* (pow x 3) (+ 21/512 (* 5/64 (/ 1 (pow x 2))))))>
#<alt (* -1 (* (pow x 3) (+ 21/512 (* 5/64 (/ 1 (pow x 2))))))>
#<alt (* -1 (* (pow x 3) (+ 21/512 (* 5/64 (/ 1 (pow x 2))))))>
Calls

75 calls:

TimeVariablePointExpression
2.0ms
x
@-inf
(/ (+ 1 (- x (- 1 x))) (+ 2 (* (* x x) (+ -1/4 (* x (* x (+ -5/64 (* (* x x) -21/512))))))))
1.0ms
x
@inf
(/ (+ 1 (- x (- 1 x))) (+ 2 (* (* x x) (+ -1/4 (* x (* x (+ -5/64 (* (* x x) -21/512))))))))
0.0ms
x
@inf
(* x (* x (+ -5/64 (* (* x x) -21/512))))
0.0ms
x
@inf
(* (* x x) -21/512)
0.0ms
x
@-inf
(+ (* (+ 1/8 (* (* x x) 7/128)) (* x (* x x))) x)

rewrite320.0ms (3.2%)

Algorithm
batch-egg-rewrite
Rules
3232×*-lowering-*.f32
3232×*-lowering-*.f64
2520×fma-lowering-fma.f32
2520×fma-lowering-fma.f64
1986×pow-lowering-pow.f64
Iterations

Useful iterations: 2 (0.0ms)

IterNodesCost
041202
1302179
22896176
08238176
Stop Event
iter limit
node limit
Counts
25 → 550
Calls
Call 1
Inputs
(* x (+ (+ 1 (* (* x x) 1/8)) (* (* x x) (* (* x x) (+ 7/128 (* (* x x) 33/1024))))))
(+ (+ 1 (* (* x x) 1/8)) (* (* x x) (* (* x x) (+ 7/128 (* (* x x) 33/1024)))))
(+ 1 (* (* x x) 1/8))
(* (* x x) 1/8)
(+ (* (+ 1/8 (* (* x x) 7/128)) (* x (* x x))) x)
(* (+ 1/8 (* (* x x) 7/128)) (* x (* x x)))
(+ 1/8 (* (* x x) 7/128))
(* (* x x) 7/128)
(/ (* x 2) (+ (pow (+ 1 x) 1/2) (pow (- 1 x) 1/2)))
(* x 2)
(+ (pow (+ 1 x) 1/2) (pow (- 1 x) 1/2))
(pow (+ 1 x) 1/2)
(/ (+ 1 (- x (- 1 x))) (+ 2 (* (* x x) (+ -1/4 (* x (* x (+ -5/64 (* (* x x) -21/512))))))))
(+ 1 (- x (- 1 x)))
(- x (- 1 x))
(- 1 x)
(* (* x x) 33/1024)
(* (* x x) (+ 7/128 (* (* x x) 33/1024)))
(* (* x x) (* (* x x) (+ 7/128 (* (* x x) 33/1024))))
(* x (* x x))
(* x x)
(pow (- 1 x) 1/2)
(* (* x x) -21/512)
(* x (* x (+ -5/64 (* (* x x) -21/512))))
(* x (+ -5/64 (* (* x x) -21/512)))
Outputs
(+.f64 x (*.f64 x (*.f64 (*.f64 x x) (+.f64 #s(literal 1/8 binary64) (*.f64 (*.f64 x x) (+.f64 #s(literal 7/128 binary64) (*.f64 (*.f64 x x) #s(literal 33/1024 binary64))))))))
(+.f64 x (*.f64 (*.f64 (*.f64 x x) (+.f64 #s(literal 1/8 binary64) (*.f64 (*.f64 x x) (+.f64 #s(literal 7/128 binary64) (*.f64 (*.f64 x x) #s(literal 33/1024 binary64)))))) x))
(+.f64 (*.f64 x (+.f64 #s(literal 1 binary64) (*.f64 x (*.f64 x #s(literal 1/8 binary64))))) (*.f64 (*.f64 x x) (*.f64 (*.f64 x (*.f64 x x)) (+.f64 #s(literal 7/128 binary64) (*.f64 (*.f64 x x) #s(literal 33/1024 binary64))))))
(+.f64 (*.f64 (*.f64 x x) (*.f64 (*.f64 x (*.f64 x x)) (+.f64 #s(literal 7/128 binary64) (*.f64 (*.f64 x x) #s(literal 33/1024 binary64))))) (*.f64 x (+.f64 #s(literal 1 binary64) (*.f64 x (*.f64 x #s(literal 1/8 binary64))))))
(fma.f64 x #s(literal 1 binary64) (*.f64 x (*.f64 (*.f64 x x) (+.f64 #s(literal 1/8 binary64) (*.f64 (*.f64 x x) (+.f64 #s(literal 7/128 binary64) (*.f64 (*.f64 x x) #s(literal 33/1024 binary64))))))))
(fma.f64 x #s(literal 1 binary64) (*.f64 (*.f64 (*.f64 x x) (+.f64 #s(literal 1/8 binary64) (*.f64 (*.f64 x x) (+.f64 #s(literal 7/128 binary64) (*.f64 (*.f64 x x) #s(literal 33/1024 binary64)))))) x))
(fma.f64 x (+.f64 #s(literal 1 binary64) (*.f64 x (*.f64 x #s(literal 1/8 binary64)))) (*.f64 (*.f64 x x) (*.f64 (*.f64 x (*.f64 x x)) (+.f64 #s(literal 7/128 binary64) (*.f64 (*.f64 x x) #s(literal 33/1024 binary64))))))
(fma.f64 x (*.f64 x (*.f64 (*.f64 x (*.f64 x x)) (+.f64 #s(literal 7/128 binary64) (*.f64 (*.f64 x x) #s(literal 33/1024 binary64))))) (*.f64 x (+.f64 #s(literal 1 binary64) (*.f64 x (*.f64 x #s(literal 1/8 binary64))))))
(fma.f64 #s(literal 1 binary64) x (*.f64 x (*.f64 (*.f64 x x) (+.f64 #s(literal 1/8 binary64) (*.f64 (*.f64 x x) (+.f64 #s(literal 7/128 binary64) (*.f64 (*.f64 x x) #s(literal 33/1024 binary64))))))))
(fma.f64 #s(literal 1 binary64) x (*.f64 (*.f64 (*.f64 x x) (+.f64 #s(literal 1/8 binary64) (*.f64 (*.f64 x x) (+.f64 #s(literal 7/128 binary64) (*.f64 (*.f64 x x) #s(literal 33/1024 binary64)))))) x))
(fma.f64 (*.f64 x x) (*.f64 (*.f64 x (*.f64 x x)) (+.f64 #s(literal 7/128 binary64) (*.f64 (*.f64 x x) #s(literal 33/1024 binary64)))) (*.f64 x (+.f64 #s(literal 1 binary64) (*.f64 x (*.f64 x #s(literal 1/8 binary64))))))
(fma.f64 (+.f64 #s(literal 1 binary64) (*.f64 x (*.f64 x #s(literal 1/8 binary64)))) x (*.f64 (*.f64 x x) (*.f64 (*.f64 x (*.f64 x x)) (+.f64 #s(literal 7/128 binary64) (*.f64 (*.f64 x x) #s(literal 33/1024 binary64))))))
(fma.f64 (*.f64 (*.f64 x x) (+.f64 #s(literal 7/128 binary64) (*.f64 (*.f64 x x) #s(literal 33/1024 binary64)))) (*.f64 x (*.f64 x x)) (*.f64 x (+.f64 #s(literal 1 binary64) (*.f64 x (*.f64 x #s(literal 1/8 binary64))))))
(fma.f64 (*.f64 x (*.f64 (*.f64 x (*.f64 x x)) (+.f64 #s(literal 7/128 binary64) (*.f64 (*.f64 x x) #s(literal 33/1024 binary64))))) x (*.f64 x (+.f64 #s(literal 1 binary64) (*.f64 x (*.f64 x #s(literal 1/8 binary64))))))
(fma.f64 (*.f64 x (*.f64 x x)) (*.f64 (*.f64 x x) (+.f64 #s(literal 7/128 binary64) (*.f64 (*.f64 x x) #s(literal 33/1024 binary64)))) (*.f64 x (+.f64 #s(literal 1 binary64) (*.f64 x (*.f64 x #s(literal 1/8 binary64))))))
(fma.f64 (*.f64 x (*.f64 x (*.f64 x x))) (*.f64 x (+.f64 #s(literal 7/128 binary64) (*.f64 (*.f64 x x) #s(literal 33/1024 binary64)))) (*.f64 x (+.f64 #s(literal 1 binary64) (*.f64 x (*.f64 x #s(literal 1/8 binary64))))))
(fma.f64 (*.f64 (*.f64 x (*.f64 x x)) (+.f64 #s(literal 7/128 binary64) (*.f64 (*.f64 x x) #s(literal 33/1024 binary64)))) (*.f64 x x) (*.f64 x (+.f64 #s(literal 1 binary64) (*.f64 x (*.f64 x #s(literal 1/8 binary64))))))
(fma.f64 (*.f64 x (*.f64 x (*.f64 x (*.f64 x x)))) (+.f64 #s(literal 7/128 binary64) (*.f64 (*.f64 x x) #s(literal 33/1024 binary64))) (*.f64 x (+.f64 #s(literal 1 binary64) (*.f64 x (*.f64 x #s(literal 1/8 binary64))))))
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(/.f64 (*.f64 (*.f64 x x) (-.f64 #s(literal 49/16384 binary64) (*.f64 (*.f64 x (*.f64 x (*.f64 x x))) #s(literal 1089/1048576 binary64)))) (-.f64 #s(literal 7/128 binary64) (*.f64 (*.f64 x x) #s(literal 33/1024 binary64))))
(/.f64 (*.f64 (+.f64 #s(literal 343/2097152 binary64) (*.f64 (*.f64 x (*.f64 x x)) (*.f64 (*.f64 x (*.f64 x x)) #s(literal 35937/1073741824 binary64)))) (*.f64 x x)) (+.f64 #s(literal 49/16384 binary64) (*.f64 (*.f64 (*.f64 x x) #s(literal 33/1024 binary64)) (-.f64 (*.f64 (*.f64 x x) #s(literal 33/1024 binary64)) #s(literal 7/128 binary64)))))
(/.f64 (*.f64 (-.f64 #s(literal 49/16384 binary64) (*.f64 (*.f64 x (*.f64 x (*.f64 x x))) #s(literal 1089/1048576 binary64))) (*.f64 x x)) (-.f64 #s(literal 7/128 binary64) (*.f64 (*.f64 x x) #s(literal 33/1024 binary64))))
(*.f64 x (*.f64 x (+.f64 #s(literal 7/128 binary64) (*.f64 (*.f64 x x) #s(literal 33/1024 binary64)))))
(*.f64 (*.f64 x x) (+.f64 #s(literal 7/128 binary64) (*.f64 (*.f64 x x) #s(literal 33/1024 binary64))))
(*.f64 (+.f64 #s(literal 7/128 binary64) (*.f64 (*.f64 x x) #s(literal 33/1024 binary64))) (*.f64 x x))
(*.f64 (*.f64 x (+.f64 #s(literal 7/128 binary64) (*.f64 (*.f64 x x) #s(literal 33/1024 binary64)))) x)
(+.f64 (*.f64 (*.f64 x x) (*.f64 x (*.f64 x #s(literal 7/128 binary64)))) (*.f64 (*.f64 x x) (*.f64 x (*.f64 x (*.f64 (*.f64 x x) #s(literal 33/1024 binary64))))))
(+.f64 (*.f64 (*.f64 x (*.f64 x (*.f64 x x))) #s(literal 7/128 binary64)) (*.f64 (*.f64 x (*.f64 x (*.f64 x x))) (*.f64 (*.f64 x x) #s(literal 33/1024 binary64))))
(+.f64 (*.f64 (*.f64 x (*.f64 x (*.f64 x x))) (*.f64 (*.f64 x x) #s(literal 33/1024 binary64))) (*.f64 (*.f64 x (*.f64 x (*.f64 x x))) #s(literal 7/128 binary64)))
(+.f64 (*.f64 (*.f64 x (*.f64 x #s(literal 7/128 binary64))) (*.f64 x x)) (*.f64 (*.f64 x (*.f64 x (*.f64 (*.f64 x x) #s(literal 33/1024 binary64)))) (*.f64 x x)))
(+.f64 (*.f64 #s(literal 7/128 binary64) (*.f64 x (*.f64 x (*.f64 x x)))) (*.f64 (*.f64 (*.f64 x x) #s(literal 33/1024 binary64)) (*.f64 x (*.f64 x (*.f64 x x)))))
(+.f64 (*.f64 (*.f64 (*.f64 x x) #s(literal 33/1024 binary64)) (*.f64 x (*.f64 x (*.f64 x x)))) (*.f64 #s(literal 7/128 binary64) (*.f64 x (*.f64 x (*.f64 x x)))))
(fma.f64 (*.f64 x x) (*.f64 x (*.f64 x #s(literal 7/128 binary64))) (*.f64 (*.f64 x x) (*.f64 x (*.f64 x (*.f64 (*.f64 x x) #s(literal 33/1024 binary64))))))
(fma.f64 #s(literal 7/128 binary64) (*.f64 x (*.f64 x (*.f64 x x))) (*.f64 (*.f64 (*.f64 x x) #s(literal 33/1024 binary64)) (*.f64 x (*.f64 x (*.f64 x x)))))
(fma.f64 (*.f64 (*.f64 x x) #s(literal 33/1024 binary64)) (*.f64 x (*.f64 x (*.f64 x x))) (*.f64 #s(literal 7/128 binary64) (*.f64 x (*.f64 x (*.f64 x x)))))
(fma.f64 (*.f64 x (*.f64 x #s(literal 7/128 binary64))) (*.f64 x x) (*.f64 (*.f64 x (*.f64 x (*.f64 (*.f64 x x) #s(literal 33/1024 binary64)))) (*.f64 x x)))
(fma.f64 (*.f64 x (*.f64 x (*.f64 x x))) #s(literal 7/128 binary64) (*.f64 (*.f64 x (*.f64 x (*.f64 x x))) (*.f64 (*.f64 x x) #s(literal 33/1024 binary64))))
(fma.f64 (*.f64 x (*.f64 x (*.f64 x x))) (*.f64 (*.f64 x x) #s(literal 33/1024 binary64)) (*.f64 (*.f64 x (*.f64 x (*.f64 x x))) #s(literal 7/128 binary64)))
(/.f64 (*.f64 (*.f64 x (*.f64 x (*.f64 x x))) (+.f64 #s(literal 343/2097152 binary64) (*.f64 (*.f64 x (*.f64 x x)) (*.f64 (*.f64 x (*.f64 x x)) #s(literal 35937/1073741824 binary64))))) (+.f64 #s(literal 49/16384 binary64) (*.f64 (*.f64 (*.f64 x x) #s(literal 33/1024 binary64)) (-.f64 (*.f64 (*.f64 x x) #s(literal 33/1024 binary64)) #s(literal 7/128 binary64)))))
(/.f64 (*.f64 (*.f64 x (*.f64 x (*.f64 x x))) (-.f64 #s(literal 49/16384 binary64) (*.f64 (*.f64 x (*.f64 x (*.f64 x x))) #s(literal 1089/1048576 binary64)))) (-.f64 #s(literal 7/128 binary64) (*.f64 (*.f64 x x) #s(literal 33/1024 binary64))))
(*.f64 x (*.f64 (*.f64 x (*.f64 x x)) (+.f64 #s(literal 7/128 binary64) (*.f64 (*.f64 x x) #s(literal 33/1024 binary64)))))
(*.f64 (*.f64 x x) (*.f64 (*.f64 x x) (+.f64 #s(literal 7/128 binary64) (*.f64 (*.f64 x x) #s(literal 33/1024 binary64)))))
(*.f64 (+.f64 #s(literal 7/128 binary64) (*.f64 (*.f64 x x) #s(literal 33/1024 binary64))) (*.f64 x (*.f64 x (*.f64 x x))))
(*.f64 (*.f64 (*.f64 x x) (+.f64 #s(literal 7/128 binary64) (*.f64 (*.f64 x x) #s(literal 33/1024 binary64)))) (*.f64 x x))
(*.f64 (*.f64 x (*.f64 x x)) (*.f64 x (+.f64 #s(literal 7/128 binary64) (*.f64 (*.f64 x x) #s(literal 33/1024 binary64)))))
(*.f64 (*.f64 x (*.f64 x (*.f64 x x))) (+.f64 #s(literal 7/128 binary64) (*.f64 (*.f64 x x) #s(literal 33/1024 binary64))))
(*.f64 (*.f64 (*.f64 x (*.f64 x x)) (+.f64 #s(literal 7/128 binary64) (*.f64 (*.f64 x x) #s(literal 33/1024 binary64)))) x)
(exp.f64 (*.f64 (log.f64 x) #s(literal 3 binary64)))
(pow.f64 x #s(literal 3 binary64))
(pow.f64 (*.f64 x x) #s(literal 3/2 binary64))
(pow.f64 (pow.f64 x #s(literal 3/2 binary64)) #s(literal 2 binary64))
(pow.f64 (exp.f64 (log.f64 x)) #s(literal 3 binary64))
(*.f64 x (*.f64 x x))
(*.f64 #s(literal 1 binary64) (*.f64 x (*.f64 x x)))
(*.f64 (*.f64 x x) x)
(*.f64 (*.f64 x (*.f64 x x)) #s(literal 1 binary64))
(*.f64 (pow.f64 x #s(literal 3/2 binary64)) (pow.f64 x #s(literal 3/2 binary64)))
(exp.f64 (*.f64 (log.f64 x) #s(literal 2 binary64)))
(pow.f64 x #s(literal 2 binary64))
(pow.f64 (*.f64 x x) #s(literal 1 binary64))
(pow.f64 (exp.f64 (log.f64 x)) #s(literal 2 binary64))
(*.f64 x x)
(*.f64 #s(literal 1 binary64) (*.f64 x x))
(*.f64 (*.f64 x x) #s(literal 1 binary64))
(*.f64 (exp.f64 (log.f64 x)) (exp.f64 (log.f64 x)))
(exp.f64 (*.f64 #s(literal 1/2 binary64) (log.f64 (-.f64 #s(literal 1 binary64) x))))
(exp.f64 (*.f64 (log.f64 (*.f64 (-.f64 #s(literal 1 binary64) x) (-.f64 #s(literal 1 binary64) x))) #s(literal 1/4 binary64)))
(exp.f64 (*.f64 (log.f64 (pow.f64 (-.f64 #s(literal 1 binary64) x) #s(literal 1/4 binary64))) #s(literal 2 binary64)))
(exp.f64 (*.f64 (*.f64 (log.f64 (-.f64 #s(literal 1 binary64) x)) #s(literal 1/4 binary64)) #s(literal 2 binary64)))
(exp.f64 (+.f64 (*.f64 (log.f64 (-.f64 #s(literal 1 binary64) x)) #s(literal 1/4 binary64)) (*.f64 (log.f64 (-.f64 #s(literal 1 binary64) x)) #s(literal 1/4 binary64))))
(sqrt.f64 (-.f64 #s(literal 1 binary64) x))
(/.f64 #s(literal 1 binary64) (sqrt.f64 (/.f64 (+.f64 #s(literal 1 binary64) (*.f64 x (+.f64 x #s(literal 1 binary64)))) (-.f64 #s(literal 1 binary64) (*.f64 x (*.f64 x x))))))
(/.f64 #s(literal 1 binary64) (sqrt.f64 (/.f64 (+.f64 x #s(literal 1 binary64)) (-.f64 #s(literal 1 binary64) (*.f64 x x)))))
(/.f64 (sqrt.f64 (-.f64 #s(literal 1 binary64) (*.f64 x (*.f64 x x)))) (sqrt.f64 (+.f64 #s(literal 1 binary64) (*.f64 x (+.f64 x #s(literal 1 binary64))))))
(/.f64 (sqrt.f64 (-.f64 #s(literal 1 binary64) (*.f64 x (*.f64 x x)))) (sqrt.f64 (+.f64 #s(literal 1 binary64) (-.f64 (*.f64 (-.f64 #s(literal 0 binary64) x) (-.f64 #s(literal 0 binary64) x)) (*.f64 #s(literal 1 binary64) (-.f64 #s(literal 0 binary64) x))))))
(/.f64 (sqrt.f64 (-.f64 #s(literal 1 binary64) (*.f64 x x))) (pow.f64 (+.f64 x #s(literal 1 binary64)) #s(literal 1/2 binary64)))
(/.f64 (sqrt.f64 (neg.f64 (-.f64 #s(literal 1 binary64) (*.f64 x x)))) (sqrt.f64 (neg.f64 (+.f64 x #s(literal 1 binary64)))))
(/.f64 (sqrt.f64 (neg.f64 (-.f64 #s(literal 1 binary64) (*.f64 x (*.f64 x x))))) (sqrt.f64 (neg.f64 (+.f64 #s(literal 1 binary64) (*.f64 x (+.f64 x #s(literal 1 binary64)))))))
(/.f64 (sqrt.f64 (-.f64 #s(literal 1 binary64) (*.f64 (-.f64 #s(literal 0 binary64) x) (-.f64 #s(literal 0 binary64) x)))) (sqrt.f64 (-.f64 #s(literal 1 binary64) (-.f64 #s(literal 0 binary64) x))))
(pow.f64 (-.f64 #s(literal 1 binary64) x) #s(literal 1/2 binary64))
(pow.f64 (pow.f64 (-.f64 #s(literal 1 binary64) x) #s(literal 1/2 binary64)) #s(literal 1 binary64))
(pow.f64 (*.f64 (-.f64 #s(literal 1 binary64) x) (-.f64 #s(literal 1 binary64) x)) #s(literal 1/4 binary64))
(pow.f64 (pow.f64 (-.f64 #s(literal 1 binary64) x) #s(literal 1/4 binary64)) #s(literal 2 binary64))
(pow.f64 (exp.f64 #s(literal 1/2 binary64)) (log.f64 (-.f64 #s(literal 1 binary64) x)))
(*.f64 (pow.f64 (-.f64 #s(literal 1 binary64) x) #s(literal 1/4 binary64)) (pow.f64 (-.f64 #s(literal 1 binary64) x) #s(literal 1/4 binary64)))
(*.f64 (sqrt.f64 (-.f64 #s(literal 1 binary64) (*.f64 x (*.f64 x x)))) (pow.f64 (/.f64 #s(literal 1 binary64) (+.f64 #s(literal 1 binary64) (*.f64 x (+.f64 x #s(literal 1 binary64))))) #s(literal 1/2 binary64)))
(*.f64 (sqrt.f64 (-.f64 #s(literal 1 binary64) (*.f64 x (*.f64 x x)))) (sqrt.f64 (/.f64 #s(literal 1 binary64) (+.f64 #s(literal 1 binary64) (*.f64 x (+.f64 x #s(literal 1 binary64)))))))
(*.f64 (sqrt.f64 (-.f64 #s(literal 1 binary64) (*.f64 x x))) (pow.f64 (/.f64 #s(literal 1 binary64) (+.f64 x #s(literal 1 binary64))) #s(literal 1/2 binary64)))
(*.f64 (sqrt.f64 (-.f64 #s(literal 1 binary64) (*.f64 x x))) (sqrt.f64 (/.f64 #s(literal 1 binary64) (+.f64 x #s(literal 1 binary64)))))
(*.f64 (pow.f64 (/.f64 (-.f64 #s(literal 1 binary64) (*.f64 x x)) (-.f64 #s(literal 1 binary64) (*.f64 x x))) #s(literal 1/2 binary64)) (pow.f64 (-.f64 #s(literal 1 binary64) x) #s(literal 1/2 binary64)))
(*.f64 (pow.f64 (pow.f64 (-.f64 #s(literal 1 binary64) x) #s(literal 1/4 binary64)) #s(literal 1/2 binary64)) (pow.f64 (pow.f64 (-.f64 #s(literal 1 binary64) x) #s(literal 3/4 binary64)) #s(literal 1/2 binary64)))
(*.f64 (pow.f64 (pow.f64 (-.f64 #s(literal 1 binary64) x) #s(literal 3/4 binary64)) #s(literal 1/2 binary64)) (pow.f64 (pow.f64 (-.f64 #s(literal 1 binary64) x) #s(literal 1/4 binary64)) #s(literal 1/2 binary64)))
(*.f64 (pow.f64 (/.f64 (-.f64 #s(literal 1 binary64) (*.f64 x x)) (+.f64 #s(literal 1 binary64) (*.f64 x (*.f64 x x)))) #s(literal 1/2 binary64)) (sqrt.f64 (+.f64 #s(literal 1 binary64) (*.f64 x (+.f64 x #s(literal -1 binary64))))))
(*.f64 (sqrt.f64 (/.f64 (-.f64 #s(literal 1 binary64) (*.f64 x x)) (-.f64 #s(literal 1 binary64) (*.f64 x x)))) (pow.f64 (-.f64 #s(literal 1 binary64) x) #s(literal 1/2 binary64)))
(*.f64 (sqrt.f64 (pow.f64 (-.f64 #s(literal 1 binary64) x) #s(literal 1/2 binary64))) (sqrt.f64 (pow.f64 (-.f64 #s(literal 1 binary64) x) #s(literal 1/2 binary64))))
(*.f64 (sqrt.f64 (pow.f64 (-.f64 #s(literal 1 binary64) x) #s(literal 1/4 binary64))) (sqrt.f64 (pow.f64 (-.f64 #s(literal 1 binary64) x) #s(literal 3/4 binary64))))
(*.f64 (sqrt.f64 (pow.f64 (-.f64 #s(literal 1 binary64) x) #s(literal 3/4 binary64))) (sqrt.f64 (pow.f64 (-.f64 #s(literal 1 binary64) x) #s(literal 1/4 binary64))))
(*.f64 (sqrt.f64 (/.f64 (-.f64 #s(literal 1 binary64) (*.f64 x x)) (+.f64 #s(literal 1 binary64) (*.f64 x (*.f64 x x))))) (sqrt.f64 (+.f64 #s(literal 1 binary64) (*.f64 x (+.f64 x #s(literal -1 binary64))))))
(*.f64 x (*.f64 x #s(literal -21/512 binary64)))
(*.f64 (*.f64 x x) #s(literal -21/512 binary64))
(*.f64 #s(literal -21/512 binary64) (*.f64 x x))
(*.f64 (*.f64 x #s(literal -21/512 binary64)) x)
(+.f64 (*.f64 x (*.f64 x #s(literal -5/64 binary64))) (*.f64 x (*.f64 x (*.f64 (*.f64 x x) #s(literal -21/512 binary64)))))
(+.f64 (*.f64 (*.f64 x x) #s(literal -5/64 binary64)) (*.f64 (*.f64 x x) (*.f64 (*.f64 x x) #s(literal -21/512 binary64))))
(+.f64 (*.f64 (*.f64 x x) (*.f64 (*.f64 x x) #s(literal -21/512 binary64))) (*.f64 (*.f64 x x) #s(literal -5/64 binary64)))
(+.f64 (*.f64 (*.f64 x #s(literal -5/64 binary64)) x) (*.f64 (*.f64 x (*.f64 (*.f64 x x) #s(literal -21/512 binary64))) x))
(+.f64 (*.f64 #s(literal -5/64 binary64) (*.f64 x x)) (*.f64 (*.f64 (*.f64 x x) #s(literal -21/512 binary64)) (*.f64 x x)))
(+.f64 (*.f64 (*.f64 (*.f64 x x) #s(literal -21/512 binary64)) (*.f64 x x)) (*.f64 #s(literal -5/64 binary64) (*.f64 x x)))
(fma.f64 x (*.f64 x #s(literal -5/64 binary64)) (*.f64 x (*.f64 x (*.f64 (*.f64 x x) #s(literal -21/512 binary64)))))
(fma.f64 (*.f64 x x) #s(literal -5/64 binary64) (*.f64 (*.f64 x x) (*.f64 (*.f64 x x) #s(literal -21/512 binary64))))
(fma.f64 (*.f64 x x) (*.f64 (*.f64 x x) #s(literal -21/512 binary64)) (*.f64 (*.f64 x x) #s(literal -5/64 binary64)))
(fma.f64 #s(literal -5/64 binary64) (*.f64 x x) (*.f64 (*.f64 (*.f64 x x) #s(literal -21/512 binary64)) (*.f64 x x)))
(fma.f64 (*.f64 (*.f64 x x) #s(literal -21/512 binary64)) (*.f64 x x) (*.f64 #s(literal -5/64 binary64) (*.f64 x x)))
(fma.f64 (*.f64 x #s(literal -5/64 binary64)) x (*.f64 (*.f64 x (*.f64 (*.f64 x x) #s(literal -21/512 binary64))) x))
(/.f64 (*.f64 (*.f64 x x) (+.f64 #s(literal -125/262144 binary64) (*.f64 (*.f64 x (*.f64 x x)) (*.f64 (*.f64 x (*.f64 x x)) #s(literal -9261/134217728 binary64))))) (+.f64 #s(literal 25/4096 binary64) (*.f64 (*.f64 (*.f64 x x) #s(literal -21/512 binary64)) (-.f64 (*.f64 (*.f64 x x) #s(literal -21/512 binary64)) #s(literal -5/64 binary64)))))
(/.f64 (*.f64 (*.f64 x x) (-.f64 #s(literal 25/4096 binary64) (*.f64 (*.f64 x (*.f64 x (*.f64 x x))) #s(literal 441/262144 binary64)))) (-.f64 #s(literal -5/64 binary64) (*.f64 (*.f64 x x) #s(literal -21/512 binary64))))
(*.f64 x (*.f64 x (+.f64 #s(literal -5/64 binary64) (*.f64 (*.f64 x x) #s(literal -21/512 binary64)))))
(*.f64 (*.f64 x x) (+.f64 #s(literal -5/64 binary64) (*.f64 (*.f64 x x) #s(literal -21/512 binary64))))
(*.f64 (+.f64 #s(literal -5/64 binary64) (*.f64 (*.f64 x x) #s(literal -21/512 binary64))) (*.f64 x x))
(*.f64 (*.f64 x (+.f64 #s(literal -5/64 binary64) (*.f64 (*.f64 x x) #s(literal -21/512 binary64)))) x)
(+.f64 (*.f64 x #s(literal -5/64 binary64)) (*.f64 x (*.f64 (*.f64 x x) #s(literal -21/512 binary64))))
(+.f64 (*.f64 x (*.f64 (*.f64 x x) #s(literal -21/512 binary64))) (*.f64 x #s(literal -5/64 binary64)))
(fma.f64 x #s(literal -5/64 binary64) (*.f64 x (*.f64 (*.f64 x x) #s(literal -21/512 binary64))))
(fma.f64 x (*.f64 (*.f64 x x) #s(literal -21/512 binary64)) (*.f64 x #s(literal -5/64 binary64)))
(fma.f64 (*.f64 x x) (*.f64 x #s(literal -21/512 binary64)) (*.f64 x #s(literal -5/64 binary64)))
(fma.f64 (*.f64 x (*.f64 x x)) #s(literal -21/512 binary64) (*.f64 x #s(literal -5/64 binary64)))
(fma.f64 #s(literal -5/64 binary64) x (*.f64 x (*.f64 (*.f64 x x) #s(literal -21/512 binary64))))
(fma.f64 #s(literal -21/512 binary64) (*.f64 x (*.f64 x x)) (*.f64 x #s(literal -5/64 binary64)))
(fma.f64 (*.f64 (*.f64 x x) #s(literal -21/512 binary64)) x (*.f64 x #s(literal -5/64 binary64)))
(fma.f64 (*.f64 x #s(literal -21/512 binary64)) (*.f64 x x) (*.f64 x #s(literal -5/64 binary64)))
(/.f64 (+.f64 (*.f64 (*.f64 x (*.f64 x x)) #s(literal -125/262144 binary64)) (*.f64 (*.f64 x (*.f64 x x)) (*.f64 (*.f64 x (*.f64 x x)) (*.f64 (*.f64 x (*.f64 x x)) #s(literal -9261/134217728 binary64))))) (+.f64 (*.f64 (*.f64 x #s(literal -5/64 binary64)) (*.f64 x #s(literal -5/64 binary64))) (-.f64 (*.f64 (*.f64 x (*.f64 (*.f64 x x) #s(literal -21/512 binary64))) (*.f64 x (*.f64 (*.f64 x x) #s(literal -21/512 binary64)))) (*.f64 (*.f64 x #s(literal -5/64 binary64)) (*.f64 x (*.f64 (*.f64 x x) #s(literal -21/512 binary64)))))))
(/.f64 (-.f64 (*.f64 (*.f64 x #s(literal -5/64 binary64)) (*.f64 x #s(literal -5/64 binary64))) (*.f64 (*.f64 x (*.f64 (*.f64 x x) #s(literal -21/512 binary64))) (*.f64 x (*.f64 (*.f64 x x) #s(literal -21/512 binary64))))) (-.f64 (*.f64 x #s(literal -5/64 binary64)) (*.f64 x (*.f64 (*.f64 x x) #s(literal -21/512 binary64)))))
(/.f64 (*.f64 x (+.f64 #s(literal -125/262144 binary64) (*.f64 (*.f64 x (*.f64 x x)) (*.f64 (*.f64 x (*.f64 x x)) #s(literal -9261/134217728 binary64))))) (+.f64 #s(literal 25/4096 binary64) (*.f64 (*.f64 (*.f64 x x) #s(literal -21/512 binary64)) (-.f64 (*.f64 (*.f64 x x) #s(literal -21/512 binary64)) #s(literal -5/64 binary64)))))
(/.f64 (*.f64 x (-.f64 #s(literal 25/4096 binary64) (*.f64 (*.f64 x (*.f64 x (*.f64 x x))) #s(literal 441/262144 binary64)))) (-.f64 #s(literal -5/64 binary64) (*.f64 (*.f64 x x) #s(literal -21/512 binary64))))
(/.f64 (*.f64 (+.f64 #s(literal -125/262144 binary64) (*.f64 (*.f64 x (*.f64 x x)) (*.f64 (*.f64 x (*.f64 x x)) #s(literal -9261/134217728 binary64)))) x) (+.f64 #s(literal 25/4096 binary64) (*.f64 (*.f64 (*.f64 x x) #s(literal -21/512 binary64)) (-.f64 (*.f64 (*.f64 x x) #s(literal -21/512 binary64)) #s(literal -5/64 binary64)))))
(/.f64 (*.f64 (-.f64 #s(literal 25/4096 binary64) (*.f64 (*.f64 x (*.f64 x (*.f64 x x))) #s(literal 441/262144 binary64))) x) (-.f64 #s(literal -5/64 binary64) (*.f64 (*.f64 x x) #s(literal -21/512 binary64))))
(*.f64 x (+.f64 #s(literal -5/64 binary64) (*.f64 (*.f64 x x) #s(literal -21/512 binary64))))
(*.f64 (+.f64 #s(literal -5/64 binary64) (*.f64 (*.f64 x x) #s(literal -21/512 binary64))) x)

simplify295.0ms (3%)

Algorithm
egg-herbie
Rules
5918×*-lowering-*.f32
5918×*-lowering-*.f64
2686×+-lowering-+.f64
2686×+-lowering-+.f32
2010×/-lowering-/.f32
Iterations

Useful iterations: 2 (0.0ms)

IterNodesCost
04063523
113692939
253762894
080982894
Stop Event
iter limit
node limit
Counts
300 → 300
Calls
Call 1
Inputs
x
(* x (+ 1 (* 1/8 (pow x 2))))
(* x (+ 1 (* (pow x 2) (+ 1/8 (* 7/128 (pow x 2))))))
(* x (+ 1 (* (pow x 2) (+ 1/8 (* (pow x 2) (+ 7/128 (* 33/1024 (pow x 2))))))))
(* 33/1024 (pow x 7))
(* (pow x 7) (+ 33/1024 (* 7/128 (/ 1 (pow x 2)))))
(* (pow x 7) (+ 33/1024 (+ (/ 1/8 (pow x 4)) (* 7/128 (/ 1 (pow x 2))))))
(* (pow x 7) (+ 33/1024 (+ (/ 1/8 (pow x 4)) (+ (* 7/128 (/ 1 (pow x 2))) (/ 1 (pow x 6))))))
(* 33/1024 (pow x 7))
(* (pow x 7) (+ 33/1024 (* 7/128 (/ 1 (pow x 2)))))
(* -1 (* (pow x 7) (- (* -1 (/ (+ 7/128 (* 1/8 (/ 1 (pow x 2)))) (pow x 2))) 33/1024)))
(* -1 (* (pow x 7) (- (* -1 (/ (+ 1/8 (/ 1 (pow x 2))) (pow x 4))) (+ 33/1024 (* 7/128 (/ 1 (pow x 2)))))))
1
(+ 1 (* 1/8 (pow x 2)))
(+ 1 (* (pow x 2) (+ 1/8 (* 7/128 (pow x 2)))))
(+ 1 (* (pow x 2) (+ 1/8 (* (pow x 2) (+ 7/128 (* 33/1024 (pow x 2)))))))
(* 33/1024 (pow x 6))
(* (pow x 6) (+ 33/1024 (* 7/128 (/ 1 (pow x 2)))))
(* (pow x 6) (+ 33/1024 (+ (/ 1/8 (pow x 4)) (* 7/128 (/ 1 (pow x 2))))))
(* (pow x 6) (+ 33/1024 (+ (/ 1/8 (pow x 4)) (+ (* 7/128 (/ 1 (pow x 2))) (/ 1 (pow x 6))))))
(* 33/1024 (pow x 6))
(* (pow x 6) (+ 33/1024 (* 7/128 (/ 1 (pow x 2)))))
(* (pow x 6) (+ 33/1024 (+ (/ 1/8 (pow x 4)) (* 7/128 (/ 1 (pow x 2))))))
(* (pow x 6) (+ 33/1024 (+ (/ 1/8 (pow x 4)) (+ (* 7/128 (/ 1 (pow x 2))) (/ 1 (pow x 6))))))
1
(+ 1 (* 1/8 (pow x 2)))
(+ 1 (* 1/8 (pow x 2)))
(+ 1 (* 1/8 (pow x 2)))
(* 1/8 (pow x 2))
(* (pow x 2) (+ 1/8 (/ 1 (pow x 2))))
(* (pow x 2) (+ 1/8 (/ 1 (pow x 2))))
(* (pow x 2) (+ 1/8 (/ 1 (pow x 2))))
(* 1/8 (pow x 2))
(* (pow x 2) (+ 1/8 (/ 1 (pow x 2))))
(* (pow x 2) (+ 1/8 (/ 1 (pow x 2))))
(* (pow x 2) (+ 1/8 (/ 1 (pow x 2))))
(* 1/8 (pow x 2))
(* 1/8 (pow x 2))
(* 1/8 (pow x 2))
(* 1/8 (pow x 2))
(* 1/8 (pow x 2))
(* 1/8 (pow x 2))
(* 1/8 (pow x 2))
(* 1/8 (pow x 2))
(* 1/8 (pow x 2))
(* 1/8 (pow x 2))
(* 1/8 (pow x 2))
(* 1/8 (pow x 2))
x
(* x (+ 1 (* 1/8 (pow x 2))))
(* x (+ 1 (* (pow x 2) (+ 1/8 (* 7/128 (pow x 2))))))
(* x (+ 1 (* (pow x 2) (+ 1/8 (* 7/128 (pow x 2))))))
(* 7/128 (pow x 5))
(* (pow x 5) (+ 7/128 (* 1/8 (/ 1 (pow x 2)))))
(* (pow x 5) (+ 7/128 (+ (* 1/8 (/ 1 (pow x 2))) (/ 1 (pow x 4)))))
(* (pow x 5) (+ 7/128 (+ (* 1/8 (/ 1 (pow x 2))) (/ 1 (pow x 4)))))
(* 7/128 (pow x 5))
(* (pow x 5) (+ 7/128 (* 1/8 (/ 1 (pow x 2)))))
(* -1 (* (pow x 5) (- (* -1 (/ (+ 1/8 (/ 1 (pow x 2))) (pow x 2))) 7/128)))
(* -1 (* (pow x 5) (- (* -1 (/ (+ 1/8 (/ 1 (pow x 2))) (pow x 2))) 7/128)))
(* 1/8 (pow x 3))
(* (pow x 3) (+ 1/8 (* 7/128 (pow x 2))))
(* (pow x 3) (+ 1/8 (* 7/128 (pow x 2))))
(* (pow x 3) (+ 1/8 (* 7/128 (pow x 2))))
(* 7/128 (pow x 5))
(* (pow x 5) (+ 7/128 (* 1/8 (/ 1 (pow x 2)))))
(* (pow x 5) (+ 7/128 (* 1/8 (/ 1 (pow x 2)))))
(* (pow x 5) (+ 7/128 (* 1/8 (/ 1 (pow x 2)))))
(* 7/128 (pow x 5))
(* (pow x 5) (+ 7/128 (* 1/8 (/ 1 (pow x 2)))))
(* (pow x 5) (+ 7/128 (* 1/8 (/ 1 (pow x 2)))))
(* (pow x 5) (+ 7/128 (* 1/8 (/ 1 (pow x 2)))))
1/8
(+ 1/8 (* 7/128 (pow x 2)))
(+ 1/8 (* 7/128 (pow x 2)))
(+ 1/8 (* 7/128 (pow x 2)))
(* 7/128 (pow x 2))
(* (pow x 2) (+ 7/128 (* 1/8 (/ 1 (pow x 2)))))
(* (pow x 2) (+ 7/128 (* 1/8 (/ 1 (pow x 2)))))
(* (pow x 2) (+ 7/128 (* 1/8 (/ 1 (pow x 2)))))
(* 7/128 (pow x 2))
(* (pow x 2) (+ 7/128 (* 1/8 (/ 1 (pow x 2)))))
(* (pow x 2) (+ 7/128 (* 1/8 (/ 1 (pow x 2)))))
(* (pow x 2) (+ 7/128 (* 1/8 (/ 1 (pow x 2)))))
(* 7/128 (pow x 2))
(* 7/128 (pow x 2))
(* 7/128 (pow x 2))
(* 7/128 (pow x 2))
(* 7/128 (pow x 2))
(* 7/128 (pow x 2))
(* 7/128 (pow x 2))
(* 7/128 (pow x 2))
(* 7/128 (pow x 2))
(* 7/128 (pow x 2))
(* 7/128 (pow x 2))
(* 7/128 (pow x 2))
x
(* x (+ 1 (* 1/8 (pow x 2))))
(* x (+ 1 (* (pow x 2) (+ 1/8 (* 7/128 (pow x 2))))))
(* x (+ 1 (* (pow x 2) (+ 1/8 (* (pow x 2) (+ 7/128 (* 33/1024 (pow x 2))))))))
(/ 2 (+ (sqrt (/ 1 x)) (* (sqrt (/ 1 x)) (sqrt -1))))
(+ (* -2 (/ (+ (* 1/2 (sqrt x)) (* 1/2 (* (sqrt x) (/ 1 (sqrt -1))))) (* (pow x 2) (pow (+ (sqrt (/ 1 x)) (* (sqrt (/ 1 x)) (sqrt -1))) 2)))) (* 2 (/ 1 (+ (sqrt (/ 1 x)) (* (sqrt (/ 1 x)) (sqrt -1))))))
(- (+ (* -1 (/ (+ (* -2 (/ (pow (+ (* 1/2 (sqrt x)) (* 1/2 (* (sqrt x) (/ 1 (sqrt -1))))) 2) (pow (+ (sqrt (/ 1 x)) (* (sqrt (/ 1 x)) (sqrt -1))) 3))) (* 2 (/ (+ (* -1/8 (sqrt (pow x 3))) (* -1/8 (* (sqrt (pow x 3)) (/ 1 (pow (sqrt -1) 3))))) (pow (+ (sqrt (/ 1 x)) (* (sqrt (/ 1 x)) (sqrt -1))) 2)))) (pow x 4))) (* 2 (/ 1 (+ (sqrt (/ 1 x)) (* (sqrt (/ 1 x)) (sqrt -1)))))) (* 2 (/ (+ (* 1/2 (sqrt x)) (* 1/2 (* (sqrt x) (/ 1 (sqrt -1))))) (* (pow x 2) (pow (+ (sqrt (/ 1 x)) (* (sqrt (/ 1 x)) (sqrt -1))) 2)))))
(- (+ (* -1 (/ (+ (* -2 (/ (* (+ (* -1/8 (sqrt (pow x 3))) (* -1/8 (* (sqrt (pow x 3)) (/ 1 (pow (sqrt -1) 3))))) (+ (* 1/2 (sqrt x)) (* 1/2 (* (sqrt x) (/ 1 (sqrt -1)))))) (pow (+ (sqrt (/ 1 x)) (* (sqrt (/ 1 x)) (sqrt -1))) 3))) (+ (* -1 (/ (* (+ (* -2 (/ (pow (+ (* 1/2 (sqrt x)) (* 1/2 (* (sqrt x) (/ 1 (sqrt -1))))) 2) (pow (+ (sqrt (/ 1 x)) (* (sqrt (/ 1 x)) (sqrt -1))) 3))) (* 2 (/ (+ (* -1/8 (sqrt (pow x 3))) (* -1/8 (* (sqrt (pow x 3)) (/ 1 (pow (sqrt -1) 3))))) (pow (+ (sqrt (/ 1 x)) (* (sqrt (/ 1 x)) (sqrt -1))) 2)))) (+ (* 1/2 (sqrt x)) (* 1/2 (* (sqrt x) (/ 1 (sqrt -1)))))) (+ (sqrt (/ 1 x)) (* (sqrt (/ 1 x)) (sqrt -1))))) (* 2 (/ (+ (* 1/16 (sqrt (pow x 5))) (* 1/16 (* (sqrt (pow x 5)) (/ 1 (pow (sqrt -1) 5))))) (pow (+ (sqrt (/ 1 x)) (* (sqrt (/ 1 x)) (sqrt -1))) 2))))) (pow x 6))) (* 2 (/ 1 (+ (sqrt (/ 1 x)) (* (sqrt (/ 1 x)) (sqrt -1)))))) (+ (* -2 (/ (pow (+ (* 1/2 (sqrt x)) (* 1/2 (* (sqrt x) (/ 1 (sqrt -1))))) 2) (* (pow x 4) (pow (+ (sqrt (/ 1 x)) (* (sqrt (/ 1 x)) (sqrt -1))) 3)))) (+ (* 2 (/ (+ (* -1/8 (sqrt (pow x 3))) (* -1/8 (* (sqrt (pow x 3)) (/ 1 (pow (sqrt -1) 3))))) (* (pow x 4) (pow (+ (sqrt (/ 1 x)) (* (sqrt (/ 1 x)) (sqrt -1))) 2)))) (* 2 (/ (+ (* 1/2 (sqrt x)) (* 1/2 (* (sqrt x) (/ 1 (sqrt -1))))) (* (pow x 2) (pow (+ (sqrt (/ 1 x)) (* (sqrt (/ 1 x)) (sqrt -1))) 2)))))))
(/ -2 (+ (* (sqrt (/ 1 x)) (sqrt -1)) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))))
(- (* 2 (/ (+ (* 1/2 (sqrt x)) (* 1/2 (* (sqrt x) (sqrt -1)))) (* (pow x 2) (pow (+ (* (sqrt (/ 1 x)) (sqrt -1)) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))) 2)))) (* 2 (/ 1 (+ (* (sqrt (/ 1 x)) (sqrt -1)) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))))))
(- (* -1 (/ (+ (* -2 (/ (+ (* -1/8 (* (sqrt (pow x 3)) (sqrt -1))) (* -1/8 (* (sqrt (pow x 3)) (/ 1 (pow (sqrt -1) 2))))) (pow (+ (* (sqrt (/ 1 x)) (sqrt -1)) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))) 2))) (* 2 (/ (pow (+ (* 1/2 (sqrt x)) (* 1/2 (* (sqrt x) (sqrt -1)))) 2) (pow (+ (* (sqrt (/ 1 x)) (sqrt -1)) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))) 3)))) (pow x 4))) (+ (* -2 (/ (+ (* 1/2 (sqrt x)) (* 1/2 (* (sqrt x) (sqrt -1)))) (* (pow x 2) (pow (+ (* (sqrt (/ 1 x)) (sqrt -1)) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))) 2)))) (* 2 (/ 1 (+ (* (sqrt (/ 1 x)) (sqrt -1)) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)))))))
(- (* -1 (/ (+ (* -2 (/ (+ (* 1/16 (* (sqrt (pow x 5)) (sqrt -1))) (* 1/16 (* (sqrt (pow x 5)) (/ 1 (pow (sqrt -1) 4))))) (pow (+ (* (sqrt (/ 1 x)) (sqrt -1)) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))) 2))) (+ (* -1 (/ (* (+ (* -2 (/ (+ (* -1/8 (* (sqrt (pow x 3)) (sqrt -1))) (* -1/8 (* (sqrt (pow x 3)) (/ 1 (pow (sqrt -1) 2))))) (pow (+ (* (sqrt (/ 1 x)) (sqrt -1)) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))) 2))) (* 2 (/ (pow (+ (* 1/2 (sqrt x)) (* 1/2 (* (sqrt x) (sqrt -1)))) 2) (pow (+ (* (sqrt (/ 1 x)) (sqrt -1)) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))) 3)))) (+ (* 1/2 (sqrt x)) (* 1/2 (* (sqrt x) (sqrt -1))))) (+ (* (sqrt (/ 1 x)) (sqrt -1)) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))))) (* 2 (/ (* (+ (* -1/8 (* (sqrt (pow x 3)) (sqrt -1))) (* -1/8 (* (sqrt (pow x 3)) (/ 1 (pow (sqrt -1) 2))))) (+ (* 1/2 (sqrt x)) (* 1/2 (* (sqrt x) (sqrt -1))))) (pow (+ (* (sqrt (/ 1 x)) (sqrt -1)) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))) 3))))) (pow x 6))) (+ (* -2 (/ (+ (* -1/8 (* (sqrt (pow x 3)) (sqrt -1))) (* -1/8 (* (sqrt (pow x 3)) (/ 1 (pow (sqrt -1) 2))))) (* (pow x 4) (pow (+ (* (sqrt (/ 1 x)) (sqrt -1)) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))) 2)))) (+ (* -2 (/ (+ (* 1/2 (sqrt x)) (* 1/2 (* (sqrt x) (sqrt -1)))) (* (pow x 2) (pow (+ (* (sqrt (/ 1 x)) (sqrt -1)) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))) 2)))) (+ (* 2 (/ (pow (+ (* 1/2 (sqrt x)) (* 1/2 (* (sqrt x) (sqrt -1)))) 2) (* (pow x 4) (pow (+ (* (sqrt (/ 1 x)) (sqrt -1)) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))) 3)))) (* 2 (/ 1 (+ (* (sqrt (/ 1 x)) (sqrt -1)) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)))))))))
(* 2 x)
(* 2 x)
(* 2 x)
(* 2 x)
(* 2 x)
(* 2 x)
(* 2 x)
(* 2 x)
(* 2 x)
(* 2 x)
(* 2 x)
(* 2 x)
2
(+ 2 (* -1/4 (pow x 2)))
(+ 2 (* (pow x 2) (- (* -5/64 (pow x 2)) 1/4)))
(+ 2 (* (pow x 2) (- (* (pow x 2) (- (* -21/512 (pow x 2)) 5/64)) 1/4)))
(* x (+ (sqrt (/ 1 x)) (* (sqrt (/ 1 x)) (sqrt -1))))
(* x (+ (sqrt (/ 1 x)) (+ (* 1/2 (sqrt (/ 1 (pow x 3)))) (+ (* 1/2 (* (sqrt (/ 1 (pow x 3))) (/ 1 (sqrt -1)))) (* (sqrt (/ 1 x)) (sqrt -1))))))
(* x (+ (sqrt (/ 1 x)) (+ (* -1/8 (sqrt (/ 1 (pow x 5)))) (+ (* -1/8 (* (sqrt (/ 1 (pow x 5))) (/ 1 (pow (sqrt -1) 3)))) (+ (* 1/2 (sqrt (/ 1 (pow x 3)))) (+ (* 1/2 (* (sqrt (/ 1 (pow x 3))) (/ 1 (sqrt -1)))) (* (sqrt (/ 1 x)) (sqrt -1))))))))
(* x (+ (sqrt (/ 1 x)) (+ (* -1/8 (sqrt (/ 1 (pow x 5)))) (+ (* -1/8 (* (sqrt (/ 1 (pow x 5))) (/ 1 (pow (sqrt -1) 3)))) (+ (* 1/16 (sqrt (/ 1 (pow x 7)))) (+ (* 1/16 (* (sqrt (/ 1 (pow x 7))) (/ 1 (pow (sqrt -1) 5)))) (+ (* 1/2 (sqrt (/ 1 (pow x 3)))) (+ (* 1/2 (* (sqrt (/ 1 (pow x 3))) (/ 1 (sqrt -1)))) (* (sqrt (/ 1 x)) (sqrt -1))))))))))
(* -1 (* x (+ (* (sqrt (/ 1 x)) (sqrt -1)) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)))))
(* -1 (* x (+ (* 1/2 (sqrt (/ 1 (pow x 3)))) (+ (* 1/2 (* (sqrt (/ 1 (pow x 3))) (sqrt -1))) (+ (* (sqrt (/ 1 x)) (sqrt -1)) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)))))))
(* -1 (* x (+ (* -1/8 (* (sqrt (/ 1 (pow x 5))) (sqrt -1))) (+ (* -1/8 (* (sqrt (/ 1 (pow x 5))) (/ 1 (pow (sqrt -1) 2)))) (+ (* 1/2 (sqrt (/ 1 (pow x 3)))) (+ (* 1/2 (* (sqrt (/ 1 (pow x 3))) (sqrt -1))) (+ (* (sqrt (/ 1 x)) (sqrt -1)) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)))))))))
(* -1 (* x (+ (* -1/8 (* (sqrt (/ 1 (pow x 5))) (sqrt -1))) (+ (* -1/8 (* (sqrt (/ 1 (pow x 5))) (/ 1 (pow (sqrt -1) 2)))) (+ (* 1/16 (* (sqrt (/ 1 (pow x 7))) (sqrt -1))) (+ (* 1/16 (* (sqrt (/ 1 (pow x 7))) (/ 1 (pow (sqrt -1) 4)))) (+ (* 1/2 (sqrt (/ 1 (pow x 3)))) (+ (* 1/2 (* (sqrt (/ 1 (pow x 3))) (sqrt -1))) (+ (* (sqrt (/ 1 x)) (sqrt -1)) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)))))))))))
1
(+ 1 (* 1/2 x))
(+ 1 (* x (+ 1/2 (* -1/8 x))))
(+ 1 (* x (+ 1/2 (* x (- (* 1/16 x) 1/8)))))
(sqrt x)
(* x (+ (sqrt (/ 1 x)) (* 1/2 (sqrt (/ 1 (pow x 3))))))
(* x (+ (sqrt (/ 1 x)) (+ (* -1/8 (sqrt (/ 1 (pow x 5)))) (* 1/2 (sqrt (/ 1 (pow x 3)))))))
(* x (+ (sqrt (/ 1 x)) (+ (* -1/8 (sqrt (/ 1 (pow x 5)))) (+ (* 1/16 (sqrt (/ 1 (pow x 7)))) (* 1/2 (sqrt (/ 1 (pow x 3))))))))
(* -1 (* (sqrt x) (pow (sqrt -1) 2)))
(* -1 (* x (+ (* 1/2 (sqrt (/ 1 (pow x 3)))) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)))))
(* -1 (* x (+ (* -1/8 (* (sqrt (/ 1 (pow x 5))) (/ 1 (pow (sqrt -1) 2)))) (+ (* 1/2 (sqrt (/ 1 (pow x 3)))) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))))))
(* -1 (* x (+ (* -1/8 (* (sqrt (/ 1 (pow x 5))) (/ 1 (pow (sqrt -1) 2)))) (+ (* 1/16 (* (sqrt (/ 1 (pow x 7))) (/ 1 (pow (sqrt -1) 4)))) (+ (* 1/2 (sqrt (/ 1 (pow x 3)))) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)))))))
x
(* x (+ 1 (* 1/8 (pow x 2))))
(* x (+ 1 (* (pow x 2) (+ 1/8 (* 7/128 (pow x 2))))))
(* x (+ 1 (* (pow x 2) (+ 1/8 (* (pow x 2) (+ 7/128 (* 33/1024 (pow x 2))))))))
(/ -1024/21 (pow x 5))
(/ (- (* 40960/441 (/ 1 (pow x 2))) 1024/21) (pow x 5))
(/ (- (+ (* 40960/441 (/ 1 (pow x 2))) (/ 1114112/9261 (pow x 4))) 1024/21) (pow x 5))
(/ (- (+ (* 40960/441 (/ 1 (pow x 2))) (/ 1114112/9261 (pow x 4))) (+ 1024/21 (* 617086976/194481 (/ 1 (pow x 6))))) (pow x 5))
(/ -1024/21 (pow x 5))
(* -1 (/ (- 1024/21 (* 40960/441 (/ 1 (pow x 2)))) (pow x 5)))
(* -1 (/ (+ 1024/21 (* -1 (/ (+ 40960/441 (* 1114112/9261 (/ 1 (pow x 2)))) (pow x 2)))) (pow x 5)))
(* -1 (/ (- (+ 1024/21 (* 617086976/194481 (/ 1 (pow x 6)))) (+ (* 40960/441 (/ 1 (pow x 2))) (/ 1114112/9261 (pow x 4)))) (pow x 5)))
(* 2 x)
(* 2 x)
(* 2 x)
(* 2 x)
(* 2 x)
(* 2 x)
(* 2 x)
(* 2 x)
(* 2 x)
(* 2 x)
(* 2 x)
(* 2 x)
-1
(- (* 2 x) 1)
(- (* 2 x) 1)
(- (* 2 x) 1)
(* 2 x)
(* x (- 2 (/ 1 x)))
(* x (- 2 (/ 1 x)))
(* x (- 2 (/ 1 x)))
(* 2 x)
(* -1 (* x (- (/ 1 x) 2)))
(* -1 (* x (- (/ 1 x) 2)))
(* -1 (* x (- (/ 1 x) 2)))
1
(+ 1 (* -1 x))
(+ 1 (* -1 x))
(+ 1 (* -1 x))
(* -1 x)
(* x (- (/ 1 x) 1))
(* x (- (/ 1 x) 1))
(* x (- (/ 1 x) 1))
(* -1 x)
(* -1 (* x (- 1 (/ 1 x))))
(* -1 (* x (- 1 (/ 1 x))))
(* -1 (* x (- 1 (/ 1 x))))
(* 33/1024 (pow x 2))
(* 33/1024 (pow x 2))
(* 33/1024 (pow x 2))
(* 33/1024 (pow x 2))
(* 33/1024 (pow x 2))
(* 33/1024 (pow x 2))
(* 33/1024 (pow x 2))
(* 33/1024 (pow x 2))
(* 33/1024 (pow x 2))
(* 33/1024 (pow x 2))
(* 33/1024 (pow x 2))
(* 33/1024 (pow x 2))
(* 7/128 (pow x 2))
(* (pow x 2) (+ 7/128 (* 33/1024 (pow x 2))))
(* (pow x 2) (+ 7/128 (* 33/1024 (pow x 2))))
(* (pow x 2) (+ 7/128 (* 33/1024 (pow x 2))))
(* 33/1024 (pow x 4))
(* (pow x 4) (+ 33/1024 (* 7/128 (/ 1 (pow x 2)))))
(* (pow x 4) (+ 33/1024 (* 7/128 (/ 1 (pow x 2)))))
(* (pow x 4) (+ 33/1024 (* 7/128 (/ 1 (pow x 2)))))
(* 33/1024 (pow x 4))
(* (pow x 4) (+ 33/1024 (* 7/128 (/ 1 (pow x 2)))))
(* (pow x 4) (+ 33/1024 (* 7/128 (/ 1 (pow x 2)))))
(* (pow x 4) (+ 33/1024 (* 7/128 (/ 1 (pow x 2)))))
(* 7/128 (pow x 4))
(* (pow x 4) (+ 7/128 (* 33/1024 (pow x 2))))
(* (pow x 4) (+ 7/128 (* 33/1024 (pow x 2))))
(* (pow x 4) (+ 7/128 (* 33/1024 (pow x 2))))
(* 33/1024 (pow x 6))
(* (pow x 6) (+ 33/1024 (* 7/128 (/ 1 (pow x 2)))))
(* (pow x 6) (+ 33/1024 (* 7/128 (/ 1 (pow x 2)))))
(* (pow x 6) (+ 33/1024 (* 7/128 (/ 1 (pow x 2)))))
(* 33/1024 (pow x 6))
(* (pow x 6) (+ 33/1024 (* 7/128 (/ 1 (pow x 2)))))
(* (pow x 6) (+ 33/1024 (* 7/128 (/ 1 (pow x 2)))))
(* (pow x 6) (+ 33/1024 (* 7/128 (/ 1 (pow x 2)))))
(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)
1
(+ 1 (* -1/2 x))
(+ 1 (* x (- (* -1/8 x) 1/2)))
(+ 1 (* x (- (* x (- (* -1/16 x) 1/8)) 1/2)))
(* (sqrt x) (sqrt -1))
(* x (+ (* 1/2 (* (sqrt (/ 1 (pow x 3))) (/ 1 (sqrt -1)))) (* (sqrt (/ 1 x)) (sqrt -1))))
(* x (+ (* -1/8 (* (sqrt (/ 1 (pow x 5))) (/ 1 (pow (sqrt -1) 3)))) (+ (* 1/2 (* (sqrt (/ 1 (pow x 3))) (/ 1 (sqrt -1)))) (* (sqrt (/ 1 x)) (sqrt -1)))))
(* x (+ (* -1/8 (* (sqrt (/ 1 (pow x 5))) (/ 1 (pow (sqrt -1) 3)))) (+ (* 1/16 (* (sqrt (/ 1 (pow x 7))) (/ 1 (pow (sqrt -1) 5)))) (+ (* 1/2 (* (sqrt (/ 1 (pow x 3))) (/ 1 (sqrt -1)))) (* (sqrt (/ 1 x)) (sqrt -1))))))
(* -1 (* (sqrt x) (sqrt -1)))
(* -1 (* x (+ (* 1/2 (* (sqrt (/ 1 (pow x 3))) (sqrt -1))) (* (sqrt (/ 1 x)) (sqrt -1)))))
(* -1 (* x (+ (* -1/8 (* (sqrt (/ 1 (pow x 5))) (sqrt -1))) (+ (* 1/2 (* (sqrt (/ 1 (pow x 3))) (sqrt -1))) (* (sqrt (/ 1 x)) (sqrt -1))))))
(* -1 (* x (+ (* -1/8 (* (sqrt (/ 1 (pow x 5))) (sqrt -1))) (+ (* 1/16 (* (sqrt (/ 1 (pow x 7))) (sqrt -1))) (+ (* 1/2 (* (sqrt (/ 1 (pow x 3))) (sqrt -1))) (* (sqrt (/ 1 x)) (sqrt -1)))))))
(* -21/512 (pow x 2))
(* -21/512 (pow x 2))
(* -21/512 (pow x 2))
(* -21/512 (pow x 2))
(* -21/512 (pow x 2))
(* -21/512 (pow x 2))
(* -21/512 (pow x 2))
(* -21/512 (pow x 2))
(* -21/512 (pow x 2))
(* -21/512 (pow x 2))
(* -21/512 (pow x 2))
(* -21/512 (pow x 2))
(* -5/64 (pow x 2))
(* (pow x 2) (- (* -21/512 (pow x 2)) 5/64))
(* (pow x 2) (- (* -21/512 (pow x 2)) 5/64))
(* (pow x 2) (- (* -21/512 (pow x 2)) 5/64))
(* -21/512 (pow x 4))
(* -1 (* (pow x 4) (+ 21/512 (* 5/64 (/ 1 (pow x 2))))))
(* -1 (* (pow x 4) (+ 21/512 (* 5/64 (/ 1 (pow x 2))))))
(* -1 (* (pow x 4) (+ 21/512 (* 5/64 (/ 1 (pow x 2))))))
(* -21/512 (pow x 4))
(* -1 (* (pow x 4) (+ 21/512 (* 5/64 (/ 1 (pow x 2))))))
(* -1 (* (pow x 4) (+ 21/512 (* 5/64 (/ 1 (pow x 2))))))
(* -1 (* (pow x 4) (+ 21/512 (* 5/64 (/ 1 (pow x 2))))))
(* -5/64 x)
(* x (- (* -21/512 (pow x 2)) 5/64))
(* x (- (* -21/512 (pow x 2)) 5/64))
(* x (- (* -21/512 (pow x 2)) 5/64))
(* -21/512 (pow x 3))
(* -1 (* (pow x 3) (+ 21/512 (* 5/64 (/ 1 (pow x 2))))))
(* -1 (* (pow x 3) (+ 21/512 (* 5/64 (/ 1 (pow x 2))))))
(* -1 (* (pow x 3) (+ 21/512 (* 5/64 (/ 1 (pow x 2))))))
(* -21/512 (pow x 3))
(* -1 (* (pow x 3) (+ 21/512 (* 5/64 (/ 1 (pow x 2))))))
(* -1 (* (pow x 3) (+ 21/512 (* 5/64 (/ 1 (pow x 2))))))
(* -1 (* (pow x 3) (+ 21/512 (* 5/64 (/ 1 (pow x 2))))))
Outputs
x
(* x (+ 1 (* 1/8 (pow x 2))))
(*.f64 x (+.f64 #s(literal 1 binary64) (*.f64 #s(literal 1/8 binary64) (*.f64 x x))))
(* x (+ 1 (* (pow x 2) (+ 1/8 (* 7/128 (pow x 2))))))
(*.f64 x (+.f64 #s(literal 1 binary64) (*.f64 (*.f64 x x) (+.f64 #s(literal 1/8 binary64) (*.f64 (*.f64 x x) #s(literal 7/128 binary64))))))
(* x (+ 1 (* (pow x 2) (+ 1/8 (* (pow x 2) (+ 7/128 (* 33/1024 (pow x 2))))))))
(*.f64 x (+.f64 #s(literal 1 binary64) (*.f64 (*.f64 x x) (+.f64 #s(literal 1/8 binary64) (*.f64 (*.f64 x x) (+.f64 #s(literal 7/128 binary64) (*.f64 (*.f64 x x) #s(literal 33/1024 binary64))))))))
(* 33/1024 (pow x 7))
(*.f64 #s(literal 33/1024 binary64) (pow.f64 x #s(literal 7 binary64)))
(* (pow x 7) (+ 33/1024 (* 7/128 (/ 1 (pow x 2)))))
(*.f64 (pow.f64 x #s(literal 7 binary64)) (+.f64 #s(literal 33/1024 binary64) (/.f64 #s(literal 7/128 binary64) (*.f64 x x))))
(* (pow x 7) (+ 33/1024 (+ (/ 1/8 (pow x 4)) (* 7/128 (/ 1 (pow x 2))))))
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(*.f64 (sqrt.f64 #s(literal -1 binary64)) (-.f64 #s(literal 0 binary64) (sqrt.f64 x)))
(* -1 (* x (+ (* 1/2 (* (sqrt (/ 1 (pow x 3))) (sqrt -1))) (* (sqrt (/ 1 x)) (sqrt -1)))))
(-.f64 #s(literal 0 binary64) (*.f64 x (*.f64 (sqrt.f64 #s(literal -1 binary64)) (+.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) (*.f64 #s(literal 1/2 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) (*.f64 x (*.f64 x x)))))))))
(* -1 (* x (+ (* -1/8 (* (sqrt (/ 1 (pow x 5))) (sqrt -1))) (+ (* 1/2 (* (sqrt (/ 1 (pow x 3))) (sqrt -1))) (* (sqrt (/ 1 x)) (sqrt -1))))))
(*.f64 (-.f64 #s(literal 0 binary64) x) (+.f64 (*.f64 #s(literal -1/8 binary64) (*.f64 (sqrt.f64 #s(literal -1 binary64)) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 5 binary64)))))) (*.f64 (sqrt.f64 #s(literal -1 binary64)) (+.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) (*.f64 #s(literal 1/2 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) (*.f64 x (*.f64 x x)))))))))
(* -1 (* x (+ (* -1/8 (* (sqrt (/ 1 (pow x 5))) (sqrt -1))) (+ (* 1/16 (* (sqrt (/ 1 (pow x 7))) (sqrt -1))) (+ (* 1/2 (* (sqrt (/ 1 (pow x 3))) (sqrt -1))) (* (sqrt (/ 1 x)) (sqrt -1)))))))
(*.f64 x (*.f64 (+.f64 (*.f64 (sqrt.f64 #s(literal -1 binary64)) (+.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) (*.f64 #s(literal 1/2 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) (*.f64 x (*.f64 x x))))))) (*.f64 (sqrt.f64 #s(literal -1 binary64)) (+.f64 (*.f64 #s(literal -1/8 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 5 binary64))))) (*.f64 #s(literal 1/16 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 7 binary64)))))))) #s(literal -1 binary64)))
(* -21/512 (pow x 2))
(*.f64 (*.f64 x x) #s(literal -21/512 binary64))
(* -21/512 (pow x 2))
(*.f64 (*.f64 x x) #s(literal -21/512 binary64))
(* -21/512 (pow x 2))
(*.f64 (*.f64 x x) #s(literal -21/512 binary64))
(* -21/512 (pow x 2))
(*.f64 (*.f64 x x) #s(literal -21/512 binary64))
(* -21/512 (pow x 2))
(*.f64 (*.f64 x x) #s(literal -21/512 binary64))
(* -21/512 (pow x 2))
(*.f64 (*.f64 x x) #s(literal -21/512 binary64))
(* -21/512 (pow x 2))
(*.f64 (*.f64 x x) #s(literal -21/512 binary64))
(* -21/512 (pow x 2))
(*.f64 (*.f64 x x) #s(literal -21/512 binary64))
(* -21/512 (pow x 2))
(*.f64 (*.f64 x x) #s(literal -21/512 binary64))
(* -21/512 (pow x 2))
(*.f64 (*.f64 x x) #s(literal -21/512 binary64))
(* -21/512 (pow x 2))
(*.f64 (*.f64 x x) #s(literal -21/512 binary64))
(* -21/512 (pow x 2))
(*.f64 (*.f64 x x) #s(literal -21/512 binary64))
(* -5/64 (pow x 2))
(*.f64 (*.f64 x x) #s(literal -5/64 binary64))
(* (pow x 2) (- (* -21/512 (pow x 2)) 5/64))
(*.f64 x (*.f64 x (+.f64 #s(literal -5/64 binary64) (*.f64 (*.f64 x x) #s(literal -21/512 binary64)))))
(* (pow x 2) (- (* -21/512 (pow x 2)) 5/64))
(*.f64 x (*.f64 x (+.f64 #s(literal -5/64 binary64) (*.f64 (*.f64 x x) #s(literal -21/512 binary64)))))
(* (pow x 2) (- (* -21/512 (pow x 2)) 5/64))
(*.f64 x (*.f64 x (+.f64 #s(literal -5/64 binary64) (*.f64 (*.f64 x x) #s(literal -21/512 binary64)))))
(* -21/512 (pow x 4))
(*.f64 (*.f64 (*.f64 x x) (*.f64 x x)) #s(literal -21/512 binary64))
(* -1 (* (pow x 4) (+ 21/512 (* 5/64 (/ 1 (pow x 2))))))
(*.f64 (*.f64 (*.f64 x x) (*.f64 x x)) (-.f64 #s(literal 0 binary64) (+.f64 #s(literal 21/512 binary64) (/.f64 #s(literal 5/64 binary64) (*.f64 x x)))))
(* -1 (* (pow x 4) (+ 21/512 (* 5/64 (/ 1 (pow x 2))))))
(*.f64 (*.f64 (*.f64 x x) (*.f64 x x)) (-.f64 #s(literal 0 binary64) (+.f64 #s(literal 21/512 binary64) (/.f64 #s(literal 5/64 binary64) (*.f64 x x)))))
(* -1 (* (pow x 4) (+ 21/512 (* 5/64 (/ 1 (pow x 2))))))
(*.f64 (*.f64 (*.f64 x x) (*.f64 x x)) (-.f64 #s(literal 0 binary64) (+.f64 #s(literal 21/512 binary64) (/.f64 #s(literal 5/64 binary64) (*.f64 x x)))))
(* -21/512 (pow x 4))
(*.f64 (*.f64 (*.f64 x x) (*.f64 x x)) #s(literal -21/512 binary64))
(* -1 (* (pow x 4) (+ 21/512 (* 5/64 (/ 1 (pow x 2))))))
(*.f64 (*.f64 (*.f64 x x) (*.f64 x x)) (-.f64 #s(literal 0 binary64) (+.f64 #s(literal 21/512 binary64) (/.f64 #s(literal 5/64 binary64) (*.f64 x x)))))
(* -1 (* (pow x 4) (+ 21/512 (* 5/64 (/ 1 (pow x 2))))))
(*.f64 (*.f64 (*.f64 x x) (*.f64 x x)) (-.f64 #s(literal 0 binary64) (+.f64 #s(literal 21/512 binary64) (/.f64 #s(literal 5/64 binary64) (*.f64 x x)))))
(* -1 (* (pow x 4) (+ 21/512 (* 5/64 (/ 1 (pow x 2))))))
(*.f64 (*.f64 (*.f64 x x) (*.f64 x x)) (-.f64 #s(literal 0 binary64) (+.f64 #s(literal 21/512 binary64) (/.f64 #s(literal 5/64 binary64) (*.f64 x x)))))
(* -5/64 x)
(*.f64 x #s(literal -5/64 binary64))
(* x (- (* -21/512 (pow x 2)) 5/64))
(*.f64 x (+.f64 #s(literal -5/64 binary64) (*.f64 (*.f64 x x) #s(literal -21/512 binary64))))
(* x (- (* -21/512 (pow x 2)) 5/64))
(*.f64 x (+.f64 #s(literal -5/64 binary64) (*.f64 (*.f64 x x) #s(literal -21/512 binary64))))
(* x (- (* -21/512 (pow x 2)) 5/64))
(*.f64 x (+.f64 #s(literal -5/64 binary64) (*.f64 (*.f64 x x) #s(literal -21/512 binary64))))
(* -21/512 (pow x 3))
(*.f64 x (*.f64 (*.f64 x x) #s(literal -21/512 binary64)))
(* -1 (* (pow x 3) (+ 21/512 (* 5/64 (/ 1 (pow x 2))))))
(*.f64 (*.f64 x x) (neg.f64 (*.f64 x (+.f64 #s(literal 21/512 binary64) (/.f64 #s(literal 5/64 binary64) (*.f64 x x))))))
(* -1 (* (pow x 3) (+ 21/512 (* 5/64 (/ 1 (pow x 2))))))
(*.f64 (*.f64 x x) (neg.f64 (*.f64 x (+.f64 #s(literal 21/512 binary64) (/.f64 #s(literal 5/64 binary64) (*.f64 x x))))))
(* -1 (* (pow x 3) (+ 21/512 (* 5/64 (/ 1 (pow x 2))))))
(*.f64 (*.f64 x x) (neg.f64 (*.f64 x (+.f64 #s(literal 21/512 binary64) (/.f64 #s(literal 5/64 binary64) (*.f64 x x))))))
(* -21/512 (pow x 3))
(*.f64 x (*.f64 (*.f64 x x) #s(literal -21/512 binary64)))
(* -1 (* (pow x 3) (+ 21/512 (* 5/64 (/ 1 (pow x 2))))))
(*.f64 (*.f64 x x) (neg.f64 (*.f64 x (+.f64 #s(literal 21/512 binary64) (/.f64 #s(literal 5/64 binary64) (*.f64 x x))))))
(* -1 (* (pow x 3) (+ 21/512 (* 5/64 (/ 1 (pow x 2))))))
(*.f64 (*.f64 x x) (neg.f64 (*.f64 x (+.f64 #s(literal 21/512 binary64) (/.f64 #s(literal 5/64 binary64) (*.f64 x x))))))
(* -1 (* (pow x 3) (+ 21/512 (* 5/64 (/ 1 (pow x 2))))))
(*.f64 (*.f64 x x) (neg.f64 (*.f64 x (+.f64 #s(literal 21/512 binary64) (/.f64 #s(literal 5/64 binary64) (*.f64 x x))))))

eval147.0ms (1.5%)

Compiler

Compiled 30974 to 2875 computations (90.7% saved)

prune87.0ms (0.9%)

Pruning

13 alts after pruning (7 fresh and 6 done)

PrunedKeptTotal
New104471051
Fresh000
Picked224
Done044
Total1046131059
Accuracy
100.0%
Counts
1059 → 13
Alt Table
Click to see full alt table
StatusAccuracyProgram
7.7%
(/.f64 (/.f64 (-.f64 (*.f64 (-.f64 #s(literal 1 binary64) (*.f64 x x)) (+.f64 #s(literal 1 binary64) (*.f64 x (+.f64 x #s(literal 1 binary64))))) (*.f64 (-.f64 #s(literal 1 binary64) x) (-.f64 #s(literal 1 binary64) (*.f64 x (*.f64 x x))))) (*.f64 (-.f64 #s(literal 1 binary64) x) (+.f64 #s(literal 1 binary64) (*.f64 x (+.f64 x #s(literal 1 binary64)))))) (+.f64 #s(literal 2 binary64) (*.f64 (*.f64 x x) (+.f64 #s(literal -1/4 binary64) (*.f64 x (*.f64 x (+.f64 #s(literal -5/64 binary64) (*.f64 (*.f64 x x) #s(literal -21/512 binary64)))))))))
7.7%
(/.f64 (/.f64 (-.f64 (*.f64 (+.f64 #s(literal 1 binary64) (*.f64 x (*.f64 x x))) (+.f64 #s(literal 1 binary64) (*.f64 x (+.f64 x #s(literal 1 binary64))))) (*.f64 (+.f64 #s(literal 1 binary64) (*.f64 x (+.f64 x #s(literal -1 binary64)))) (-.f64 #s(literal 1 binary64) (*.f64 x (*.f64 x x))))) (*.f64 (+.f64 #s(literal 1 binary64) (*.f64 x (+.f64 x #s(literal -1 binary64)))) (+.f64 #s(literal 1 binary64) (*.f64 x (+.f64 x #s(literal 1 binary64)))))) (+.f64 #s(literal 2 binary64) (*.f64 (*.f64 x x) (+.f64 #s(literal -1/4 binary64) (*.f64 x (*.f64 x (+.f64 #s(literal -5/64 binary64) (*.f64 (*.f64 x x) #s(literal -21/512 binary64)))))))))
7.8%
(/.f64 (+.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (/.f64 (+.f64 x (-.f64 #s(literal 1 binary64) x)) (*.f64 (+.f64 x (-.f64 #s(literal 1 binary64) x)) (-.f64 x (-.f64 #s(literal 1 binary64) x)))))) (+.f64 #s(literal 2 binary64) (*.f64 (*.f64 x x) (+.f64 #s(literal -1/4 binary64) (*.f64 x (*.f64 x (+.f64 #s(literal -5/64 binary64) (*.f64 (*.f64 x x) #s(literal -21/512 binary64)))))))))
7.8%
(/.f64 (+.f64 #s(literal 1 binary64) (-.f64 x (-.f64 #s(literal 1 binary64) x))) (+.f64 #s(literal 2 binary64) (*.f64 (*.f64 x x) (+.f64 #s(literal -1/4 binary64) (*.f64 x (*.f64 x (+.f64 #s(literal -5/64 binary64) (*.f64 (*.f64 x x) #s(literal -21/512 binary64)))))))))
100.0%
(/.f64 (*.f64 x #s(literal 2 binary64)) (+.f64 (pow.f64 (+.f64 #s(literal 1 binary64) x) #s(literal 1/2 binary64)) (sqrt.f64 (-.f64 #s(literal 1 binary64) x))))
99.9%
(/.f64 (*.f64 x #s(literal 2 binary64)) (+.f64 #s(literal 2 binary64) (*.f64 (*.f64 x x) (+.f64 #s(literal -1/4 binary64) (*.f64 (*.f64 x x) #s(literal -5/64 binary64))))))
99.9%
(/.f64 (*.f64 x #s(literal 2 binary64)) (+.f64 #s(literal 2 binary64) (*.f64 (*.f64 x x) (+.f64 #s(literal -1/4 binary64) (*.f64 x (*.f64 x (+.f64 #s(literal -5/64 binary64) (*.f64 (*.f64 x x) #s(literal -21/512 binary64)))))))))
99.8%
(/.f64 (*.f64 x #s(literal 2 binary64)) (+.f64 #s(literal 2 binary64) (*.f64 (*.f64 x x) #s(literal -1/4 binary64))))
7.7%
(-.f64 (sqrt.f64 (+.f64 #s(literal 1 binary64) x)) (sqrt.f64 (-.f64 #s(literal 1 binary64) x)))
99.9%
(+.f64 (*.f64 (+.f64 #s(literal 1/8 binary64) (*.f64 (*.f64 x x) #s(literal 7/128 binary64))) (*.f64 x (*.f64 x x))) x)
99.9%
(*.f64 x (+.f64 #s(literal 1 binary64) (*.f64 (*.f64 x x) (+.f64 #s(literal 1/8 binary64) (*.f64 x (*.f64 x (+.f64 #s(literal 7/128 binary64) (*.f64 (*.f64 x x) #s(literal 33/1024 binary64)))))))))
99.8%
(*.f64 x (+.f64 #s(literal 1 binary64) (*.f64 #s(literal 1/8 binary64) (*.f64 x x))))
99.5%
x
Compiler

Compiled 562 to 304 computations (45.9% saved)

simplify168.0ms (1.7%)

Algorithm
egg-herbie
Localize:

Found 20 expressions of interest:

NewMetricScoreProgram
cost-diff640
(/.f64 (+.f64 x (-.f64 #s(literal 1 binary64) x)) (*.f64 (+.f64 x (-.f64 #s(literal 1 binary64) x)) (-.f64 x (-.f64 #s(literal 1 binary64) x))))
cost-diff896
(/.f64 #s(literal 1 binary64) (/.f64 (+.f64 x (-.f64 #s(literal 1 binary64) x)) (*.f64 (+.f64 x (-.f64 #s(literal 1 binary64) x)) (-.f64 x (-.f64 #s(literal 1 binary64) x)))))
cost-diff1152
(+.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (/.f64 (+.f64 x (-.f64 #s(literal 1 binary64) x)) (*.f64 (+.f64 x (-.f64 #s(literal 1 binary64) x)) (-.f64 x (-.f64 #s(literal 1 binary64) x))))))
cost-diff1152
(/.f64 (+.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (/.f64 (+.f64 x (-.f64 #s(literal 1 binary64) x)) (*.f64 (+.f64 x (-.f64 #s(literal 1 binary64) x)) (-.f64 x (-.f64 #s(literal 1 binary64) x)))))) (+.f64 #s(literal 2 binary64) (*.f64 (*.f64 x x) (+.f64 #s(literal -1/4 binary64) (*.f64 x (*.f64 x (+.f64 #s(literal -5/64 binary64) (*.f64 (*.f64 x x) #s(literal -21/512 binary64)))))))))
cost-diff0
(*.f64 (*.f64 x x) (+.f64 #s(literal -1/4 binary64) (*.f64 x (*.f64 x (+.f64 #s(literal -5/64 binary64) (*.f64 (*.f64 x x) #s(literal -21/512 binary64)))))))
cost-diff0
(+.f64 #s(literal 2 binary64) (*.f64 (*.f64 x x) (+.f64 #s(literal -1/4 binary64) (*.f64 x (*.f64 x (+.f64 #s(literal -5/64 binary64) (*.f64 (*.f64 x x) #s(literal -21/512 binary64))))))))
cost-diff0
(*.f64 x #s(literal 2 binary64))
cost-diff0
(/.f64 (*.f64 x #s(literal 2 binary64)) (+.f64 #s(literal 2 binary64) (*.f64 (*.f64 x x) (+.f64 #s(literal -1/4 binary64) (*.f64 x (*.f64 x (+.f64 #s(literal -5/64 binary64) (*.f64 (*.f64 x x) #s(literal -21/512 binary64)))))))))
cost-diff0
(*.f64 (*.f64 x x) (+.f64 #s(literal -1/4 binary64) (*.f64 (*.f64 x x) #s(literal -5/64 binary64))))
cost-diff0
(+.f64 #s(literal 2 binary64) (*.f64 (*.f64 x x) (+.f64 #s(literal -1/4 binary64) (*.f64 (*.f64 x x) #s(literal -5/64 binary64)))))
cost-diff0
(*.f64 x #s(literal 2 binary64))
cost-diff0
(/.f64 (*.f64 x #s(literal 2 binary64)) (+.f64 #s(literal 2 binary64) (*.f64 (*.f64 x x) (+.f64 #s(literal -1/4 binary64) (*.f64 (*.f64 x x) #s(literal -5/64 binary64))))))
cost-diff0
(*.f64 (*.f64 x x) #s(literal -1/4 binary64))
cost-diff0
(+.f64 #s(literal 2 binary64) (*.f64 (*.f64 x x) #s(literal -1/4 binary64)))
cost-diff0
(*.f64 x #s(literal 2 binary64))
cost-diff0
(/.f64 (*.f64 x #s(literal 2 binary64)) (+.f64 #s(literal 2 binary64) (*.f64 (*.f64 x x) #s(literal -1/4 binary64))))
cost-diff0
(pow.f64 (+.f64 #s(literal 1 binary64) x) #s(literal 1/2 binary64))
cost-diff0
(+.f64 (pow.f64 (+.f64 #s(literal 1 binary64) x) #s(literal 1/2 binary64)) (sqrt.f64 (-.f64 #s(literal 1 binary64) x)))
cost-diff0
(*.f64 x #s(literal 2 binary64))
cost-diff0
(/.f64 (*.f64 x #s(literal 2 binary64)) (+.f64 (pow.f64 (+.f64 #s(literal 1 binary64) x) #s(literal 1/2 binary64)) (sqrt.f64 (-.f64 #s(literal 1 binary64) x))))
Rules
2736×*-lowering-*.f32
2736×*-lowering-*.f64
1582×neg-lowering-neg.f64
1582×neg-lowering-neg.f32
1448×+-lowering-+.f64
Iterations

Useful iterations: 2 (0.0ms)

IterNodesCost
038397
1108320
2309309
3999309
44402309
08147309
Stop Event
iter limit
node limit
Calls
Call 1
Inputs
(/ (* x 2) (+ (pow (+ 1 x) 1/2) (sqrt (- 1 x))))
(* x 2)
x
2
(+ (pow (+ 1 x) 1/2) (sqrt (- 1 x)))
(pow (+ 1 x) 1/2)
(+ 1 x)
1
1/2
(sqrt (- 1 x))
(- 1 x)
(/ (* x 2) (+ 2 (* (* x x) -1/4)))
(* x 2)
x
2
(+ 2 (* (* x x) -1/4))
(* (* x x) -1/4)
(* x x)
-1/4
(/ (* x 2) (+ 2 (* (* x x) (+ -1/4 (* (* x x) -5/64)))))
(* x 2)
x
2
(+ 2 (* (* x x) (+ -1/4 (* (* x x) -5/64))))
(* (* x x) (+ -1/4 (* (* x x) -5/64)))
(* x x)
(+ -1/4 (* (* x x) -5/64))
-1/4
(* (* x x) -5/64)
-5/64
(/ (* x 2) (+ 2 (* (* x x) (+ -1/4 (* x (* x (+ -5/64 (* (* x x) -21/512))))))))
(* x 2)
x
2
(+ 2 (* (* x x) (+ -1/4 (* x (* x (+ -5/64 (* (* x x) -21/512)))))))
(* (* x x) (+ -1/4 (* x (* x (+ -5/64 (* (* x x) -21/512))))))
(* x x)
(+ -1/4 (* x (* x (+ -5/64 (* (* x x) -21/512)))))
-1/4
(* x (* x (+ -5/64 (* (* x x) -21/512))))
(* x (+ -5/64 (* (* x x) -21/512)))
(+ -5/64 (* (* x x) -21/512))
-5/64
(* (* x x) -21/512)
-21/512
(/ (+ 1 (/ 1 (/ (+ x (- 1 x)) (* (+ x (- 1 x)) (- x (- 1 x)))))) (+ 2 (* (* x x) (+ -1/4 (* x (* x (+ -5/64 (* (* x x) -21/512))))))))
(+ 1 (/ 1 (/ (+ x (- 1 x)) (* (+ x (- 1 x)) (- x (- 1 x))))))
1
(/ 1 (/ (+ x (- 1 x)) (* (+ x (- 1 x)) (- x (- 1 x)))))
(/ (+ x (- 1 x)) (* (+ x (- 1 x)) (- x (- 1 x))))
(+ x (- 1 x))
x
(- 1 x)
(* (+ x (- 1 x)) (- x (- 1 x)))
(- x (- 1 x))
(+ 2 (* (* x x) (+ -1/4 (* x (* x (+ -5/64 (* (* x x) -21/512)))))))
2
(* (* x x) (+ -1/4 (* x (* x (+ -5/64 (* (* x x) -21/512))))))
(* x x)
(+ -1/4 (* x (* x (+ -5/64 (* (* x x) -21/512)))))
-1/4
(* x (* x (+ -5/64 (* (* x x) -21/512))))
(* x (+ -5/64 (* (* x x) -21/512)))
(+ -5/64 (* (* x x) -21/512))
-5/64
(* (* x x) -21/512)
-21/512
Outputs
(/ (* x 2) (+ (pow (+ 1 x) 1/2) (sqrt (- 1 x))))
(/.f64 (*.f64 x #s(literal 2 binary64)) (+.f64 (pow.f64 (+.f64 x #s(literal 1 binary64)) #s(literal 1/2 binary64)) (sqrt.f64 (-.f64 #s(literal 1 binary64) x))))
(* x 2)
(*.f64 x #s(literal 2 binary64))
x
2
#s(literal 2 binary64)
(+ (pow (+ 1 x) 1/2) (sqrt (- 1 x)))
(+.f64 (pow.f64 (+.f64 x #s(literal 1 binary64)) #s(literal 1/2 binary64)) (sqrt.f64 (-.f64 #s(literal 1 binary64) x)))
(pow (+ 1 x) 1/2)
(pow.f64 (+.f64 x #s(literal 1 binary64)) #s(literal 1/2 binary64))
(+ 1 x)
(+.f64 x #s(literal 1 binary64))
1
#s(literal 1 binary64)
1/2
#s(literal 1/2 binary64)
(sqrt (- 1 x))
(sqrt.f64 (-.f64 #s(literal 1 binary64) x))
(- 1 x)
(-.f64 #s(literal 1 binary64) x)
(/ (* x 2) (+ 2 (* (* x x) -1/4)))
(/.f64 (*.f64 x #s(literal 2 binary64)) (+.f64 #s(literal 2 binary64) (*.f64 (*.f64 x x) #s(literal -1/4 binary64))))
(* x 2)
(*.f64 x #s(literal 2 binary64))
x
2
#s(literal 2 binary64)
(+ 2 (* (* x x) -1/4))
(+.f64 #s(literal 2 binary64) (*.f64 (*.f64 x x) #s(literal -1/4 binary64)))
(* (* x x) -1/4)
(*.f64 (*.f64 x x) #s(literal -1/4 binary64))
(* x x)
(*.f64 x x)
-1/4
#s(literal -1/4 binary64)
(/ (* x 2) (+ 2 (* (* x x) (+ -1/4 (* (* x x) -5/64)))))
(/.f64 (*.f64 x #s(literal 2 binary64)) (+.f64 #s(literal 2 binary64) (*.f64 (*.f64 x x) (+.f64 #s(literal -1/4 binary64) (*.f64 (*.f64 x x) #s(literal -5/64 binary64))))))
(* x 2)
(*.f64 x #s(literal 2 binary64))
x
2
#s(literal 2 binary64)
(+ 2 (* (* x x) (+ -1/4 (* (* x x) -5/64))))
(+.f64 #s(literal 2 binary64) (*.f64 (*.f64 x x) (+.f64 #s(literal -1/4 binary64) (*.f64 (*.f64 x x) #s(literal -5/64 binary64)))))
(* (* x x) (+ -1/4 (* (* x x) -5/64)))
(*.f64 (*.f64 x x) (+.f64 #s(literal -1/4 binary64) (*.f64 (*.f64 x x) #s(literal -5/64 binary64))))
(* x x)
(*.f64 x x)
(+ -1/4 (* (* x x) -5/64))
(+.f64 #s(literal -1/4 binary64) (*.f64 (*.f64 x x) #s(literal -5/64 binary64)))
-1/4
#s(literal -1/4 binary64)
(* (* x x) -5/64)
(*.f64 (*.f64 x x) #s(literal -5/64 binary64))
-5/64
#s(literal -5/64 binary64)
(/ (* x 2) (+ 2 (* (* x x) (+ -1/4 (* x (* x (+ -5/64 (* (* x x) -21/512))))))))
(/.f64 (*.f64 x #s(literal 2 binary64)) (+.f64 #s(literal 2 binary64) (*.f64 (*.f64 x x) (+.f64 #s(literal -1/4 binary64) (*.f64 x (*.f64 x (+.f64 #s(literal -5/64 binary64) (*.f64 (*.f64 x x) #s(literal -21/512 binary64)))))))))
(* x 2)
(*.f64 x #s(literal 2 binary64))
x
2
#s(literal 2 binary64)
(+ 2 (* (* x x) (+ -1/4 (* x (* x (+ -5/64 (* (* x x) -21/512)))))))
(+.f64 #s(literal 2 binary64) (*.f64 (*.f64 x x) (+.f64 #s(literal -1/4 binary64) (*.f64 x (*.f64 x (+.f64 #s(literal -5/64 binary64) (*.f64 (*.f64 x x) #s(literal -21/512 binary64))))))))
(* (* x x) (+ -1/4 (* x (* x (+ -5/64 (* (* x x) -21/512))))))
(*.f64 (*.f64 x x) (+.f64 #s(literal -1/4 binary64) (*.f64 x (*.f64 x (+.f64 #s(literal -5/64 binary64) (*.f64 (*.f64 x x) #s(literal -21/512 binary64)))))))
(* x x)
(*.f64 x x)
(+ -1/4 (* x (* x (+ -5/64 (* (* x x) -21/512)))))
(+.f64 #s(literal -1/4 binary64) (*.f64 x (*.f64 x (+.f64 #s(literal -5/64 binary64) (*.f64 (*.f64 x x) #s(literal -21/512 binary64))))))
-1/4
#s(literal -1/4 binary64)
(* x (* x (+ -5/64 (* (* x x) -21/512))))
(*.f64 x (*.f64 x (+.f64 #s(literal -5/64 binary64) (*.f64 (*.f64 x x) #s(literal -21/512 binary64)))))
(* x (+ -5/64 (* (* x x) -21/512)))
(*.f64 x (+.f64 #s(literal -5/64 binary64) (*.f64 (*.f64 x x) #s(literal -21/512 binary64))))
(+ -5/64 (* (* x x) -21/512))
(+.f64 #s(literal -5/64 binary64) (*.f64 (*.f64 x x) #s(literal -21/512 binary64)))
-5/64
#s(literal -5/64 binary64)
(* (* x x) -21/512)
(*.f64 (*.f64 x x) #s(literal -21/512 binary64))
-21/512
#s(literal -21/512 binary64)
(/ (+ 1 (/ 1 (/ (+ x (- 1 x)) (* (+ x (- 1 x)) (- x (- 1 x)))))) (+ 2 (* (* x x) (+ -1/4 (* x (* x (+ -5/64 (* (* x x) -21/512))))))))
(/.f64 (*.f64 x #s(literal 2 binary64)) (+.f64 #s(literal 2 binary64) (*.f64 (*.f64 x x) (+.f64 #s(literal -1/4 binary64) (*.f64 x (*.f64 x (+.f64 #s(literal -5/64 binary64) (*.f64 (*.f64 x x) #s(literal -21/512 binary64)))))))))
(+ 1 (/ 1 (/ (+ x (- 1 x)) (* (+ x (- 1 x)) (- x (- 1 x))))))
(*.f64 x #s(literal 2 binary64))
1
#s(literal 1 binary64)
(/ 1 (/ (+ x (- 1 x)) (* (+ x (- 1 x)) (- x (- 1 x)))))
(+.f64 #s(literal -1 binary64) (*.f64 x #s(literal 2 binary64)))
(/ (+ x (- 1 x)) (* (+ x (- 1 x)) (- x (- 1 x))))
(/.f64 #s(literal 1 binary64) (+.f64 #s(literal -1 binary64) (*.f64 x #s(literal 2 binary64))))
(+ x (- 1 x))
#s(literal 1 binary64)
x
(- 1 x)
(-.f64 #s(literal 1 binary64) x)
(* (+ x (- 1 x)) (- x (- 1 x)))
(+.f64 #s(literal -1 binary64) (*.f64 x #s(literal 2 binary64)))
(- x (- 1 x))
(+.f64 #s(literal -1 binary64) (*.f64 x #s(literal 2 binary64)))
(+ 2 (* (* x x) (+ -1/4 (* x (* x (+ -5/64 (* (* x x) -21/512)))))))
(+.f64 #s(literal 2 binary64) (*.f64 (*.f64 x x) (+.f64 #s(literal -1/4 binary64) (*.f64 x (*.f64 x (+.f64 #s(literal -5/64 binary64) (*.f64 (*.f64 x x) #s(literal -21/512 binary64))))))))
2
#s(literal 2 binary64)
(* (* x x) (+ -1/4 (* x (* x (+ -5/64 (* (* x x) -21/512))))))
(*.f64 (*.f64 x x) (+.f64 #s(literal -1/4 binary64) (*.f64 x (*.f64 x (+.f64 #s(literal -5/64 binary64) (*.f64 (*.f64 x x) #s(literal -21/512 binary64)))))))
(* x x)
(*.f64 x x)
(+ -1/4 (* x (* x (+ -5/64 (* (* x x) -21/512)))))
(+.f64 #s(literal -1/4 binary64) (*.f64 x (*.f64 x (+.f64 #s(literal -5/64 binary64) (*.f64 (*.f64 x x) #s(literal -21/512 binary64))))))
-1/4
#s(literal -1/4 binary64)
(* x (* x (+ -5/64 (* (* x x) -21/512))))
(*.f64 x (*.f64 x (+.f64 #s(literal -5/64 binary64) (*.f64 (*.f64 x x) #s(literal -21/512 binary64)))))
(* x (+ -5/64 (* (* x x) -21/512)))
(*.f64 x (+.f64 #s(literal -5/64 binary64) (*.f64 (*.f64 x x) #s(literal -21/512 binary64))))
(+ -5/64 (* (* x x) -21/512))
(+.f64 #s(literal -5/64 binary64) (*.f64 (*.f64 x x) #s(literal -21/512 binary64)))
-5/64
#s(literal -5/64 binary64)
(* (* x x) -21/512)
(*.f64 (*.f64 x x) #s(literal -21/512 binary64))
-21/512
#s(literal -21/512 binary64)

localize455.0ms (4.6%)

Localize:

Found 20 expressions of interest:

NewMetricScoreProgram
accuracy99.8%
(*.f64 x (+.f64 #s(literal -5/64 binary64) (*.f64 (*.f64 x x) #s(literal -21/512 binary64))))
accuracy99.8%
(*.f64 x (*.f64 x (+.f64 #s(literal -5/64 binary64) (*.f64 (*.f64 x x) #s(literal -21/512 binary64)))))
accuracy99.8%
(*.f64 (*.f64 x x) #s(literal -21/512 binary64))
accuracy7.9%
(+.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (/.f64 (+.f64 x (-.f64 #s(literal 1 binary64) x)) (*.f64 (+.f64 x (-.f64 #s(literal 1 binary64) x)) (-.f64 x (-.f64 #s(literal 1 binary64) x))))))
accuracy100.0%
(*.f64 (*.f64 x x) (+.f64 #s(literal -1/4 binary64) (*.f64 x (*.f64 x (+.f64 #s(literal -5/64 binary64) (*.f64 (*.f64 x x) #s(literal -21/512 binary64)))))))
accuracy99.8%
(*.f64 x (+.f64 #s(literal -5/64 binary64) (*.f64 (*.f64 x x) #s(literal -21/512 binary64))))
accuracy99.8%
(*.f64 x (*.f64 x (+.f64 #s(literal -5/64 binary64) (*.f64 (*.f64 x x) #s(literal -21/512 binary64)))))
accuracy99.8%
(*.f64 (*.f64 x x) #s(literal -21/512 binary64))
accuracy100.0%
(*.f64 x #s(literal 2 binary64))
accuracy100.0%
(/.f64 (*.f64 x #s(literal 2 binary64)) (+.f64 #s(literal 2 binary64) (*.f64 (*.f64 x x) (+.f64 #s(literal -1/4 binary64) (*.f64 (*.f64 x x) #s(literal -5/64 binary64))))))
accuracy100.0%
(*.f64 (*.f64 x x) (+.f64 #s(literal -1/4 binary64) (*.f64 (*.f64 x x) #s(literal -5/64 binary64))))
accuracy99.8%
(*.f64 (*.f64 x x) #s(literal -5/64 binary64))
accuracy100.0%
(+.f64 #s(literal 2 binary64) (*.f64 (*.f64 x x) #s(literal -1/4 binary64)))
accuracy100.0%
(*.f64 (*.f64 x x) #s(literal -1/4 binary64))
accuracy100.0%
(*.f64 x x)
accuracy100.0%
(*.f64 x #s(literal 2 binary64))
accuracy100.0%
(*.f64 x #s(literal 2 binary64))
accuracy100.0%
(pow.f64 (+.f64 #s(literal 1 binary64) x) #s(literal 1/2 binary64))
accuracy100.0%
(+.f64 (pow.f64 (+.f64 #s(literal 1 binary64) x) #s(literal 1/2 binary64)) (sqrt.f64 (-.f64 #s(literal 1 binary64) x)))
accuracy100.0%
(sqrt.f64 (-.f64 #s(literal 1 binary64) x))
Results
167.0ms101×2valid
142.0ms135×1valid
45.0ms15×3valid
2.0ms0valid
Compiler

Compiled 470 to 39 computations (91.7% saved)

Precisions
Click to see histograms. Total time spent on operations: 215.0ms
ival-div: 58.0ms (27% of total)
ival-mult: 55.0ms (25.6% of total)
backward-pass: 36.0ms (16.8% of total)
ival-add: 34.0ms (15.8% of total)
ival-pow: 18.0ms (8.4% of total)
ival-sub: 7.0ms (3.3% of total)
ival-sqrt: 5.0ms (2.3% of total)
const: 2.0ms (0.9% of total)

series14.0ms (0.1%)

Counts
23 → 276
Calls
Call 1
Inputs
#<alt (/ (* x 2) (+ (pow (+ 1 x) 1/2) (sqrt (- 1 x))))>
#<alt (* x 2)>
#<alt (+ (pow (+ 1 x) 1/2) (sqrt (- 1 x)))>
#<alt (pow (+ 1 x) 1/2)>
#<alt (/ (* x 2) (+ 2 (* (* x x) -1/4)))>
#<alt (+ 2 (* (* x x) -1/4))>
#<alt (* (* x x) -1/4)>
#<alt (/ (* x 2) (+ 2 (* (* x x) (+ -1/4 (* (* x x) -5/64)))))>
#<alt (+ 2 (* (* x x) (+ -1/4 (* (* x x) -5/64))))>
#<alt (* (* x x) (+ -1/4 (* (* x x) -5/64)))>
#<alt (/ (* x 2) (+ 2 (* (* x x) (+ -1/4 (* x (* x (+ -5/64 (* (* x x) -21/512))))))))>
#<alt (+ 2 (* (* x x) (+ -1/4 (* x (* x (+ -5/64 (* (* x x) -21/512)))))))>
#<alt (* (* x x) (+ -1/4 (* x (* x (+ -5/64 (* (* x x) -21/512))))))>
#<alt (/ (+ 1 (/ 1 (/ (+ x (- 1 x)) (* (+ x (- 1 x)) (- x (- 1 x)))))) (+ 2 (* (* x x) (+ -1/4 (* x (* x (+ -5/64 (* (* x x) -21/512))))))))>
#<alt (+ 1 (/ 1 (/ (+ x (- 1 x)) (* (+ x (- 1 x)) (- x (- 1 x))))))>
#<alt (/ 1 (/ (+ x (- 1 x)) (* (+ x (- 1 x)) (- x (- 1 x)))))>
#<alt (/ (+ x (- 1 x)) (* (+ x (- 1 x)) (- x (- 1 x))))>
#<alt (sqrt (- 1 x))>
#<alt (* x x)>
#<alt (* (* x x) -5/64)>
#<alt (* (* x x) -21/512)>
#<alt (* x (* x (+ -5/64 (* (* x x) -21/512))))>
#<alt (* x (+ -5/64 (* (* x x) -21/512)))>
Outputs
#<alt x>
#<alt (* x (+ 1 (* 1/8 (pow x 2))))>
#<alt (* x (+ 1 (* (pow x 2) (+ 1/8 (* 7/128 (pow x 2))))))>
#<alt (* x (+ 1 (* (pow x 2) (+ 1/8 (* (pow x 2) (+ 7/128 (* 33/1024 (pow x 2))))))))>
#<alt (/ 2 (+ (sqrt (/ 1 x)) (* (sqrt (/ 1 x)) (sqrt -1))))>
#<alt (+ (* -2 (/ (+ (* 1/2 (sqrt x)) (* 1/2 (* (sqrt x) (/ 1 (sqrt -1))))) (* (pow x 2) (pow (+ (sqrt (/ 1 x)) (* (sqrt (/ 1 x)) (sqrt -1))) 2)))) (* 2 (/ 1 (+ (sqrt (/ 1 x)) (* (sqrt (/ 1 x)) (sqrt -1))))))>
#<alt (- (+ (* -1 (/ (+ (* -2 (/ (pow (+ (* 1/2 (sqrt x)) (* 1/2 (* (sqrt x) (/ 1 (sqrt -1))))) 2) (pow (+ (sqrt (/ 1 x)) (* (sqrt (/ 1 x)) (sqrt -1))) 3))) (* 2 (/ (+ (* -1/8 (sqrt (pow x 3))) (* -1/8 (* (sqrt (pow x 3)) (/ 1 (pow (sqrt -1) 3))))) (pow (+ (sqrt (/ 1 x)) (* (sqrt (/ 1 x)) (sqrt -1))) 2)))) (pow x 4))) (* 2 (/ 1 (+ (sqrt (/ 1 x)) (* (sqrt (/ 1 x)) (sqrt -1)))))) (* 2 (/ (+ (* 1/2 (sqrt x)) (* 1/2 (* (sqrt x) (/ 1 (sqrt -1))))) (* (pow x 2) (pow (+ (sqrt (/ 1 x)) (* (sqrt (/ 1 x)) (sqrt -1))) 2)))))>
#<alt (- (+ (* -1 (/ (+ (* -2 (/ (* (+ (* -1/8 (sqrt (pow x 3))) (* -1/8 (* (sqrt (pow x 3)) (/ 1 (pow (sqrt -1) 3))))) (+ (* 1/2 (sqrt x)) (* 1/2 (* (sqrt x) (/ 1 (sqrt -1)))))) (pow (+ (sqrt (/ 1 x)) (* (sqrt (/ 1 x)) (sqrt -1))) 3))) (+ (* -1 (/ (* (+ (* -2 (/ (pow (+ (* 1/2 (sqrt x)) (* 1/2 (* (sqrt x) (/ 1 (sqrt -1))))) 2) (pow (+ (sqrt (/ 1 x)) (* (sqrt (/ 1 x)) (sqrt -1))) 3))) (* 2 (/ (+ (* -1/8 (sqrt (pow x 3))) (* -1/8 (* (sqrt (pow x 3)) (/ 1 (pow (sqrt -1) 3))))) (pow (+ (sqrt (/ 1 x)) (* (sqrt (/ 1 x)) (sqrt -1))) 2)))) (+ (* 1/2 (sqrt x)) (* 1/2 (* (sqrt x) (/ 1 (sqrt -1)))))) (+ (sqrt (/ 1 x)) (* (sqrt (/ 1 x)) (sqrt -1))))) (* 2 (/ (+ (* 1/16 (sqrt (pow x 5))) (* 1/16 (* (sqrt (pow x 5)) (/ 1 (pow (sqrt -1) 5))))) (pow (+ (sqrt (/ 1 x)) (* (sqrt (/ 1 x)) (sqrt -1))) 2))))) (pow x 6))) (* 2 (/ 1 (+ (sqrt (/ 1 x)) (* (sqrt (/ 1 x)) (sqrt -1)))))) (+ (* -2 (/ (pow (+ (* 1/2 (sqrt x)) (* 1/2 (* (sqrt x) (/ 1 (sqrt -1))))) 2) (* (pow x 4) (pow (+ (sqrt (/ 1 x)) (* (sqrt (/ 1 x)) (sqrt -1))) 3)))) (+ (* 2 (/ (+ (* -1/8 (sqrt (pow x 3))) (* -1/8 (* (sqrt (pow x 3)) (/ 1 (pow (sqrt -1) 3))))) (* (pow x 4) (pow (+ (sqrt (/ 1 x)) (* (sqrt (/ 1 x)) (sqrt -1))) 2)))) (* 2 (/ (+ (* 1/2 (sqrt x)) (* 1/2 (* (sqrt x) (/ 1 (sqrt -1))))) (* (pow x 2) (pow (+ (sqrt (/ 1 x)) (* (sqrt (/ 1 x)) (sqrt -1))) 2)))))))>
#<alt (/ -2 (+ (* (sqrt (/ 1 x)) (sqrt -1)) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))))>
#<alt (- (* 2 (/ (+ (* 1/2 (sqrt x)) (* 1/2 (* (sqrt x) (sqrt -1)))) (* (pow x 2) (pow (+ (* (sqrt (/ 1 x)) (sqrt -1)) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))) 2)))) (* 2 (/ 1 (+ (* (sqrt (/ 1 x)) (sqrt -1)) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))))))>
#<alt (- (* -1 (/ (+ (* -2 (/ (+ (* -1/8 (* (sqrt (pow x 3)) (sqrt -1))) (* -1/8 (* (sqrt (pow x 3)) (/ 1 (pow (sqrt -1) 2))))) (pow (+ (* (sqrt (/ 1 x)) (sqrt -1)) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))) 2))) (* 2 (/ (pow (+ (* 1/2 (sqrt x)) (* 1/2 (* (sqrt x) (sqrt -1)))) 2) (pow (+ (* (sqrt (/ 1 x)) (sqrt -1)) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))) 3)))) (pow x 4))) (+ (* -2 (/ (+ (* 1/2 (sqrt x)) (* 1/2 (* (sqrt x) (sqrt -1)))) (* (pow x 2) (pow (+ (* (sqrt (/ 1 x)) (sqrt -1)) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))) 2)))) (* 2 (/ 1 (+ (* (sqrt (/ 1 x)) (sqrt -1)) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)))))))>
#<alt (- (* -1 (/ (+ (* -2 (/ (+ (* 1/16 (* (sqrt (pow x 5)) (sqrt -1))) (* 1/16 (* (sqrt (pow x 5)) (/ 1 (pow (sqrt -1) 4))))) (pow (+ (* (sqrt (/ 1 x)) (sqrt -1)) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))) 2))) (+ (* -1 (/ (* (+ (* -2 (/ (+ (* -1/8 (* (sqrt (pow x 3)) (sqrt -1))) (* -1/8 (* (sqrt (pow x 3)) (/ 1 (pow (sqrt -1) 2))))) (pow (+ (* (sqrt (/ 1 x)) (sqrt -1)) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))) 2))) (* 2 (/ (pow (+ (* 1/2 (sqrt x)) (* 1/2 (* (sqrt x) (sqrt -1)))) 2) (pow (+ (* (sqrt (/ 1 x)) (sqrt -1)) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))) 3)))) (+ (* 1/2 (sqrt x)) (* 1/2 (* (sqrt x) (sqrt -1))))) (+ (* (sqrt (/ 1 x)) (sqrt -1)) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))))) (* 2 (/ (* (+ (* -1/8 (* (sqrt (pow x 3)) (sqrt -1))) (* -1/8 (* (sqrt (pow x 3)) (/ 1 (pow (sqrt -1) 2))))) (+ (* 1/2 (sqrt x)) (* 1/2 (* (sqrt x) (sqrt -1))))) (pow (+ (* (sqrt (/ 1 x)) (sqrt -1)) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))) 3))))) (pow x 6))) (+ (* -2 (/ (+ (* -1/8 (* (sqrt (pow x 3)) (sqrt -1))) (* -1/8 (* (sqrt (pow x 3)) (/ 1 (pow (sqrt -1) 2))))) (* (pow x 4) (pow (+ (* (sqrt (/ 1 x)) (sqrt -1)) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))) 2)))) (+ (* -2 (/ (+ (* 1/2 (sqrt x)) (* 1/2 (* (sqrt x) (sqrt -1)))) (* (pow x 2) (pow (+ (* (sqrt (/ 1 x)) (sqrt -1)) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))) 2)))) (+ (* 2 (/ (pow (+ (* 1/2 (sqrt x)) (* 1/2 (* (sqrt x) (sqrt -1)))) 2) (* (pow x 4) (pow (+ (* (sqrt (/ 1 x)) (sqrt -1)) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))) 3)))) (* 2 (/ 1 (+ (* (sqrt (/ 1 x)) (sqrt -1)) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)))))))))>
#<alt (* 2 x)>
#<alt (* 2 x)>
#<alt (* 2 x)>
#<alt (* 2 x)>
#<alt (* 2 x)>
#<alt (* 2 x)>
#<alt (* 2 x)>
#<alt (* 2 x)>
#<alt (* 2 x)>
#<alt (* 2 x)>
#<alt (* 2 x)>
#<alt (* 2 x)>
#<alt 2>
#<alt (+ 2 (* -1/4 (pow x 2)))>
#<alt (+ 2 (* (pow x 2) (- (* -5/64 (pow x 2)) 1/4)))>
#<alt (+ 2 (* (pow x 2) (- (* (pow x 2) (- (* -21/512 (pow x 2)) 5/64)) 1/4)))>
#<alt (* x (+ (sqrt (/ 1 x)) (* (sqrt (/ 1 x)) (sqrt -1))))>
#<alt (* x (+ (sqrt (/ 1 x)) (+ (* 1/2 (sqrt (/ 1 (pow x 3)))) (+ (* 1/2 (* (sqrt (/ 1 (pow x 3))) (/ 1 (sqrt -1)))) (* (sqrt (/ 1 x)) (sqrt -1))))))>
#<alt (* x (+ (sqrt (/ 1 x)) (+ (* -1/8 (sqrt (/ 1 (pow x 5)))) (+ (* -1/8 (* (sqrt (/ 1 (pow x 5))) (/ 1 (pow (sqrt -1) 3)))) (+ (* 1/2 (sqrt (/ 1 (pow x 3)))) (+ (* 1/2 (* (sqrt (/ 1 (pow x 3))) (/ 1 (sqrt -1)))) (* (sqrt (/ 1 x)) (sqrt -1))))))))>
#<alt (* x (+ (sqrt (/ 1 x)) (+ (* -1/8 (sqrt (/ 1 (pow x 5)))) (+ (* -1/8 (* (sqrt (/ 1 (pow x 5))) (/ 1 (pow (sqrt -1) 3)))) (+ (* 1/16 (sqrt (/ 1 (pow x 7)))) (+ (* 1/16 (* (sqrt (/ 1 (pow x 7))) (/ 1 (pow (sqrt -1) 5)))) (+ (* 1/2 (sqrt (/ 1 (pow x 3)))) (+ (* 1/2 (* (sqrt (/ 1 (pow x 3))) (/ 1 (sqrt -1)))) (* (sqrt (/ 1 x)) (sqrt -1))))))))))>
#<alt (* -1 (* x (+ (* (sqrt (/ 1 x)) (sqrt -1)) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)))))>
#<alt (* -1 (* x (+ (* 1/2 (sqrt (/ 1 (pow x 3)))) (+ (* 1/2 (* (sqrt (/ 1 (pow x 3))) (sqrt -1))) (+ (* (sqrt (/ 1 x)) (sqrt -1)) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)))))))>
#<alt (* -1 (* x (+ (* -1/8 (* (sqrt (/ 1 (pow x 5))) (sqrt -1))) (+ (* -1/8 (* (sqrt (/ 1 (pow x 5))) (/ 1 (pow (sqrt -1) 2)))) (+ (* 1/2 (sqrt (/ 1 (pow x 3)))) (+ (* 1/2 (* (sqrt (/ 1 (pow x 3))) (sqrt -1))) (+ (* (sqrt (/ 1 x)) (sqrt -1)) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)))))))))>
#<alt (* -1 (* x (+ (* -1/8 (* (sqrt (/ 1 (pow x 5))) (sqrt -1))) (+ (* -1/8 (* (sqrt (/ 1 (pow x 5))) (/ 1 (pow (sqrt -1) 2)))) (+ (* 1/16 (* (sqrt (/ 1 (pow x 7))) (sqrt -1))) (+ (* 1/16 (* (sqrt (/ 1 (pow x 7))) (/ 1 (pow (sqrt -1) 4)))) (+ (* 1/2 (sqrt (/ 1 (pow x 3)))) (+ (* 1/2 (* (sqrt (/ 1 (pow x 3))) (sqrt -1))) (+ (* (sqrt (/ 1 x)) (sqrt -1)) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)))))))))))>
#<alt 1>
#<alt (+ 1 (* 1/2 x))>
#<alt (+ 1 (* x (+ 1/2 (* -1/8 x))))>
#<alt (+ 1 (* x (+ 1/2 (* x (- (* 1/16 x) 1/8)))))>
#<alt (sqrt x)>
#<alt (* x (+ (sqrt (/ 1 x)) (* 1/2 (sqrt (/ 1 (pow x 3))))))>
#<alt (* x (+ (sqrt (/ 1 x)) (+ (* -1/8 (sqrt (/ 1 (pow x 5)))) (* 1/2 (sqrt (/ 1 (pow x 3)))))))>
#<alt (* x (+ (sqrt (/ 1 x)) (+ (* -1/8 (sqrt (/ 1 (pow x 5)))) (+ (* 1/16 (sqrt (/ 1 (pow x 7)))) (* 1/2 (sqrt (/ 1 (pow x 3))))))))>
#<alt (* -1 (* (sqrt x) (pow (sqrt -1) 2)))>
#<alt (* -1 (* x (+ (* 1/2 (sqrt (/ 1 (pow x 3)))) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)))))>
#<alt (* -1 (* x (+ (* -1/8 (* (sqrt (/ 1 (pow x 5))) (/ 1 (pow (sqrt -1) 2)))) (+ (* 1/2 (sqrt (/ 1 (pow x 3)))) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))))))>
#<alt (* -1 (* x (+ (* -1/8 (* (sqrt (/ 1 (pow x 5))) (/ 1 (pow (sqrt -1) 2)))) (+ (* 1/16 (* (sqrt (/ 1 (pow x 7))) (/ 1 (pow (sqrt -1) 4)))) (+ (* 1/2 (sqrt (/ 1 (pow x 3)))) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)))))))>
#<alt x>
#<alt (* x (+ 1 (* 1/8 (pow x 2))))>
#<alt (* x (+ 1 (* (pow x 2) (+ 1/8 (* 1/64 (pow x 2))))))>
#<alt (* x (+ 1 (* (pow x 2) (+ 1/8 (* (pow x 2) (+ 1/64 (* 1/512 (pow x 2))))))))>
#<alt (/ -8 x)>
#<alt (* -1 (/ (+ 8 (* 64 (/ 1 (pow x 2)))) x))>
#<alt (/ (- (* -1 (/ (+ 64 (* 512 (/ 1 (pow x 2)))) (pow x 2))) 8) x)>
#<alt (/ (- (* -1 (/ (+ 512 (* 4096 (/ 1 (pow x 2)))) (pow x 4))) (+ 8 (* 64 (/ 1 (pow x 2))))) x)>
#<alt (/ -8 x)>
#<alt (* -1 (/ (+ 8 (* 64 (/ 1 (pow x 2)))) x))>
#<alt (* -1 (/ (+ 8 (+ (* 64 (/ 1 (pow x 2))) (/ 512 (pow x 4)))) x))>
#<alt (* -1 (/ (+ 8 (+ (* 64 (/ 1 (pow x 2))) (+ (* 4096 (/ 1 (pow x 6))) (/ 512 (pow x 4))))) x))>
#<alt 2>
#<alt (+ 2 (* -1/4 (pow x 2)))>
#<alt (+ 2 (* -1/4 (pow x 2)))>
#<alt (+ 2 (* -1/4 (pow x 2)))>
#<alt (* -1/4 (pow x 2))>
#<alt (* (pow x 2) (- (* 2 (/ 1 (pow x 2))) 1/4))>
#<alt (* (pow x 2) (- (* 2 (/ 1 (pow x 2))) 1/4))>
#<alt (* (pow x 2) (- (* 2 (/ 1 (pow x 2))) 1/4))>
#<alt (* -1/4 (pow x 2))>
#<alt (* (pow x 2) (- (* 2 (/ 1 (pow x 2))) 1/4))>
#<alt (* (pow x 2) (- (* 2 (/ 1 (pow x 2))) 1/4))>
#<alt (* (pow x 2) (- (* 2 (/ 1 (pow x 2))) 1/4))>
#<alt (* -1/4 (pow x 2))>
#<alt (* -1/4 (pow x 2))>
#<alt (* -1/4 (pow x 2))>
#<alt (* -1/4 (pow x 2))>
#<alt (* -1/4 (pow x 2))>
#<alt (* -1/4 (pow x 2))>
#<alt (* -1/4 (pow x 2))>
#<alt (* -1/4 (pow x 2))>
#<alt (* -1/4 (pow x 2))>
#<alt (* -1/4 (pow x 2))>
#<alt (* -1/4 (pow x 2))>
#<alt (* -1/4 (pow x 2))>
#<alt x>
#<alt (* x (+ 1 (* 1/8 (pow x 2))))>
#<alt (* x (+ 1 (* (pow x 2) (+ 1/8 (* 7/128 (pow x 2))))))>
#<alt (* x (+ 1 (* (pow x 2) (+ 1/8 (* (pow x 2) (+ 7/128 (* 3/256 (pow x 2))))))))>
#<alt (/ -128/5 (pow x 3))>
#<alt (/ (- (* 2048/25 (/ 1 (pow x 2))) 128/5) (pow x 3))>
#<alt (/ (- (* 2048/25 (/ 1 (pow x 2))) (+ 128/5 (/ 114688/125 (pow x 4)))) (pow x 3))>
#<alt (/ (- (+ (* 2048/25 (/ 1 (pow x 2))) (* 3145728/625 (/ 1 (pow x 6)))) (+ 128/5 (/ 114688/125 (pow x 4)))) (pow x 3))>
#<alt (/ -128/5 (pow x 3))>
#<alt (* -1 (/ (- 128/5 (* 2048/25 (/ 1 (pow x 2)))) (pow x 3)))>
#<alt (* -1 (/ (- (+ 128/5 (/ 114688/125 (pow x 4))) (* 2048/25 (/ 1 (pow x 2)))) (pow x 3)))>
#<alt (* -1 (/ (- (+ 128/5 (/ 114688/125 (pow x 4))) (+ (* 2048/25 (/ 1 (pow x 2))) (* 3145728/625 (/ 1 (pow x 6))))) (pow x 3)))>
#<alt 2>
#<alt (+ 2 (* -1/4 (pow x 2)))>
#<alt (+ 2 (* (pow x 2) (- (* -5/64 (pow x 2)) 1/4)))>
#<alt (+ 2 (* (pow x 2) (- (* -5/64 (pow x 2)) 1/4)))>
#<alt (* -5/64 (pow x 4))>
#<alt (* -1 (* (pow x 4) (+ 5/64 (* 1/4 (/ 1 (pow x 2))))))>
#<alt (* (pow x 4) (- (/ 2 (pow x 4)) (+ 5/64 (* 1/4 (/ 1 (pow x 2))))))>
#<alt (* (pow x 4) (- (/ 2 (pow x 4)) (+ 5/64 (* 1/4 (/ 1 (pow x 2))))))>
#<alt (* -5/64 (pow x 4))>
#<alt (* -1 (* (pow x 4) (+ 5/64 (* 1/4 (/ 1 (pow x 2))))))>
#<alt (* (pow x 4) (- (/ 2 (pow x 4)) (+ 5/64 (* 1/4 (/ 1 (pow x 2))))))>
#<alt (* (pow x 4) (- (/ 2 (pow x 4)) (+ 5/64 (* 1/4 (/ 1 (pow x 2))))))>
#<alt (* -1/4 (pow x 2))>
#<alt (* (pow x 2) (- (* -5/64 (pow x 2)) 1/4))>
#<alt (* (pow x 2) (- (* -5/64 (pow x 2)) 1/4))>
#<alt (* (pow x 2) (- (* -5/64 (pow x 2)) 1/4))>
#<alt (* -5/64 (pow x 4))>
#<alt (* -1 (* (pow x 4) (+ 5/64 (* 1/4 (/ 1 (pow x 2))))))>
#<alt (* -1 (* (pow x 4) (+ 5/64 (* 1/4 (/ 1 (pow x 2))))))>
#<alt (* -1 (* (pow x 4) (+ 5/64 (* 1/4 (/ 1 (pow x 2))))))>
#<alt (* -5/64 (pow x 4))>
#<alt (* -1 (* (pow x 4) (+ 5/64 (* 1/4 (/ 1 (pow x 2))))))>
#<alt (* -1 (* (pow x 4) (+ 5/64 (* 1/4 (/ 1 (pow x 2))))))>
#<alt (* -1 (* (pow x 4) (+ 5/64 (* 1/4 (/ 1 (pow x 2))))))>
#<alt x>
#<alt (* x (+ 1 (* 1/8 (pow x 2))))>
#<alt (* x (+ 1 (* (pow x 2) (+ 1/8 (* 7/128 (pow x 2))))))>
#<alt (* x (+ 1 (* (pow x 2) (+ 1/8 (* (pow x 2) (+ 7/128 (* 33/1024 (pow x 2))))))))>
#<alt (/ -1024/21 (pow x 5))>
#<alt (/ (- (* 40960/441 (/ 1 (pow x 2))) 1024/21) (pow x 5))>
#<alt (/ (- (+ (* 40960/441 (/ 1 (pow x 2))) (/ 1114112/9261 (pow x 4))) 1024/21) (pow x 5))>
#<alt (/ (- (+ (* 40960/441 (/ 1 (pow x 2))) (/ 1114112/9261 (pow x 4))) (+ 1024/21 (* 617086976/194481 (/ 1 (pow x 6))))) (pow x 5))>
#<alt (/ -1024/21 (pow x 5))>
#<alt (* -1 (/ (- 1024/21 (* 40960/441 (/ 1 (pow x 2)))) (pow x 5)))>
#<alt (* -1 (/ (+ 1024/21 (* -1 (/ (+ 40960/441 (* 1114112/9261 (/ 1 (pow x 2)))) (pow x 2)))) (pow x 5)))>
#<alt (* -1 (/ (- (+ 1024/21 (* 617086976/194481 (/ 1 (pow x 6)))) (+ (* 40960/441 (/ 1 (pow x 2))) (/ 1114112/9261 (pow x 4)))) (pow x 5)))>
#<alt 2>
#<alt (+ 2 (* -1/4 (pow x 2)))>
#<alt (+ 2 (* (pow x 2) (- (* -5/64 (pow x 2)) 1/4)))>
#<alt (+ 2 (* (pow x 2) (- (* (pow x 2) (- (* -21/512 (pow x 2)) 5/64)) 1/4)))>
#<alt (* -21/512 (pow x 6))>
#<alt (* -1 (* (pow x 6) (+ 21/512 (* 5/64 (/ 1 (pow x 2))))))>
#<alt (* (pow x 6) (- (* -1 (/ (+ 5/64 (* 1/4 (/ 1 (pow x 2)))) (pow x 2))) 21/512))>
#<alt (* (pow x 6) (- (* 2 (/ 1 (pow x 6))) (+ 21/512 (+ (/ 1/4 (pow x 4)) (* 5/64 (/ 1 (pow x 2)))))))>
#<alt (* -21/512 (pow x 6))>
#<alt (* -1 (* (pow x 6) (+ 21/512 (* 5/64 (/ 1 (pow x 2))))))>
#<alt (* (pow x 6) (- (* -1 (/ (+ 5/64 (* 1/4 (/ 1 (pow x 2)))) (pow x 2))) 21/512))>
#<alt (* (pow x 6) (- (* 2 (/ 1 (pow x 6))) (+ 21/512 (+ (/ 1/4 (pow x 4)) (* 5/64 (/ 1 (pow x 2)))))))>
#<alt (* -1/4 (pow x 2))>
#<alt (* (pow x 2) (- (* -5/64 (pow x 2)) 1/4))>
#<alt (* (pow x 2) (- (* (pow x 2) (- (* -21/512 (pow x 2)) 5/64)) 1/4))>
#<alt (* (pow x 2) (- (* (pow x 2) (- (* -21/512 (pow x 2)) 5/64)) 1/4))>
#<alt (* -21/512 (pow x 6))>
#<alt (* -1 (* (pow x 6) (+ 21/512 (* 5/64 (/ 1 (pow x 2))))))>
#<alt (* (pow x 6) (- (* -1 (/ (+ 5/64 (* 1/4 (/ 1 (pow x 2)))) (pow x 2))) 21/512))>
#<alt (* (pow x 6) (- (* -1 (/ (+ 5/64 (* 1/4 (/ 1 (pow x 2)))) (pow x 2))) 21/512))>
#<alt (* -21/512 (pow x 6))>
#<alt (* -1 (* (pow x 6) (+ 21/512 (* 5/64 (/ 1 (pow x 2))))))>
#<alt (* (pow x 6) (- (* -1 (/ (+ 5/64 (* 1/4 (/ 1 (pow x 2)))) (pow x 2))) 21/512))>
#<alt (* (pow x 6) (- (* -1 (/ (+ 5/64 (* 1/4 (/ 1 (pow x 2)))) (pow x 2))) 21/512))>
#<alt x>
#<alt (* x (+ 1 (* 1/8 (pow x 2))))>
#<alt (* x (+ 1 (* (pow x 2) (+ 1/8 (* 7/128 (pow x 2))))))>
#<alt (* x (+ 1 (* (pow x 2) (+ 1/8 (* (pow x 2) (+ 7/128 (* 33/1024 (pow x 2))))))))>
#<alt (/ -1024/21 (pow x 5))>
#<alt (/ (- (* 40960/441 (/ 1 (pow x 2))) 1024/21) (pow x 5))>
#<alt (/ (- (+ (* 40960/441 (/ 1 (pow x 2))) (/ 1114112/9261 (pow x 4))) 1024/21) (pow x 5))>
#<alt (/ (- (+ (* 40960/441 (/ 1 (pow x 2))) (/ 1114112/9261 (pow x 4))) (+ 1024/21 (* 617086976/194481 (/ 1 (pow x 6))))) (pow x 5))>
#<alt (/ -1024/21 (pow x 5))>
#<alt (* -1 (/ (- 1024/21 (* 40960/441 (/ 1 (pow x 2)))) (pow x 5)))>
#<alt (* -1 (/ (+ 1024/21 (* -1 (/ (+ 40960/441 (* 1114112/9261 (/ 1 (pow x 2)))) (pow x 2)))) (pow x 5)))>
#<alt (* -1 (/ (- (+ 1024/21 (* 617086976/194481 (/ 1 (pow x 6)))) (+ (* 40960/441 (/ 1 (pow x 2))) (/ 1114112/9261 (pow x 4)))) (pow x 5)))>
#<alt (* 2 x)>
#<alt (* 2 x)>
#<alt (* 2 x)>
#<alt (* 2 x)>
#<alt (* 2 x)>
#<alt (* 2 x)>
#<alt (* 2 x)>
#<alt (* 2 x)>
#<alt (* 2 x)>
#<alt (* 2 x)>
#<alt (* 2 x)>
#<alt (* 2 x)>
#<alt -1>
#<alt (- (* 2 x) 1)>
#<alt (- (* 2 x) 1)>
#<alt (- (* 2 x) 1)>
#<alt (* 2 x)>
#<alt (* x (- 2 (/ 1 x)))>
#<alt (* x (- 2 (/ 1 x)))>
#<alt (* x (- 2 (/ 1 x)))>
#<alt (* 2 x)>
#<alt (* -1 (* x (- (/ 1 x) 2)))>
#<alt (* -1 (* x (- (/ 1 x) 2)))>
#<alt (* -1 (* x (- (/ 1 x) 2)))>
#<alt -1>
#<alt (- (* -2 x) 1)>
#<alt (- (* x (- (* -4 x) 2)) 1)>
#<alt (- (* x (- (* x (- (* -8 x) 4)) 2)) 1)>
#<alt (/ 1/2 x)>
#<alt (/ (+ 1/2 (* 1/4 (/ 1 x))) x)>
#<alt (/ (+ 1/2 (+ (/ 1/8 (pow x 2)) (* 1/4 (/ 1 x)))) x)>
#<alt (/ (+ 1/2 (+ (/ 1/8 (pow x 2)) (+ (* 1/4 (/ 1 x)) (* 1/16 (/ 1 (pow x 3)))))) x)>
#<alt (/ 1/2 x)>
#<alt (/ (+ 1/2 (* 1/4 (/ 1 x))) x)>
#<alt (* -1 (/ (- (* -1 (/ (+ 1/4 (* 1/8 (/ 1 x))) x)) 1/2) x))>
#<alt (* -1 (/ (- (* -1 (/ (+ 1/4 (+ (/ 1/16 (pow x 2)) (* 1/8 (/ 1 x)))) x)) 1/2) x))>
#<alt 1>
#<alt (+ 1 (* -1/2 x))>
#<alt (+ 1 (* x (- (* -1/8 x) 1/2)))>
#<alt (+ 1 (* x (- (* x (- (* -1/16 x) 1/8)) 1/2)))>
#<alt (* (sqrt x) (sqrt -1))>
#<alt (* x (+ (* 1/2 (* (sqrt (/ 1 (pow x 3))) (/ 1 (sqrt -1)))) (* (sqrt (/ 1 x)) (sqrt -1))))>
#<alt (* x (+ (* -1/8 (* (sqrt (/ 1 (pow x 5))) (/ 1 (pow (sqrt -1) 3)))) (+ (* 1/2 (* (sqrt (/ 1 (pow x 3))) (/ 1 (sqrt -1)))) (* (sqrt (/ 1 x)) (sqrt -1)))))>
#<alt (* x (+ (* -1/8 (* (sqrt (/ 1 (pow x 5))) (/ 1 (pow (sqrt -1) 3)))) (+ (* 1/16 (* (sqrt (/ 1 (pow x 7))) (/ 1 (pow (sqrt -1) 5)))) (+ (* 1/2 (* (sqrt (/ 1 (pow x 3))) (/ 1 (sqrt -1)))) (* (sqrt (/ 1 x)) (sqrt -1))))))>
#<alt (* -1 (* (sqrt x) (sqrt -1)))>
#<alt (* -1 (* x (+ (* 1/2 (* (sqrt (/ 1 (pow x 3))) (sqrt -1))) (* (sqrt (/ 1 x)) (sqrt -1)))))>
#<alt (* -1 (* x (+ (* -1/8 (* (sqrt (/ 1 (pow x 5))) (sqrt -1))) (+ (* 1/2 (* (sqrt (/ 1 (pow x 3))) (sqrt -1))) (* (sqrt (/ 1 x)) (sqrt -1))))))>
#<alt (* -1 (* x (+ (* -1/8 (* (sqrt (/ 1 (pow x 5))) (sqrt -1))) (+ (* 1/16 (* (sqrt (/ 1 (pow x 7))) (sqrt -1))) (+ (* 1/2 (* (sqrt (/ 1 (pow x 3))) (sqrt -1))) (* (sqrt (/ 1 x)) (sqrt -1)))))))>
#<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 (* -5/64 (pow x 2))>
#<alt (* -5/64 (pow x 2))>
#<alt (* -5/64 (pow x 2))>
#<alt (* -5/64 (pow x 2))>
#<alt (* -5/64 (pow x 2))>
#<alt (* -5/64 (pow x 2))>
#<alt (* -5/64 (pow x 2))>
#<alt (* -5/64 (pow x 2))>
#<alt (* -5/64 (pow x 2))>
#<alt (* -5/64 (pow x 2))>
#<alt (* -5/64 (pow x 2))>
#<alt (* -5/64 (pow x 2))>
#<alt (* -21/512 (pow x 2))>
#<alt (* -21/512 (pow x 2))>
#<alt (* -21/512 (pow x 2))>
#<alt (* -21/512 (pow x 2))>
#<alt (* -21/512 (pow x 2))>
#<alt (* -21/512 (pow x 2))>
#<alt (* -21/512 (pow x 2))>
#<alt (* -21/512 (pow x 2))>
#<alt (* -21/512 (pow x 2))>
#<alt (* -21/512 (pow x 2))>
#<alt (* -21/512 (pow x 2))>
#<alt (* -21/512 (pow x 2))>
#<alt (* -5/64 (pow x 2))>
#<alt (* (pow x 2) (- (* -21/512 (pow x 2)) 5/64))>
#<alt (* (pow x 2) (- (* -21/512 (pow x 2)) 5/64))>
#<alt (* (pow x 2) (- (* -21/512 (pow x 2)) 5/64))>
#<alt (* -21/512 (pow x 4))>
#<alt (* -1 (* (pow x 4) (+ 21/512 (* 5/64 (/ 1 (pow x 2))))))>
#<alt (* -1 (* (pow x 4) (+ 21/512 (* 5/64 (/ 1 (pow x 2))))))>
#<alt (* -1 (* (pow x 4) (+ 21/512 (* 5/64 (/ 1 (pow x 2))))))>
#<alt (* -21/512 (pow x 4))>
#<alt (* -1 (* (pow x 4) (+ 21/512 (* 5/64 (/ 1 (pow x 2))))))>
#<alt (* -1 (* (pow x 4) (+ 21/512 (* 5/64 (/ 1 (pow x 2))))))>
#<alt (* -1 (* (pow x 4) (+ 21/512 (* 5/64 (/ 1 (pow x 2))))))>
#<alt (* -5/64 x)>
#<alt (* x (- (* -21/512 (pow x 2)) 5/64))>
#<alt (* x (- (* -21/512 (pow x 2)) 5/64))>
#<alt (* x (- (* -21/512 (pow x 2)) 5/64))>
#<alt (* -21/512 (pow x 3))>
#<alt (* -1 (* (pow x 3) (+ 21/512 (* 5/64 (/ 1 (pow x 2))))))>
#<alt (* -1 (* (pow x 3) (+ 21/512 (* 5/64 (/ 1 (pow x 2))))))>
#<alt (* -1 (* (pow x 3) (+ 21/512 (* 5/64 (/ 1 (pow x 2))))))>
#<alt (* -21/512 (pow x 3))>
#<alt (* -1 (* (pow x 3) (+ 21/512 (* 5/64 (/ 1 (pow x 2))))))>
#<alt (* -1 (* (pow x 3) (+ 21/512 (* 5/64 (/ 1 (pow x 2))))))>
#<alt (* -1 (* (pow x 3) (+ 21/512 (* 5/64 (/ 1 (pow x 2))))))>
Calls

69 calls:

TimeVariablePointExpression
3.0ms
x
@inf
(/ (* x 2) (+ (pow (+ 1 x) 1/2) (sqrt (- 1 x))))
0.0ms
x
@inf
(/ (* x 2) (+ 2 (* (* x x) (+ -1/4 (* (* x x) -5/64)))))
0.0ms
x
@inf
(/ (* x 2) (+ 2 (* (* x x) -1/4)))
0.0ms
x
@-inf
(/ (* x 2) (+ (pow (+ 1 x) 1/2) (sqrt (- 1 x))))
0.0ms
x
@inf
(* (* x x) -1/4)

rewrite349.0ms (3.5%)

Algorithm
batch-egg-rewrite
Rules
2876×fma-lowering-fma.f32
2876×fma-lowering-fma.f64
2764×*-lowering-*.f32
2764×*-lowering-*.f64
1814×pow-lowering-pow.f64
Iterations

Useful iterations: 2 (0.0ms)

IterNodesCost
038257
1286187
22734183
08439183
Stop Event
iter limit
node limit
Counts
23 → 488
Calls
Call 1
Inputs
(/ (* x 2) (+ (pow (+ 1 x) 1/2) (sqrt (- 1 x))))
(* x 2)
(+ (pow (+ 1 x) 1/2) (sqrt (- 1 x)))
(pow (+ 1 x) 1/2)
(/ (* x 2) (+ 2 (* (* x x) -1/4)))
(+ 2 (* (* x x) -1/4))
(* (* x x) -1/4)
(/ (* x 2) (+ 2 (* (* x x) (+ -1/4 (* (* x x) -5/64)))))
(+ 2 (* (* x x) (+ -1/4 (* (* x x) -5/64))))
(* (* x x) (+ -1/4 (* (* x x) -5/64)))
(/ (* x 2) (+ 2 (* (* x x) (+ -1/4 (* x (* x (+ -5/64 (* (* x x) -21/512))))))))
(+ 2 (* (* x x) (+ -1/4 (* x (* x (+ -5/64 (* (* x x) -21/512)))))))
(* (* x x) (+ -1/4 (* x (* x (+ -5/64 (* (* x x) -21/512))))))
(/ (+ 1 (/ 1 (/ (+ x (- 1 x)) (* (+ x (- 1 x)) (- x (- 1 x)))))) (+ 2 (* (* x x) (+ -1/4 (* x (* x (+ -5/64 (* (* x x) -21/512))))))))
(+ 1 (/ 1 (/ (+ x (- 1 x)) (* (+ x (- 1 x)) (- x (- 1 x))))))
(/ 1 (/ (+ x (- 1 x)) (* (+ x (- 1 x)) (- x (- 1 x)))))
(/ (+ x (- 1 x)) (* (+ x (- 1 x)) (- x (- 1 x))))
(sqrt (- 1 x))
(* x x)
(* (* x x) -5/64)
(* (* x x) -21/512)
(* x (* x (+ -5/64 (* (* x x) -21/512))))
(* x (+ -5/64 (* (* x x) -21/512)))
Outputs
(exp.f64 (*.f64 (log.f64 (/.f64 (+.f64 (pow.f64 (+.f64 x #s(literal 1 binary64)) #s(literal 1/2 binary64)) (pow.f64 (-.f64 #s(literal 1 binary64) x) #s(literal 1/2 binary64))) (*.f64 x #s(literal 2 binary64)))) #s(literal -1 binary64)))
(neg.f64 (/.f64 (*.f64 x #s(literal 2 binary64)) (-.f64 #s(literal 0 binary64) (+.f64 (pow.f64 (+.f64 x #s(literal 1 binary64)) #s(literal 1/2 binary64)) (pow.f64 (-.f64 #s(literal 1 binary64) x) #s(literal 1/2 binary64))))))
(neg.f64 (/.f64 (*.f64 x #s(literal -2 binary64)) (+.f64 (pow.f64 (+.f64 x #s(literal 1 binary64)) #s(literal 1/2 binary64)) (pow.f64 (-.f64 #s(literal 1 binary64) x) #s(literal 1/2 binary64)))))
(/.f64 (*.f64 x #s(literal 2 binary64)) (+.f64 (pow.f64 (+.f64 x #s(literal 1 binary64)) #s(literal 1/2 binary64)) (pow.f64 (-.f64 #s(literal 1 binary64) x) #s(literal 1/2 binary64))))
(/.f64 #s(literal 1 binary64) (/.f64 (+.f64 (pow.f64 (+.f64 x #s(literal 1 binary64)) #s(literal 1/2 binary64)) (pow.f64 (-.f64 #s(literal 1 binary64) x) #s(literal 1/2 binary64))) (*.f64 x #s(literal 2 binary64))))
(/.f64 #s(literal 1 binary64) (/.f64 (/.f64 (+.f64 (pow.f64 (+.f64 x #s(literal 1 binary64)) #s(literal 1/2 binary64)) (pow.f64 (-.f64 #s(literal 1 binary64) x) #s(literal 1/2 binary64))) (*.f64 x #s(literal 2 binary64))) #s(literal 1 binary64)))
(/.f64 #s(literal -1 binary64) (neg.f64 (/.f64 (+.f64 (pow.f64 (+.f64 x #s(literal 1 binary64)) #s(literal 1/2 binary64)) (pow.f64 (-.f64 #s(literal 1 binary64) x) #s(literal 1/2 binary64))) (*.f64 x #s(literal 2 binary64)))))
(/.f64 (*.f64 x #s(literal -2 binary64)) (-.f64 #s(literal 0 binary64) (+.f64 (pow.f64 (+.f64 x #s(literal 1 binary64)) #s(literal 1/2 binary64)) (pow.f64 (-.f64 #s(literal 1 binary64) x) #s(literal 1/2 binary64)))))
(/.f64 (neg.f64 (*.f64 x #s(literal -2 binary64))) (neg.f64 (-.f64 #s(literal 0 binary64) (+.f64 (pow.f64 (+.f64 x #s(literal 1 binary64)) #s(literal 1/2 binary64)) (pow.f64 (-.f64 #s(literal 1 binary64) x) #s(literal 1/2 binary64))))))
(/.f64 (*.f64 (*.f64 x #s(literal 2 binary64)) #s(literal 1 binary64)) (+.f64 (pow.f64 (+.f64 x #s(literal 1 binary64)) #s(literal 1/2 binary64)) (pow.f64 (-.f64 #s(literal 1 binary64) x) #s(literal 1/2 binary64))))
(pow.f64 (/.f64 (+.f64 (pow.f64 (+.f64 x #s(literal 1 binary64)) #s(literal 1/2 binary64)) (pow.f64 (-.f64 #s(literal 1 binary64) x) #s(literal 1/2 binary64))) (*.f64 x #s(literal 2 binary64))) #s(literal -1 binary64))
(pow.f64 (/.f64 (/.f64 (+.f64 (pow.f64 (+.f64 x #s(literal 1 binary64)) #s(literal 1/2 binary64)) (pow.f64 (-.f64 #s(literal 1 binary64) x) #s(literal 1/2 binary64))) (*.f64 x #s(literal 2 binary64))) #s(literal 1 binary64)) #s(literal -1 binary64))
(*.f64 x (/.f64 #s(literal 2 binary64) (+.f64 (pow.f64 (+.f64 x #s(literal 1 binary64)) #s(literal 1/2 binary64)) (pow.f64 (-.f64 #s(literal 1 binary64) x) #s(literal 1/2 binary64)))))
(*.f64 #s(literal 2 binary64) (*.f64 x (/.f64 #s(literal 1 binary64) (+.f64 (pow.f64 (+.f64 x #s(literal 1 binary64)) #s(literal 1/2 binary64)) (pow.f64 (-.f64 #s(literal 1 binary64) x) #s(literal 1/2 binary64))))))
(*.f64 #s(literal 2 binary64) (/.f64 x (+.f64 (pow.f64 (+.f64 x #s(literal 1 binary64)) #s(literal 1/2 binary64)) (pow.f64 (-.f64 #s(literal 1 binary64) x) #s(literal 1/2 binary64)))))
(*.f64 (*.f64 x #s(literal 2 binary64)) (/.f64 #s(literal 1 binary64) (+.f64 (pow.f64 (+.f64 x #s(literal 1 binary64)) #s(literal 1/2 binary64)) (pow.f64 (-.f64 #s(literal 1 binary64) x) #s(literal 1/2 binary64)))))
(*.f64 #s(literal 1 binary64) (/.f64 (*.f64 x #s(literal 2 binary64)) (+.f64 (pow.f64 (+.f64 x #s(literal 1 binary64)) #s(literal 1/2 binary64)) (pow.f64 (-.f64 #s(literal 1 binary64) x) #s(literal 1/2 binary64)))))
(*.f64 (*.f64 x #s(literal -2 binary64)) (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 0 binary64) (+.f64 (pow.f64 (+.f64 x #s(literal 1 binary64)) #s(literal 1/2 binary64)) (pow.f64 (-.f64 #s(literal 1 binary64) x) #s(literal 1/2 binary64))))))
(*.f64 (/.f64 #s(literal 1 binary64) (+.f64 (pow.f64 (+.f64 x #s(literal 1 binary64)) #s(literal 1/2 binary64)) (pow.f64 (-.f64 #s(literal 1 binary64) x) #s(literal 1/2 binary64)))) (*.f64 x #s(literal 2 binary64)))
(*.f64 (/.f64 #s(literal 1 binary64) (+.f64 (pow.f64 (+.f64 x #s(literal 1 binary64)) #s(literal 1/2 binary64)) (pow.f64 (-.f64 #s(literal 1 binary64) x) #s(literal 1/2 binary64)))) (pow.f64 (/.f64 #s(literal 1 binary64) (*.f64 x #s(literal 2 binary64))) #s(literal -1 binary64)))
(*.f64 (/.f64 #s(literal 2 binary64) (+.f64 (pow.f64 (+.f64 x #s(literal 1 binary64)) #s(literal 1/2 binary64)) (pow.f64 (-.f64 #s(literal 1 binary64) x) #s(literal 1/2 binary64)))) x)
(*.f64 (/.f64 (*.f64 x #s(literal 2 binary64)) (+.f64 (pow.f64 (+.f64 x #s(literal 1 binary64)) #s(literal 3/2 binary64)) (pow.f64 (-.f64 #s(literal 1 binary64) x) #s(literal 3/2 binary64)))) (-.f64 (+.f64 (+.f64 x #s(literal 1 binary64)) (-.f64 #s(literal 1 binary64) x)) (sqrt.f64 (*.f64 (+.f64 x #s(literal 1 binary64)) (-.f64 #s(literal 1 binary64) x)))))
(*.f64 (/.f64 (*.f64 x #s(literal 2 binary64)) (-.f64 (+.f64 x #s(literal 1 binary64)) (-.f64 #s(literal 1 binary64) x))) (-.f64 (pow.f64 (+.f64 x #s(literal 1 binary64)) #s(literal 1/2 binary64)) (pow.f64 (-.f64 #s(literal 1 binary64) x) #s(literal 1/2 binary64))))
(*.f64 x #s(literal 2 binary64))
(*.f64 #s(literal 2 binary64) x)
(+.f64 (pow.f64 (+.f64 x #s(literal 1 binary64)) #s(literal 1/2 binary64)) (pow.f64 (-.f64 #s(literal 1 binary64) x) #s(literal 1/2 binary64)))
(+.f64 (pow.f64 (-.f64 #s(literal 1 binary64) x) #s(literal 1/2 binary64)) (pow.f64 (+.f64 x #s(literal 1 binary64)) #s(literal 1/2 binary64)))
(-.f64 (/.f64 (+.f64 x #s(literal 1 binary64)) (-.f64 (pow.f64 (+.f64 x #s(literal 1 binary64)) #s(literal 1/2 binary64)) (pow.f64 (-.f64 #s(literal 1 binary64) x) #s(literal 1/2 binary64)))) (/.f64 (-.f64 #s(literal 1 binary64) x) (-.f64 (pow.f64 (+.f64 x #s(literal 1 binary64)) #s(literal 1/2 binary64)) (pow.f64 (-.f64 #s(literal 1 binary64) x) #s(literal 1/2 binary64)))))
(fma.f64 (pow.f64 (+.f64 x #s(literal 1 binary64)) #s(literal 1/4 binary64)) (pow.f64 (+.f64 x #s(literal 1 binary64)) #s(literal 1/4 binary64)) (pow.f64 (-.f64 #s(literal 1 binary64) x) #s(literal 1/2 binary64)))
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(/.f64 #s(literal 1 binary64) (/.f64 (-.f64 (+.f64 (+.f64 x #s(literal 1 binary64)) (-.f64 #s(literal 1 binary64) x)) (sqrt.f64 (*.f64 (+.f64 x #s(literal 1 binary64)) (-.f64 #s(literal 1 binary64) x)))) (+.f64 (pow.f64 (+.f64 x #s(literal 1 binary64)) #s(literal 3/2 binary64)) (pow.f64 (-.f64 #s(literal 1 binary64) x) #s(literal 3/2 binary64)))))
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(+.f64 (*.f64 (*.f64 (*.f64 x x) #s(literal -21/512 binary64)) (*.f64 x x)) (*.f64 (*.f64 x x) #s(literal -5/64 binary64)))
(fma.f64 x (*.f64 x #s(literal -5/64 binary64)) (*.f64 x (*.f64 x (*.f64 (*.f64 x x) #s(literal -21/512 binary64)))))
(fma.f64 x (*.f64 x #s(literal -5/64 binary64)) (*.f64 (*.f64 x x) (*.f64 (*.f64 x x) #s(literal -21/512 binary64))))
(fma.f64 x (*.f64 x #s(literal -5/64 binary64)) (*.f64 (*.f64 x (*.f64 (*.f64 x x) #s(literal -21/512 binary64))) x))
(fma.f64 x (*.f64 x #s(literal -5/64 binary64)) (*.f64 (*.f64 (*.f64 x x) #s(literal -21/512 binary64)) (*.f64 x x)))
(fma.f64 (*.f64 x x) #s(literal -5/64 binary64) (*.f64 x (*.f64 x (*.f64 (*.f64 x x) #s(literal -21/512 binary64)))))
(fma.f64 (*.f64 x x) #s(literal -5/64 binary64) (*.f64 (*.f64 x x) (*.f64 (*.f64 x x) #s(literal -21/512 binary64))))
(fma.f64 (*.f64 x x) #s(literal -5/64 binary64) (*.f64 (*.f64 x (*.f64 (*.f64 x x) #s(literal -21/512 binary64))) x))
(fma.f64 (*.f64 x x) #s(literal -5/64 binary64) (*.f64 (*.f64 (*.f64 x x) #s(literal -21/512 binary64)) (*.f64 x x)))
(fma.f64 (*.f64 x x) (*.f64 (*.f64 x x) #s(literal -21/512 binary64)) (*.f64 (*.f64 x x) #s(literal -5/64 binary64)))
(fma.f64 #s(literal -5/64 binary64) (*.f64 x x) (*.f64 x (*.f64 x (*.f64 (*.f64 x x) #s(literal -21/512 binary64)))))
(fma.f64 #s(literal -5/64 binary64) (*.f64 x x) (*.f64 (*.f64 x x) (*.f64 (*.f64 x x) #s(literal -21/512 binary64))))
(fma.f64 #s(literal -5/64 binary64) (*.f64 x x) (*.f64 (*.f64 x (*.f64 (*.f64 x x) #s(literal -21/512 binary64))) x))
(fma.f64 #s(literal -5/64 binary64) (*.f64 x x) (*.f64 (*.f64 (*.f64 x x) #s(literal -21/512 binary64)) (*.f64 x x)))
(fma.f64 (*.f64 (*.f64 x x) #s(literal -21/512 binary64)) (*.f64 x x) (*.f64 (*.f64 x x) #s(literal -5/64 binary64)))
(fma.f64 (*.f64 x #s(literal -5/64 binary64)) x (*.f64 x (*.f64 x (*.f64 (*.f64 x x) #s(literal -21/512 binary64)))))
(fma.f64 (*.f64 x #s(literal -5/64 binary64)) x (*.f64 (*.f64 x x) (*.f64 (*.f64 x x) #s(literal -21/512 binary64))))
(fma.f64 (*.f64 x #s(literal -5/64 binary64)) x (*.f64 (*.f64 x (*.f64 (*.f64 x x) #s(literal -21/512 binary64))) x))
(fma.f64 (*.f64 x #s(literal -5/64 binary64)) x (*.f64 (*.f64 (*.f64 x x) #s(literal -21/512 binary64)) (*.f64 x x)))
(/.f64 (*.f64 (*.f64 x x) (+.f64 #s(literal -125/262144 binary64) (*.f64 (*.f64 x (*.f64 x x)) (*.f64 (*.f64 x (*.f64 x x)) #s(literal -9261/134217728 binary64))))) (+.f64 #s(literal 25/4096 binary64) (*.f64 (*.f64 (*.f64 x x) #s(literal -21/512 binary64)) (-.f64 (*.f64 (*.f64 x x) #s(literal -21/512 binary64)) #s(literal -5/64 binary64)))))
(/.f64 (*.f64 (*.f64 x x) (-.f64 #s(literal 25/4096 binary64) (*.f64 (*.f64 (*.f64 x x) (*.f64 x x)) #s(literal 441/262144 binary64)))) (-.f64 #s(literal -5/64 binary64) (*.f64 (*.f64 x x) #s(literal -21/512 binary64))))
(*.f64 x (*.f64 x (+.f64 #s(literal -5/64 binary64) (*.f64 (*.f64 x x) #s(literal -21/512 binary64)))))
(*.f64 (*.f64 x x) (+.f64 #s(literal -5/64 binary64) (*.f64 (*.f64 x x) #s(literal -21/512 binary64))))
(*.f64 (+.f64 #s(literal -5/64 binary64) (*.f64 (*.f64 x x) #s(literal -21/512 binary64))) (*.f64 x x))
(*.f64 (*.f64 x (+.f64 #s(literal -5/64 binary64) (*.f64 (*.f64 x x) #s(literal -21/512 binary64)))) x)
(+.f64 (*.f64 x #s(literal -5/64 binary64)) (*.f64 x (*.f64 (*.f64 x x) #s(literal -21/512 binary64))))
(+.f64 (*.f64 x (*.f64 (*.f64 x x) #s(literal -21/512 binary64))) (*.f64 x #s(literal -5/64 binary64)))
(fma.f64 x #s(literal -5/64 binary64) (*.f64 x (*.f64 (*.f64 x x) #s(literal -21/512 binary64))))
(fma.f64 x (*.f64 (*.f64 x x) #s(literal -21/512 binary64)) (*.f64 x #s(literal -5/64 binary64)))
(fma.f64 (*.f64 x x) (*.f64 x #s(literal -21/512 binary64)) (*.f64 x #s(literal -5/64 binary64)))
(fma.f64 #s(literal -5/64 binary64) x (*.f64 x (*.f64 (*.f64 x x) #s(literal -21/512 binary64))))
(fma.f64 #s(literal -21/512 binary64) (*.f64 x (*.f64 x x)) (*.f64 x #s(literal -5/64 binary64)))
(fma.f64 (*.f64 (*.f64 x x) #s(literal -21/512 binary64)) x (*.f64 x #s(literal -5/64 binary64)))
(fma.f64 (*.f64 x (*.f64 x x)) #s(literal -21/512 binary64) (*.f64 x #s(literal -5/64 binary64)))
(fma.f64 (*.f64 x #s(literal -21/512 binary64)) (*.f64 x x) (*.f64 x #s(literal -5/64 binary64)))
(/.f64 (+.f64 (*.f64 (*.f64 x (*.f64 x x)) #s(literal -125/262144 binary64)) (*.f64 (*.f64 x (*.f64 x x)) (*.f64 (*.f64 x (*.f64 x x)) (*.f64 (*.f64 x (*.f64 x x)) #s(literal -9261/134217728 binary64))))) (+.f64 (*.f64 (*.f64 x #s(literal -5/64 binary64)) (*.f64 x #s(literal -5/64 binary64))) (-.f64 (*.f64 (*.f64 x (*.f64 (*.f64 x x) #s(literal -21/512 binary64))) (*.f64 x (*.f64 (*.f64 x x) #s(literal -21/512 binary64)))) (*.f64 (*.f64 x #s(literal -5/64 binary64)) (*.f64 x (*.f64 (*.f64 x x) #s(literal -21/512 binary64)))))))
(/.f64 (-.f64 (*.f64 (*.f64 x #s(literal -5/64 binary64)) (*.f64 x #s(literal -5/64 binary64))) (*.f64 (*.f64 x (*.f64 (*.f64 x x) #s(literal -21/512 binary64))) (*.f64 x (*.f64 (*.f64 x x) #s(literal -21/512 binary64))))) (-.f64 (*.f64 x #s(literal -5/64 binary64)) (*.f64 x (*.f64 (*.f64 x x) #s(literal -21/512 binary64)))))
(/.f64 (*.f64 x (+.f64 #s(literal -125/262144 binary64) (*.f64 (*.f64 x (*.f64 x x)) (*.f64 (*.f64 x (*.f64 x x)) #s(literal -9261/134217728 binary64))))) (+.f64 #s(literal 25/4096 binary64) (*.f64 (*.f64 (*.f64 x x) #s(literal -21/512 binary64)) (-.f64 (*.f64 (*.f64 x x) #s(literal -21/512 binary64)) #s(literal -5/64 binary64)))))
(/.f64 (*.f64 x (-.f64 #s(literal 25/4096 binary64) (*.f64 (*.f64 (*.f64 x x) (*.f64 x x)) #s(literal 441/262144 binary64)))) (-.f64 #s(literal -5/64 binary64) (*.f64 (*.f64 x x) #s(literal -21/512 binary64))))
(/.f64 (*.f64 (+.f64 #s(literal -125/262144 binary64) (*.f64 (*.f64 x (*.f64 x x)) (*.f64 (*.f64 x (*.f64 x x)) #s(literal -9261/134217728 binary64)))) x) (+.f64 #s(literal 25/4096 binary64) (*.f64 (*.f64 (*.f64 x x) #s(literal -21/512 binary64)) (-.f64 (*.f64 (*.f64 x x) #s(literal -21/512 binary64)) #s(literal -5/64 binary64)))))
(/.f64 (*.f64 (-.f64 #s(literal 25/4096 binary64) (*.f64 (*.f64 (*.f64 x x) (*.f64 x x)) #s(literal 441/262144 binary64))) x) (-.f64 #s(literal -5/64 binary64) (*.f64 (*.f64 x x) #s(literal -21/512 binary64))))
(*.f64 x (+.f64 #s(literal -5/64 binary64) (*.f64 (*.f64 x x) #s(literal -21/512 binary64))))
(*.f64 (+.f64 #s(literal -5/64 binary64) (*.f64 (*.f64 x x) #s(literal -21/512 binary64))) x)

simplify281.0ms (2.8%)

Algorithm
egg-herbie
Rules
4642×*-lowering-*.f32
4642×*-lowering-*.f64
3488×+-lowering-+.f64
3488×+-lowering-+.f32
1198×fma-lowering-fma.f32
Iterations

Useful iterations: 2 (0.0ms)

IterNodesCost
04973661
116143088
261613029
080753029
Stop Event
iter limit
node limit
Counts
276 → 276
Calls
Call 1
Inputs
x
(* x (+ 1 (* 1/8 (pow x 2))))
(* x (+ 1 (* (pow x 2) (+ 1/8 (* 7/128 (pow x 2))))))
(* x (+ 1 (* (pow x 2) (+ 1/8 (* (pow x 2) (+ 7/128 (* 33/1024 (pow x 2))))))))
(/ 2 (+ (sqrt (/ 1 x)) (* (sqrt (/ 1 x)) (sqrt -1))))
(+ (* -2 (/ (+ (* 1/2 (sqrt x)) (* 1/2 (* (sqrt x) (/ 1 (sqrt -1))))) (* (pow x 2) (pow (+ (sqrt (/ 1 x)) (* (sqrt (/ 1 x)) (sqrt -1))) 2)))) (* 2 (/ 1 (+ (sqrt (/ 1 x)) (* (sqrt (/ 1 x)) (sqrt -1))))))
(- (+ (* -1 (/ (+ (* -2 (/ (pow (+ (* 1/2 (sqrt x)) (* 1/2 (* (sqrt x) (/ 1 (sqrt -1))))) 2) (pow (+ (sqrt (/ 1 x)) (* (sqrt (/ 1 x)) (sqrt -1))) 3))) (* 2 (/ (+ (* -1/8 (sqrt (pow x 3))) (* -1/8 (* (sqrt (pow x 3)) (/ 1 (pow (sqrt -1) 3))))) (pow (+ (sqrt (/ 1 x)) (* (sqrt (/ 1 x)) (sqrt -1))) 2)))) (pow x 4))) (* 2 (/ 1 (+ (sqrt (/ 1 x)) (* (sqrt (/ 1 x)) (sqrt -1)))))) (* 2 (/ (+ (* 1/2 (sqrt x)) (* 1/2 (* (sqrt x) (/ 1 (sqrt -1))))) (* (pow x 2) (pow (+ (sqrt (/ 1 x)) (* (sqrt (/ 1 x)) (sqrt -1))) 2)))))
(- (+ (* -1 (/ (+ (* -2 (/ (* (+ (* -1/8 (sqrt (pow x 3))) (* -1/8 (* (sqrt (pow x 3)) (/ 1 (pow (sqrt -1) 3))))) (+ (* 1/2 (sqrt x)) (* 1/2 (* (sqrt x) (/ 1 (sqrt -1)))))) (pow (+ (sqrt (/ 1 x)) (* (sqrt (/ 1 x)) (sqrt -1))) 3))) (+ (* -1 (/ (* (+ (* -2 (/ (pow (+ (* 1/2 (sqrt x)) (* 1/2 (* (sqrt x) (/ 1 (sqrt -1))))) 2) (pow (+ (sqrt (/ 1 x)) (* (sqrt (/ 1 x)) (sqrt -1))) 3))) (* 2 (/ (+ (* -1/8 (sqrt (pow x 3))) (* -1/8 (* (sqrt (pow x 3)) (/ 1 (pow (sqrt -1) 3))))) (pow (+ (sqrt (/ 1 x)) (* (sqrt (/ 1 x)) (sqrt -1))) 2)))) (+ (* 1/2 (sqrt x)) (* 1/2 (* (sqrt x) (/ 1 (sqrt -1)))))) (+ (sqrt (/ 1 x)) (* (sqrt (/ 1 x)) (sqrt -1))))) (* 2 (/ (+ (* 1/16 (sqrt (pow x 5))) (* 1/16 (* (sqrt (pow x 5)) (/ 1 (pow (sqrt -1) 5))))) (pow (+ (sqrt (/ 1 x)) (* (sqrt (/ 1 x)) (sqrt -1))) 2))))) (pow x 6))) (* 2 (/ 1 (+ (sqrt (/ 1 x)) (* (sqrt (/ 1 x)) (sqrt -1)))))) (+ (* -2 (/ (pow (+ (* 1/2 (sqrt x)) (* 1/2 (* (sqrt x) (/ 1 (sqrt -1))))) 2) (* (pow x 4) (pow (+ (sqrt (/ 1 x)) (* (sqrt (/ 1 x)) (sqrt -1))) 3)))) (+ (* 2 (/ (+ (* -1/8 (sqrt (pow x 3))) (* -1/8 (* (sqrt (pow x 3)) (/ 1 (pow (sqrt -1) 3))))) (* (pow x 4) (pow (+ (sqrt (/ 1 x)) (* (sqrt (/ 1 x)) (sqrt -1))) 2)))) (* 2 (/ (+ (* 1/2 (sqrt x)) (* 1/2 (* (sqrt x) (/ 1 (sqrt -1))))) (* (pow x 2) (pow (+ (sqrt (/ 1 x)) (* (sqrt (/ 1 x)) (sqrt -1))) 2)))))))
(/ -2 (+ (* (sqrt (/ 1 x)) (sqrt -1)) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))))
(- (* 2 (/ (+ (* 1/2 (sqrt x)) (* 1/2 (* (sqrt x) (sqrt -1)))) (* (pow x 2) (pow (+ (* (sqrt (/ 1 x)) (sqrt -1)) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))) 2)))) (* 2 (/ 1 (+ (* (sqrt (/ 1 x)) (sqrt -1)) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))))))
(- (* -1 (/ (+ (* -2 (/ (+ (* -1/8 (* (sqrt (pow x 3)) (sqrt -1))) (* -1/8 (* (sqrt (pow x 3)) (/ 1 (pow (sqrt -1) 2))))) (pow (+ (* (sqrt (/ 1 x)) (sqrt -1)) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))) 2))) (* 2 (/ (pow (+ (* 1/2 (sqrt x)) (* 1/2 (* (sqrt x) (sqrt -1)))) 2) (pow (+ (* (sqrt (/ 1 x)) (sqrt -1)) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))) 3)))) (pow x 4))) (+ (* -2 (/ (+ (* 1/2 (sqrt x)) (* 1/2 (* (sqrt x) (sqrt -1)))) (* (pow x 2) (pow (+ (* (sqrt (/ 1 x)) (sqrt -1)) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))) 2)))) (* 2 (/ 1 (+ (* (sqrt (/ 1 x)) (sqrt -1)) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)))))))
(- (* -1 (/ (+ (* -2 (/ (+ (* 1/16 (* (sqrt (pow x 5)) (sqrt -1))) (* 1/16 (* (sqrt (pow x 5)) (/ 1 (pow (sqrt -1) 4))))) (pow (+ (* (sqrt (/ 1 x)) (sqrt -1)) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))) 2))) (+ (* -1 (/ (* (+ (* -2 (/ (+ (* -1/8 (* (sqrt (pow x 3)) (sqrt -1))) (* -1/8 (* (sqrt (pow x 3)) (/ 1 (pow (sqrt -1) 2))))) (pow (+ (* (sqrt (/ 1 x)) (sqrt -1)) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))) 2))) (* 2 (/ (pow (+ (* 1/2 (sqrt x)) (* 1/2 (* (sqrt x) (sqrt -1)))) 2) (pow (+ (* (sqrt (/ 1 x)) (sqrt -1)) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))) 3)))) (+ (* 1/2 (sqrt x)) (* 1/2 (* (sqrt x) (sqrt -1))))) (+ (* (sqrt (/ 1 x)) (sqrt -1)) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))))) (* 2 (/ (* (+ (* -1/8 (* (sqrt (pow x 3)) (sqrt -1))) (* -1/8 (* (sqrt (pow x 3)) (/ 1 (pow (sqrt -1) 2))))) (+ (* 1/2 (sqrt x)) (* 1/2 (* (sqrt x) (sqrt -1))))) (pow (+ (* (sqrt (/ 1 x)) (sqrt -1)) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))) 3))))) (pow x 6))) (+ (* -2 (/ (+ (* -1/8 (* (sqrt (pow x 3)) (sqrt -1))) (* -1/8 (* (sqrt (pow x 3)) (/ 1 (pow (sqrt -1) 2))))) (* (pow x 4) (pow (+ (* (sqrt (/ 1 x)) (sqrt -1)) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))) 2)))) (+ (* -2 (/ (+ (* 1/2 (sqrt x)) (* 1/2 (* (sqrt x) (sqrt -1)))) (* (pow x 2) (pow (+ (* (sqrt (/ 1 x)) (sqrt -1)) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))) 2)))) (+ (* 2 (/ (pow (+ (* 1/2 (sqrt x)) (* 1/2 (* (sqrt x) (sqrt -1)))) 2) (* (pow x 4) (pow (+ (* (sqrt (/ 1 x)) (sqrt -1)) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))) 3)))) (* 2 (/ 1 (+ (* (sqrt (/ 1 x)) (sqrt -1)) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)))))))))
(* 2 x)
(* 2 x)
(* 2 x)
(* 2 x)
(* 2 x)
(* 2 x)
(* 2 x)
(* 2 x)
(* 2 x)
(* 2 x)
(* 2 x)
(* 2 x)
2
(+ 2 (* -1/4 (pow x 2)))
(+ 2 (* (pow x 2) (- (* -5/64 (pow x 2)) 1/4)))
(+ 2 (* (pow x 2) (- (* (pow x 2) (- (* -21/512 (pow x 2)) 5/64)) 1/4)))
(* x (+ (sqrt (/ 1 x)) (* (sqrt (/ 1 x)) (sqrt -1))))
(* x (+ (sqrt (/ 1 x)) (+ (* 1/2 (sqrt (/ 1 (pow x 3)))) (+ (* 1/2 (* (sqrt (/ 1 (pow x 3))) (/ 1 (sqrt -1)))) (* (sqrt (/ 1 x)) (sqrt -1))))))
(* x (+ (sqrt (/ 1 x)) (+ (* -1/8 (sqrt (/ 1 (pow x 5)))) (+ (* -1/8 (* (sqrt (/ 1 (pow x 5))) (/ 1 (pow (sqrt -1) 3)))) (+ (* 1/2 (sqrt (/ 1 (pow x 3)))) (+ (* 1/2 (* (sqrt (/ 1 (pow x 3))) (/ 1 (sqrt -1)))) (* (sqrt (/ 1 x)) (sqrt -1))))))))
(* x (+ (sqrt (/ 1 x)) (+ (* -1/8 (sqrt (/ 1 (pow x 5)))) (+ (* -1/8 (* (sqrt (/ 1 (pow x 5))) (/ 1 (pow (sqrt -1) 3)))) (+ (* 1/16 (sqrt (/ 1 (pow x 7)))) (+ (* 1/16 (* (sqrt (/ 1 (pow x 7))) (/ 1 (pow (sqrt -1) 5)))) (+ (* 1/2 (sqrt (/ 1 (pow x 3)))) (+ (* 1/2 (* (sqrt (/ 1 (pow x 3))) (/ 1 (sqrt -1)))) (* (sqrt (/ 1 x)) (sqrt -1))))))))))
(* -1 (* x (+ (* (sqrt (/ 1 x)) (sqrt -1)) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)))))
(* -1 (* x (+ (* 1/2 (sqrt (/ 1 (pow x 3)))) (+ (* 1/2 (* (sqrt (/ 1 (pow x 3))) (sqrt -1))) (+ (* (sqrt (/ 1 x)) (sqrt -1)) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)))))))
(* -1 (* x (+ (* -1/8 (* (sqrt (/ 1 (pow x 5))) (sqrt -1))) (+ (* -1/8 (* (sqrt (/ 1 (pow x 5))) (/ 1 (pow (sqrt -1) 2)))) (+ (* 1/2 (sqrt (/ 1 (pow x 3)))) (+ (* 1/2 (* (sqrt (/ 1 (pow x 3))) (sqrt -1))) (+ (* (sqrt (/ 1 x)) (sqrt -1)) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)))))))))
(* -1 (* x (+ (* -1/8 (* (sqrt (/ 1 (pow x 5))) (sqrt -1))) (+ (* -1/8 (* (sqrt (/ 1 (pow x 5))) (/ 1 (pow (sqrt -1) 2)))) (+ (* 1/16 (* (sqrt (/ 1 (pow x 7))) (sqrt -1))) (+ (* 1/16 (* (sqrt (/ 1 (pow x 7))) (/ 1 (pow (sqrt -1) 4)))) (+ (* 1/2 (sqrt (/ 1 (pow x 3)))) (+ (* 1/2 (* (sqrt (/ 1 (pow x 3))) (sqrt -1))) (+ (* (sqrt (/ 1 x)) (sqrt -1)) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)))))))))))
1
(+ 1 (* 1/2 x))
(+ 1 (* x (+ 1/2 (* -1/8 x))))
(+ 1 (* x (+ 1/2 (* x (- (* 1/16 x) 1/8)))))
(sqrt x)
(* x (+ (sqrt (/ 1 x)) (* 1/2 (sqrt (/ 1 (pow x 3))))))
(* x (+ (sqrt (/ 1 x)) (+ (* -1/8 (sqrt (/ 1 (pow x 5)))) (* 1/2 (sqrt (/ 1 (pow x 3)))))))
(* x (+ (sqrt (/ 1 x)) (+ (* -1/8 (sqrt (/ 1 (pow x 5)))) (+ (* 1/16 (sqrt (/ 1 (pow x 7)))) (* 1/2 (sqrt (/ 1 (pow x 3))))))))
(* -1 (* (sqrt x) (pow (sqrt -1) 2)))
(* -1 (* x (+ (* 1/2 (sqrt (/ 1 (pow x 3)))) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)))))
(* -1 (* x (+ (* -1/8 (* (sqrt (/ 1 (pow x 5))) (/ 1 (pow (sqrt -1) 2)))) (+ (* 1/2 (sqrt (/ 1 (pow x 3)))) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))))))
(* -1 (* x (+ (* -1/8 (* (sqrt (/ 1 (pow x 5))) (/ 1 (pow (sqrt -1) 2)))) (+ (* 1/16 (* (sqrt (/ 1 (pow x 7))) (/ 1 (pow (sqrt -1) 4)))) (+ (* 1/2 (sqrt (/ 1 (pow x 3)))) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)))))))
x
(* x (+ 1 (* 1/8 (pow x 2))))
(* x (+ 1 (* (pow x 2) (+ 1/8 (* 1/64 (pow x 2))))))
(* x (+ 1 (* (pow x 2) (+ 1/8 (* (pow x 2) (+ 1/64 (* 1/512 (pow x 2))))))))
(/ -8 x)
(* -1 (/ (+ 8 (* 64 (/ 1 (pow x 2)))) x))
(/ (- (* -1 (/ (+ 64 (* 512 (/ 1 (pow x 2)))) (pow x 2))) 8) x)
(/ (- (* -1 (/ (+ 512 (* 4096 (/ 1 (pow x 2)))) (pow x 4))) (+ 8 (* 64 (/ 1 (pow x 2))))) x)
(/ -8 x)
(* -1 (/ (+ 8 (* 64 (/ 1 (pow x 2)))) x))
(* -1 (/ (+ 8 (+ (* 64 (/ 1 (pow x 2))) (/ 512 (pow x 4)))) x))
(* -1 (/ (+ 8 (+ (* 64 (/ 1 (pow x 2))) (+ (* 4096 (/ 1 (pow x 6))) (/ 512 (pow x 4))))) x))
2
(+ 2 (* -1/4 (pow x 2)))
(+ 2 (* -1/4 (pow x 2)))
(+ 2 (* -1/4 (pow x 2)))
(* -1/4 (pow x 2))
(* (pow x 2) (- (* 2 (/ 1 (pow x 2))) 1/4))
(* (pow x 2) (- (* 2 (/ 1 (pow x 2))) 1/4))
(* (pow x 2) (- (* 2 (/ 1 (pow x 2))) 1/4))
(* -1/4 (pow x 2))
(* (pow x 2) (- (* 2 (/ 1 (pow x 2))) 1/4))
(* (pow x 2) (- (* 2 (/ 1 (pow x 2))) 1/4))
(* (pow x 2) (- (* 2 (/ 1 (pow x 2))) 1/4))
(* -1/4 (pow x 2))
(* -1/4 (pow x 2))
(* -1/4 (pow x 2))
(* -1/4 (pow x 2))
(* -1/4 (pow x 2))
(* -1/4 (pow x 2))
(* -1/4 (pow x 2))
(* -1/4 (pow x 2))
(* -1/4 (pow x 2))
(* -1/4 (pow x 2))
(* -1/4 (pow x 2))
(* -1/4 (pow x 2))
x
(* x (+ 1 (* 1/8 (pow x 2))))
(* x (+ 1 (* (pow x 2) (+ 1/8 (* 7/128 (pow x 2))))))
(* x (+ 1 (* (pow x 2) (+ 1/8 (* (pow x 2) (+ 7/128 (* 3/256 (pow x 2))))))))
(/ -128/5 (pow x 3))
(/ (- (* 2048/25 (/ 1 (pow x 2))) 128/5) (pow x 3))
(/ (- (* 2048/25 (/ 1 (pow x 2))) (+ 128/5 (/ 114688/125 (pow x 4)))) (pow x 3))
(/ (- (+ (* 2048/25 (/ 1 (pow x 2))) (* 3145728/625 (/ 1 (pow x 6)))) (+ 128/5 (/ 114688/125 (pow x 4)))) (pow x 3))
(/ -128/5 (pow x 3))
(* -1 (/ (- 128/5 (* 2048/25 (/ 1 (pow x 2)))) (pow x 3)))
(* -1 (/ (- (+ 128/5 (/ 114688/125 (pow x 4))) (* 2048/25 (/ 1 (pow x 2)))) (pow x 3)))
(* -1 (/ (- (+ 128/5 (/ 114688/125 (pow x 4))) (+ (* 2048/25 (/ 1 (pow x 2))) (* 3145728/625 (/ 1 (pow x 6))))) (pow x 3)))
2
(+ 2 (* -1/4 (pow x 2)))
(+ 2 (* (pow x 2) (- (* -5/64 (pow x 2)) 1/4)))
(+ 2 (* (pow x 2) (- (* -5/64 (pow x 2)) 1/4)))
(* -5/64 (pow x 4))
(* -1 (* (pow x 4) (+ 5/64 (* 1/4 (/ 1 (pow x 2))))))
(* (pow x 4) (- (/ 2 (pow x 4)) (+ 5/64 (* 1/4 (/ 1 (pow x 2))))))
(* (pow x 4) (- (/ 2 (pow x 4)) (+ 5/64 (* 1/4 (/ 1 (pow x 2))))))
(* -5/64 (pow x 4))
(* -1 (* (pow x 4) (+ 5/64 (* 1/4 (/ 1 (pow x 2))))))
(* (pow x 4) (- (/ 2 (pow x 4)) (+ 5/64 (* 1/4 (/ 1 (pow x 2))))))
(* (pow x 4) (- (/ 2 (pow x 4)) (+ 5/64 (* 1/4 (/ 1 (pow x 2))))))
(* -1/4 (pow x 2))
(* (pow x 2) (- (* -5/64 (pow x 2)) 1/4))
(* (pow x 2) (- (* -5/64 (pow x 2)) 1/4))
(* (pow x 2) (- (* -5/64 (pow x 2)) 1/4))
(* -5/64 (pow x 4))
(* -1 (* (pow x 4) (+ 5/64 (* 1/4 (/ 1 (pow x 2))))))
(* -1 (* (pow x 4) (+ 5/64 (* 1/4 (/ 1 (pow x 2))))))
(* -1 (* (pow x 4) (+ 5/64 (* 1/4 (/ 1 (pow x 2))))))
(* -5/64 (pow x 4))
(* -1 (* (pow x 4) (+ 5/64 (* 1/4 (/ 1 (pow x 2))))))
(* -1 (* (pow x 4) (+ 5/64 (* 1/4 (/ 1 (pow x 2))))))
(* -1 (* (pow x 4) (+ 5/64 (* 1/4 (/ 1 (pow x 2))))))
x
(* x (+ 1 (* 1/8 (pow x 2))))
(* x (+ 1 (* (pow x 2) (+ 1/8 (* 7/128 (pow x 2))))))
(* x (+ 1 (* (pow x 2) (+ 1/8 (* (pow x 2) (+ 7/128 (* 33/1024 (pow x 2))))))))
(/ -1024/21 (pow x 5))
(/ (- (* 40960/441 (/ 1 (pow x 2))) 1024/21) (pow x 5))
(/ (- (+ (* 40960/441 (/ 1 (pow x 2))) (/ 1114112/9261 (pow x 4))) 1024/21) (pow x 5))
(/ (- (+ (* 40960/441 (/ 1 (pow x 2))) (/ 1114112/9261 (pow x 4))) (+ 1024/21 (* 617086976/194481 (/ 1 (pow x 6))))) (pow x 5))
(/ -1024/21 (pow x 5))
(* -1 (/ (- 1024/21 (* 40960/441 (/ 1 (pow x 2)))) (pow x 5)))
(* -1 (/ (+ 1024/21 (* -1 (/ (+ 40960/441 (* 1114112/9261 (/ 1 (pow x 2)))) (pow x 2)))) (pow x 5)))
(* -1 (/ (- (+ 1024/21 (* 617086976/194481 (/ 1 (pow x 6)))) (+ (* 40960/441 (/ 1 (pow x 2))) (/ 1114112/9261 (pow x 4)))) (pow x 5)))
2
(+ 2 (* -1/4 (pow x 2)))
(+ 2 (* (pow x 2) (- (* -5/64 (pow x 2)) 1/4)))
(+ 2 (* (pow x 2) (- (* (pow x 2) (- (* -21/512 (pow x 2)) 5/64)) 1/4)))
(* -21/512 (pow x 6))
(* -1 (* (pow x 6) (+ 21/512 (* 5/64 (/ 1 (pow x 2))))))
(* (pow x 6) (- (* -1 (/ (+ 5/64 (* 1/4 (/ 1 (pow x 2)))) (pow x 2))) 21/512))
(* (pow x 6) (- (* 2 (/ 1 (pow x 6))) (+ 21/512 (+ (/ 1/4 (pow x 4)) (* 5/64 (/ 1 (pow x 2)))))))
(* -21/512 (pow x 6))
(* -1 (* (pow x 6) (+ 21/512 (* 5/64 (/ 1 (pow x 2))))))
(* (pow x 6) (- (* -1 (/ (+ 5/64 (* 1/4 (/ 1 (pow x 2)))) (pow x 2))) 21/512))
(* (pow x 6) (- (* 2 (/ 1 (pow x 6))) (+ 21/512 (+ (/ 1/4 (pow x 4)) (* 5/64 (/ 1 (pow x 2)))))))
(* -1/4 (pow x 2))
(* (pow x 2) (- (* -5/64 (pow x 2)) 1/4))
(* (pow x 2) (- (* (pow x 2) (- (* -21/512 (pow x 2)) 5/64)) 1/4))
(* (pow x 2) (- (* (pow x 2) (- (* -21/512 (pow x 2)) 5/64)) 1/4))
(* -21/512 (pow x 6))
(* -1 (* (pow x 6) (+ 21/512 (* 5/64 (/ 1 (pow x 2))))))
(* (pow x 6) (- (* -1 (/ (+ 5/64 (* 1/4 (/ 1 (pow x 2)))) (pow x 2))) 21/512))
(* (pow x 6) (- (* -1 (/ (+ 5/64 (* 1/4 (/ 1 (pow x 2)))) (pow x 2))) 21/512))
(* -21/512 (pow x 6))
(* -1 (* (pow x 6) (+ 21/512 (* 5/64 (/ 1 (pow x 2))))))
(* (pow x 6) (- (* -1 (/ (+ 5/64 (* 1/4 (/ 1 (pow x 2)))) (pow x 2))) 21/512))
(* (pow x 6) (- (* -1 (/ (+ 5/64 (* 1/4 (/ 1 (pow x 2)))) (pow x 2))) 21/512))
x
(* x (+ 1 (* 1/8 (pow x 2))))
(* x (+ 1 (* (pow x 2) (+ 1/8 (* 7/128 (pow x 2))))))
(* x (+ 1 (* (pow x 2) (+ 1/8 (* (pow x 2) (+ 7/128 (* 33/1024 (pow x 2))))))))
(/ -1024/21 (pow x 5))
(/ (- (* 40960/441 (/ 1 (pow x 2))) 1024/21) (pow x 5))
(/ (- (+ (* 40960/441 (/ 1 (pow x 2))) (/ 1114112/9261 (pow x 4))) 1024/21) (pow x 5))
(/ (- (+ (* 40960/441 (/ 1 (pow x 2))) (/ 1114112/9261 (pow x 4))) (+ 1024/21 (* 617086976/194481 (/ 1 (pow x 6))))) (pow x 5))
(/ -1024/21 (pow x 5))
(* -1 (/ (- 1024/21 (* 40960/441 (/ 1 (pow x 2)))) (pow x 5)))
(* -1 (/ (+ 1024/21 (* -1 (/ (+ 40960/441 (* 1114112/9261 (/ 1 (pow x 2)))) (pow x 2)))) (pow x 5)))
(* -1 (/ (- (+ 1024/21 (* 617086976/194481 (/ 1 (pow x 6)))) (+ (* 40960/441 (/ 1 (pow x 2))) (/ 1114112/9261 (pow x 4)))) (pow x 5)))
(* 2 x)
(* 2 x)
(* 2 x)
(* 2 x)
(* 2 x)
(* 2 x)
(* 2 x)
(* 2 x)
(* 2 x)
(* 2 x)
(* 2 x)
(* 2 x)
-1
(- (* 2 x) 1)
(- (* 2 x) 1)
(- (* 2 x) 1)
(* 2 x)
(* x (- 2 (/ 1 x)))
(* x (- 2 (/ 1 x)))
(* x (- 2 (/ 1 x)))
(* 2 x)
(* -1 (* x (- (/ 1 x) 2)))
(* -1 (* x (- (/ 1 x) 2)))
(* -1 (* x (- (/ 1 x) 2)))
-1
(- (* -2 x) 1)
(- (* x (- (* -4 x) 2)) 1)
(- (* x (- (* x (- (* -8 x) 4)) 2)) 1)
(/ 1/2 x)
(/ (+ 1/2 (* 1/4 (/ 1 x))) x)
(/ (+ 1/2 (+ (/ 1/8 (pow x 2)) (* 1/4 (/ 1 x)))) x)
(/ (+ 1/2 (+ (/ 1/8 (pow x 2)) (+ (* 1/4 (/ 1 x)) (* 1/16 (/ 1 (pow x 3)))))) x)
(/ 1/2 x)
(/ (+ 1/2 (* 1/4 (/ 1 x))) x)
(* -1 (/ (- (* -1 (/ (+ 1/4 (* 1/8 (/ 1 x))) x)) 1/2) x))
(* -1 (/ (- (* -1 (/ (+ 1/4 (+ (/ 1/16 (pow x 2)) (* 1/8 (/ 1 x)))) x)) 1/2) x))
1
(+ 1 (* -1/2 x))
(+ 1 (* x (- (* -1/8 x) 1/2)))
(+ 1 (* x (- (* x (- (* -1/16 x) 1/8)) 1/2)))
(* (sqrt x) (sqrt -1))
(* x (+ (* 1/2 (* (sqrt (/ 1 (pow x 3))) (/ 1 (sqrt -1)))) (* (sqrt (/ 1 x)) (sqrt -1))))
(* x (+ (* -1/8 (* (sqrt (/ 1 (pow x 5))) (/ 1 (pow (sqrt -1) 3)))) (+ (* 1/2 (* (sqrt (/ 1 (pow x 3))) (/ 1 (sqrt -1)))) (* (sqrt (/ 1 x)) (sqrt -1)))))
(* x (+ (* -1/8 (* (sqrt (/ 1 (pow x 5))) (/ 1 (pow (sqrt -1) 3)))) (+ (* 1/16 (* (sqrt (/ 1 (pow x 7))) (/ 1 (pow (sqrt -1) 5)))) (+ (* 1/2 (* (sqrt (/ 1 (pow x 3))) (/ 1 (sqrt -1)))) (* (sqrt (/ 1 x)) (sqrt -1))))))
(* -1 (* (sqrt x) (sqrt -1)))
(* -1 (* x (+ (* 1/2 (* (sqrt (/ 1 (pow x 3))) (sqrt -1))) (* (sqrt (/ 1 x)) (sqrt -1)))))
(* -1 (* x (+ (* -1/8 (* (sqrt (/ 1 (pow x 5))) (sqrt -1))) (+ (* 1/2 (* (sqrt (/ 1 (pow x 3))) (sqrt -1))) (* (sqrt (/ 1 x)) (sqrt -1))))))
(* -1 (* x (+ (* -1/8 (* (sqrt (/ 1 (pow x 5))) (sqrt -1))) (+ (* 1/16 (* (sqrt (/ 1 (pow x 7))) (sqrt -1))) (+ (* 1/2 (* (sqrt (/ 1 (pow x 3))) (sqrt -1))) (* (sqrt (/ 1 x)) (sqrt -1)))))))
(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)
(* -5/64 (pow x 2))
(* -5/64 (pow x 2))
(* -5/64 (pow x 2))
(* -5/64 (pow x 2))
(* -5/64 (pow x 2))
(* -5/64 (pow x 2))
(* -5/64 (pow x 2))
(* -5/64 (pow x 2))
(* -5/64 (pow x 2))
(* -5/64 (pow x 2))
(* -5/64 (pow x 2))
(* -5/64 (pow x 2))
(* -21/512 (pow x 2))
(* -21/512 (pow x 2))
(* -21/512 (pow x 2))
(* -21/512 (pow x 2))
(* -21/512 (pow x 2))
(* -21/512 (pow x 2))
(* -21/512 (pow x 2))
(* -21/512 (pow x 2))
(* -21/512 (pow x 2))
(* -21/512 (pow x 2))
(* -21/512 (pow x 2))
(* -21/512 (pow x 2))
(* -5/64 (pow x 2))
(* (pow x 2) (- (* -21/512 (pow x 2)) 5/64))
(* (pow x 2) (- (* -21/512 (pow x 2)) 5/64))
(* (pow x 2) (- (* -21/512 (pow x 2)) 5/64))
(* -21/512 (pow x 4))
(* -1 (* (pow x 4) (+ 21/512 (* 5/64 (/ 1 (pow x 2))))))
(* -1 (* (pow x 4) (+ 21/512 (* 5/64 (/ 1 (pow x 2))))))
(* -1 (* (pow x 4) (+ 21/512 (* 5/64 (/ 1 (pow x 2))))))
(* -21/512 (pow x 4))
(* -1 (* (pow x 4) (+ 21/512 (* 5/64 (/ 1 (pow x 2))))))
(* -1 (* (pow x 4) (+ 21/512 (* 5/64 (/ 1 (pow x 2))))))
(* -1 (* (pow x 4) (+ 21/512 (* 5/64 (/ 1 (pow x 2))))))
(* -5/64 x)
(* x (- (* -21/512 (pow x 2)) 5/64))
(* x (- (* -21/512 (pow x 2)) 5/64))
(* x (- (* -21/512 (pow x 2)) 5/64))
(* -21/512 (pow x 3))
(* -1 (* (pow x 3) (+ 21/512 (* 5/64 (/ 1 (pow x 2))))))
(* -1 (* (pow x 3) (+ 21/512 (* 5/64 (/ 1 (pow x 2))))))
(* -1 (* (pow x 3) (+ 21/512 (* 5/64 (/ 1 (pow x 2))))))
(* -21/512 (pow x 3))
(* -1 (* (pow x 3) (+ 21/512 (* 5/64 (/ 1 (pow x 2))))))
(* -1 (* (pow x 3) (+ 21/512 (* 5/64 (/ 1 (pow x 2))))))
(* -1 (* (pow x 3) (+ 21/512 (* 5/64 (/ 1 (pow x 2))))))
Outputs
x
(* x (+ 1 (* 1/8 (pow x 2))))
(*.f64 x (+.f64 #s(literal 1 binary64) (*.f64 #s(literal 1/8 binary64) (*.f64 x x))))
(* x (+ 1 (* (pow x 2) (+ 1/8 (* 7/128 (pow x 2))))))
(*.f64 x (+.f64 #s(literal 1 binary64) (*.f64 (*.f64 x x) (+.f64 #s(literal 1/8 binary64) (*.f64 (*.f64 x x) #s(literal 7/128 binary64))))))
(* x (+ 1 (* (pow x 2) (+ 1/8 (* (pow x 2) (+ 7/128 (* 33/1024 (pow x 2))))))))
(*.f64 x (+.f64 #s(literal 1 binary64) (*.f64 x (*.f64 x (+.f64 #s(literal 1/8 binary64) (*.f64 (*.f64 x x) (+.f64 #s(literal 7/128 binary64) (*.f64 (*.f64 x x) #s(literal 33/1024 binary64)))))))))
(/ 2 (+ (sqrt (/ 1 x)) (* (sqrt (/ 1 x)) (sqrt -1))))
(/.f64 #s(literal 2 binary64) (*.f64 (+.f64 (sqrt.f64 #s(literal -1 binary64)) #s(literal 1 binary64)) (sqrt.f64 (/.f64 #s(literal 1 binary64) x))))
(+ (* -2 (/ (+ (* 1/2 (sqrt x)) (* 1/2 (* (sqrt x) (/ 1 (sqrt -1))))) (* (pow x 2) (pow (+ (sqrt (/ 1 x)) (* (sqrt (/ 1 x)) (sqrt -1))) 2)))) (* 2 (/ 1 (+ (sqrt (/ 1 x)) (* (sqrt (/ 1 x)) (sqrt -1))))))
(-.f64 (/.f64 #s(literal 2 binary64) (*.f64 (+.f64 (sqrt.f64 #s(literal -1 binary64)) #s(literal 1 binary64)) (sqrt.f64 (/.f64 #s(literal 1 binary64) x)))) (/.f64 (/.f64 (*.f64 (+.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 #s(literal -1 binary64))) #s(literal 1 binary64)) (sqrt.f64 x)) (*.f64 x x)) (*.f64 (*.f64 (+.f64 (sqrt.f64 #s(literal -1 binary64)) #s(literal 1 binary64)) (+.f64 (sqrt.f64 #s(literal -1 binary64)) #s(literal 1 binary64))) (/.f64 #s(literal 1 binary64) x))))
(- (+ (* -1 (/ (+ (* -2 (/ (pow (+ (* 1/2 (sqrt x)) (* 1/2 (* (sqrt x) (/ 1 (sqrt -1))))) 2) (pow (+ (sqrt (/ 1 x)) (* (sqrt (/ 1 x)) (sqrt -1))) 3))) (* 2 (/ (+ (* -1/8 (sqrt (pow x 3))) (* -1/8 (* (sqrt (pow x 3)) (/ 1 (pow (sqrt -1) 3))))) (pow (+ (sqrt (/ 1 x)) (* (sqrt (/ 1 x)) (sqrt -1))) 2)))) (pow x 4))) (* 2 (/ 1 (+ (sqrt (/ 1 x)) (* (sqrt (/ 1 x)) (sqrt -1)))))) (* 2 (/ (+ (* 1/2 (sqrt x)) (* 1/2 (* (sqrt x) (/ 1 (sqrt -1))))) (* (pow x 2) (pow (+ (sqrt (/ 1 x)) (* (sqrt (/ 1 x)) (sqrt -1))) 2)))))
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(- (+ (* -1 (/ (+ (* -2 (/ (* (+ (* -1/8 (sqrt (pow x 3))) (* -1/8 (* (sqrt (pow x 3)) (/ 1 (pow (sqrt -1) 3))))) (+ (* 1/2 (sqrt x)) (* 1/2 (* (sqrt x) (/ 1 (sqrt -1)))))) (pow (+ (sqrt (/ 1 x)) (* (sqrt (/ 1 x)) (sqrt -1))) 3))) (+ (* -1 (/ (* (+ (* -2 (/ (pow (+ (* 1/2 (sqrt x)) (* 1/2 (* (sqrt x) (/ 1 (sqrt -1))))) 2) (pow (+ (sqrt (/ 1 x)) (* (sqrt (/ 1 x)) (sqrt -1))) 3))) (* 2 (/ (+ (* -1/8 (sqrt (pow x 3))) (* -1/8 (* (sqrt (pow x 3)) (/ 1 (pow (sqrt -1) 3))))) (pow (+ (sqrt (/ 1 x)) (* (sqrt (/ 1 x)) (sqrt -1))) 2)))) (+ (* 1/2 (sqrt x)) (* 1/2 (* (sqrt x) (/ 1 (sqrt -1)))))) (+ (sqrt (/ 1 x)) (* (sqrt (/ 1 x)) (sqrt -1))))) (* 2 (/ (+ (* 1/16 (sqrt (pow x 5))) (* 1/16 (* (sqrt (pow x 5)) (/ 1 (pow (sqrt -1) 5))))) (pow (+ (sqrt (/ 1 x)) (* (sqrt (/ 1 x)) (sqrt -1))) 2))))) (pow x 6))) (* 2 (/ 1 (+ (sqrt (/ 1 x)) (* (sqrt (/ 1 x)) (sqrt -1)))))) (+ (* -2 (/ (pow (+ (* 1/2 (sqrt x)) (* 1/2 (* (sqrt x) (/ 1 (sqrt -1))))) 2) (* (pow x 4) (pow (+ (sqrt (/ 1 x)) (* (sqrt (/ 1 x)) (sqrt -1))) 3)))) (+ (* 2 (/ (+ (* -1/8 (sqrt (pow x 3))) (* -1/8 (* (sqrt (pow x 3)) (/ 1 (pow (sqrt -1) 3))))) (* (pow x 4) (pow (+ (sqrt (/ 1 x)) (* (sqrt (/ 1 x)) (sqrt -1))) 2)))) (* 2 (/ (+ (* 1/2 (sqrt x)) (* 1/2 (* (sqrt x) (/ 1 (sqrt -1))))) (* (pow x 2) (pow (+ (sqrt (/ 1 x)) (* (sqrt (/ 1 x)) (sqrt -1))) 2)))))))
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(/ -2 (+ (* (sqrt (/ 1 x)) (sqrt -1)) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))))
(/.f64 #s(literal -2 binary64) (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) (+.f64 #s(literal -1 binary64) (sqrt.f64 #s(literal -1 binary64)))))
(- (* 2 (/ (+ (* 1/2 (sqrt x)) (* 1/2 (* (sqrt x) (sqrt -1)))) (* (pow x 2) (pow (+ (* (sqrt (/ 1 x)) (sqrt -1)) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))) 2)))) (* 2 (/ 1 (+ (* (sqrt (/ 1 x)) (sqrt -1)) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))))))
(+.f64 (/.f64 #s(literal -2 binary64) (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) (+.f64 #s(literal -1 binary64) (sqrt.f64 #s(literal -1 binary64))))) (/.f64 (/.f64 (*.f64 (+.f64 (sqrt.f64 #s(literal -1 binary64)) #s(literal 1 binary64)) (sqrt.f64 x)) (*.f64 x x)) (*.f64 (/.f64 #s(literal 1 binary64) x) (*.f64 (+.f64 #s(literal -1 binary64) (sqrt.f64 #s(literal -1 binary64))) (+.f64 #s(literal -1 binary64) (sqrt.f64 #s(literal -1 binary64)))))))
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2
#s(literal 2 binary64)
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#s(literal 1 binary64)
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x
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(/.f64 (+.f64 (/.f64 #s(literal 1114112/9261 binary64) (*.f64 (*.f64 x x) (*.f64 x x))) (+.f64 (/.f64 #s(literal 40960/441 binary64) (*.f64 x x)) (-.f64 #s(literal -1024/21 binary64) (/.f64 #s(literal 617086976/194481 binary64) (pow.f64 x #s(literal 6 binary64)))))) (pow.f64 x #s(literal 5 binary64)))
(/ -1024/21 (pow x 5))
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(* -1 (/ (- 1024/21 (* 40960/441 (/ 1 (pow x 2)))) (pow x 5)))
(/.f64 (+.f64 #s(literal 1024/21 binary64) (/.f64 #s(literal -40960/441 binary64) (*.f64 x x))) (-.f64 #s(literal 0 binary64) (pow.f64 x #s(literal 5 binary64))))
(* -1 (/ (+ 1024/21 (* -1 (/ (+ 40960/441 (* 1114112/9261 (/ 1 (pow x 2)))) (pow x 2)))) (pow x 5)))
(/.f64 (-.f64 #s(literal 1024/21 binary64) (/.f64 (+.f64 #s(literal 40960/441 binary64) (/.f64 #s(literal 1114112/9261 binary64) (*.f64 x x))) (*.f64 x x))) (-.f64 #s(literal 0 binary64) (pow.f64 x #s(literal 5 binary64))))
(* -1 (/ (- (+ 1024/21 (* 617086976/194481 (/ 1 (pow x 6)))) (+ (* 40960/441 (/ 1 (pow x 2))) (/ 1114112/9261 (pow x 4)))) (pow x 5)))
(/.f64 (+.f64 (+.f64 #s(literal 1024/21 binary64) (/.f64 #s(literal 617086976/194481 binary64) (pow.f64 x #s(literal 6 binary64)))) (-.f64 (/.f64 #s(literal -40960/441 binary64) (*.f64 x x)) (/.f64 #s(literal 1114112/9261 binary64) (*.f64 (*.f64 x x) (*.f64 x x))))) (-.f64 #s(literal 0 binary64) (pow.f64 x #s(literal 5 binary64))))
(* 2 x)
(*.f64 x #s(literal 2 binary64))
(* 2 x)
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-1
#s(literal -1 binary64)
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(+.f64 #s(literal -1 binary64) (*.f64 x #s(literal 2 binary64)))
(- (* 2 x) 1)
(+.f64 #s(literal -1 binary64) (*.f64 x #s(literal 2 binary64)))
(- (* 2 x) 1)
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(* 2 x)
(*.f64 x #s(literal 2 binary64))
(* x (- 2 (/ 1 x)))
(+.f64 #s(literal -1 binary64) (*.f64 x #s(literal 2 binary64)))
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(* 2 x)
(*.f64 x #s(literal 2 binary64))
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-1
#s(literal -1 binary64)
(- (* -2 x) 1)
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(- (* x (- (* -4 x) 2)) 1)
(+.f64 #s(literal -1 binary64) (*.f64 x (+.f64 #s(literal -2 binary64) (*.f64 x #s(literal -4 binary64)))))
(- (* x (- (* x (- (* -8 x) 4)) 2)) 1)
(+.f64 #s(literal -1 binary64) (*.f64 x (+.f64 #s(literal -2 binary64) (*.f64 x (+.f64 #s(literal -4 binary64) (*.f64 x #s(literal -8 binary64)))))))
(/ 1/2 x)
(/.f64 #s(literal 1/2 binary64) x)
(/ (+ 1/2 (* 1/4 (/ 1 x))) x)
(/.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 #s(literal 1/4 binary64) x)) x)
(/ (+ 1/2 (+ (/ 1/8 (pow x 2)) (* 1/4 (/ 1 x)))) x)
(/.f64 (+.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 #s(literal 1/4 binary64) x)) (/.f64 #s(literal 1/8 binary64) (*.f64 x x))) x)
(/ (+ 1/2 (+ (/ 1/8 (pow x 2)) (+ (* 1/4 (/ 1 x)) (* 1/16 (/ 1 (pow x 3)))))) x)
(/.f64 (+.f64 (+.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 #s(literal 1/4 binary64) x)) (/.f64 #s(literal 1/8 binary64) (*.f64 x x))) (/.f64 #s(literal 1/16 binary64) (*.f64 x (*.f64 x x)))) x)
(/ 1/2 x)
(/.f64 #s(literal 1/2 binary64) x)
(/ (+ 1/2 (* 1/4 (/ 1 x))) x)
(/.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 #s(literal 1/4 binary64) x)) x)
(* -1 (/ (- (* -1 (/ (+ 1/4 (* 1/8 (/ 1 x))) x)) 1/2) x))
(/.f64 (-.f64 #s(literal -1/2 binary64) (/.f64 (+.f64 #s(literal 1/4 binary64) (/.f64 #s(literal 1/8 binary64) x)) x)) (-.f64 #s(literal 0 binary64) x))
(* -1 (/ (- (* -1 (/ (+ 1/4 (+ (/ 1/16 (pow x 2)) (* 1/8 (/ 1 x)))) x)) 1/2) x))
(-.f64 #s(literal 0 binary64) (/.f64 (-.f64 #s(literal -1/2 binary64) (/.f64 (+.f64 (/.f64 #s(literal 1/8 binary64) x) (+.f64 #s(literal 1/4 binary64) (/.f64 #s(literal 1/16 binary64) (*.f64 x x)))) 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 (- (* -1/8 x) 1/2)))
(+.f64 #s(literal 1 binary64) (*.f64 x (+.f64 (*.f64 x #s(literal -1/8 binary64)) #s(literal -1/2 binary64))))
(+ 1 (* x (- (* x (- (* -1/16 x) 1/8)) 1/2)))
(+.f64 #s(literal 1 binary64) (*.f64 x (+.f64 #s(literal -1/2 binary64) (*.f64 x (+.f64 #s(literal -1/8 binary64) (*.f64 x #s(literal -1/16 binary64)))))))
(* (sqrt x) (sqrt -1))
(*.f64 (sqrt.f64 #s(literal -1 binary64)) (sqrt.f64 x))
(* x (+ (* 1/2 (* (sqrt (/ 1 (pow x 3))) (/ 1 (sqrt -1)))) (* (sqrt (/ 1 x)) (sqrt -1))))
(*.f64 x (+.f64 (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) (sqrt.f64 #s(literal -1 binary64))) (*.f64 #s(literal 1/2 binary64) (/.f64 (sqrt.f64 (/.f64 (/.f64 (/.f64 #s(literal 1 binary64) x) x) x)) (sqrt.f64 #s(literal -1 binary64))))))
(* x (+ (* -1/8 (* (sqrt (/ 1 (pow x 5))) (/ 1 (pow (sqrt -1) 3)))) (+ (* 1/2 (* (sqrt (/ 1 (pow x 3))) (/ 1 (sqrt -1)))) (* (sqrt (/ 1 x)) (sqrt -1)))))
(*.f64 x (+.f64 (*.f64 #s(literal 1/2 binary64) (/.f64 (sqrt.f64 (/.f64 (/.f64 (/.f64 #s(literal 1 binary64) x) x) x)) (sqrt.f64 #s(literal -1 binary64)))) (+.f64 (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) (sqrt.f64 #s(literal -1 binary64))) (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 5 binary64)))) (*.f64 #s(literal -1/8 binary64) (/.f64 #s(literal -1 binary64) (sqrt.f64 #s(literal -1 binary64))))))))
(* x (+ (* -1/8 (* (sqrt (/ 1 (pow x 5))) (/ 1 (pow (sqrt -1) 3)))) (+ (* 1/16 (* (sqrt (/ 1 (pow x 7))) (/ 1 (pow (sqrt -1) 5)))) (+ (* 1/2 (* (sqrt (/ 1 (pow x 3))) (/ 1 (sqrt -1)))) (* (sqrt (/ 1 x)) (sqrt -1))))))
(*.f64 x (+.f64 (+.f64 (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) (sqrt.f64 #s(literal -1 binary64))) (*.f64 #s(literal 1/2 binary64) (/.f64 (sqrt.f64 (/.f64 (/.f64 (/.f64 #s(literal 1 binary64) x) x) x)) (sqrt.f64 #s(literal -1 binary64))))) (+.f64 (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 5 binary64)))) (*.f64 #s(literal -1/8 binary64) (/.f64 #s(literal -1 binary64) (sqrt.f64 #s(literal -1 binary64))))) (/.f64 (*.f64 #s(literal 1/16 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 7 binary64))))) (pow.f64 (sqrt.f64 #s(literal -1 binary64)) #s(literal 5 binary64))))))
(* -1 (* (sqrt x) (sqrt -1)))
(*.f64 (sqrt.f64 #s(literal -1 binary64)) (-.f64 #s(literal 0 binary64) (sqrt.f64 x)))
(* -1 (* x (+ (* 1/2 (* (sqrt (/ 1 (pow x 3))) (sqrt -1))) (* (sqrt (/ 1 x)) (sqrt -1)))))
(*.f64 (*.f64 (sqrt.f64 #s(literal -1 binary64)) (+.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) (*.f64 #s(literal 1/2 binary64) (sqrt.f64 (/.f64 (/.f64 (/.f64 #s(literal 1 binary64) x) x) x))))) (-.f64 #s(literal 0 binary64) x))
(* -1 (* x (+ (* -1/8 (* (sqrt (/ 1 (pow x 5))) (sqrt -1))) (+ (* 1/2 (* (sqrt (/ 1 (pow x 3))) (sqrt -1))) (* (sqrt (/ 1 x)) (sqrt -1))))))
(*.f64 (+.f64 (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 5 binary64)))) (*.f64 #s(literal -1/8 binary64) (sqrt.f64 #s(literal -1 binary64)))) (*.f64 (sqrt.f64 #s(literal -1 binary64)) (+.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) (*.f64 #s(literal 1/2 binary64) (sqrt.f64 (/.f64 (/.f64 (/.f64 #s(literal 1 binary64) x) x) x)))))) (-.f64 #s(literal 0 binary64) x))
(* -1 (* x (+ (* -1/8 (* (sqrt (/ 1 (pow x 5))) (sqrt -1))) (+ (* 1/16 (* (sqrt (/ 1 (pow x 7))) (sqrt -1))) (+ (* 1/2 (* (sqrt (/ 1 (pow x 3))) (sqrt -1))) (* (sqrt (/ 1 x)) (sqrt -1)))))))
(*.f64 x (-.f64 #s(literal 0 binary64) (+.f64 (*.f64 (sqrt.f64 #s(literal -1 binary64)) (+.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) (*.f64 #s(literal 1/2 binary64) (sqrt.f64 (/.f64 (/.f64 (/.f64 #s(literal 1 binary64) x) x) x))))) (*.f64 (sqrt.f64 #s(literal -1 binary64)) (+.f64 (*.f64 #s(literal -1/8 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 5 binary64))))) (*.f64 #s(literal 1/16 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 7 binary64))))))))))
(pow x 2)
(*.f64 x x)
(pow x 2)
(*.f64 x x)
(pow x 2)
(*.f64 x x)
(pow x 2)
(*.f64 x x)
(pow x 2)
(*.f64 x x)
(pow x 2)
(*.f64 x x)
(pow x 2)
(*.f64 x x)
(pow x 2)
(*.f64 x x)
(pow x 2)
(*.f64 x x)
(pow x 2)
(*.f64 x x)
(pow x 2)
(*.f64 x x)
(pow x 2)
(*.f64 x x)
(* -5/64 (pow x 2))
(*.f64 x (*.f64 x #s(literal -5/64 binary64)))
(* -5/64 (pow x 2))
(*.f64 x (*.f64 x #s(literal -5/64 binary64)))
(* -5/64 (pow x 2))
(*.f64 x (*.f64 x #s(literal -5/64 binary64)))
(* -5/64 (pow x 2))
(*.f64 x (*.f64 x #s(literal -5/64 binary64)))
(* -5/64 (pow x 2))
(*.f64 x (*.f64 x #s(literal -5/64 binary64)))
(* -5/64 (pow x 2))
(*.f64 x (*.f64 x #s(literal -5/64 binary64)))
(* -5/64 (pow x 2))
(*.f64 x (*.f64 x #s(literal -5/64 binary64)))
(* -5/64 (pow x 2))
(*.f64 x (*.f64 x #s(literal -5/64 binary64)))
(* -5/64 (pow x 2))
(*.f64 x (*.f64 x #s(literal -5/64 binary64)))
(* -5/64 (pow x 2))
(*.f64 x (*.f64 x #s(literal -5/64 binary64)))
(* -5/64 (pow x 2))
(*.f64 x (*.f64 x #s(literal -5/64 binary64)))
(* -5/64 (pow x 2))
(*.f64 x (*.f64 x #s(literal -5/64 binary64)))
(* -21/512 (pow x 2))
(*.f64 (*.f64 x x) #s(literal -21/512 binary64))
(* -21/512 (pow x 2))
(*.f64 (*.f64 x x) #s(literal -21/512 binary64))
(* -21/512 (pow x 2))
(*.f64 (*.f64 x x) #s(literal -21/512 binary64))
(* -21/512 (pow x 2))
(*.f64 (*.f64 x x) #s(literal -21/512 binary64))
(* -21/512 (pow x 2))
(*.f64 (*.f64 x x) #s(literal -21/512 binary64))
(* -21/512 (pow x 2))
(*.f64 (*.f64 x x) #s(literal -21/512 binary64))
(* -21/512 (pow x 2))
(*.f64 (*.f64 x x) #s(literal -21/512 binary64))
(* -21/512 (pow x 2))
(*.f64 (*.f64 x x) #s(literal -21/512 binary64))
(* -21/512 (pow x 2))
(*.f64 (*.f64 x x) #s(literal -21/512 binary64))
(* -21/512 (pow x 2))
(*.f64 (*.f64 x x) #s(literal -21/512 binary64))
(* -21/512 (pow x 2))
(*.f64 (*.f64 x x) #s(literal -21/512 binary64))
(* -21/512 (pow x 2))
(*.f64 (*.f64 x x) #s(literal -21/512 binary64))
(* -5/64 (pow x 2))
(*.f64 x (*.f64 x #s(literal -5/64 binary64)))
(* (pow x 2) (- (* -21/512 (pow x 2)) 5/64))
(*.f64 (*.f64 x x) (+.f64 #s(literal -5/64 binary64) (*.f64 (*.f64 x x) #s(literal -21/512 binary64))))
(* (pow x 2) (- (* -21/512 (pow x 2)) 5/64))
(*.f64 (*.f64 x x) (+.f64 #s(literal -5/64 binary64) (*.f64 (*.f64 x x) #s(literal -21/512 binary64))))
(* (pow x 2) (- (* -21/512 (pow x 2)) 5/64))
(*.f64 (*.f64 x x) (+.f64 #s(literal -5/64 binary64) (*.f64 (*.f64 x x) #s(literal -21/512 binary64))))
(* -21/512 (pow x 4))
(*.f64 (*.f64 (*.f64 x x) (*.f64 x x)) #s(literal -21/512 binary64))
(* -1 (* (pow x 4) (+ 21/512 (* 5/64 (/ 1 (pow x 2))))))
(*.f64 (*.f64 (*.f64 x x) (*.f64 x x)) (+.f64 #s(literal -21/512 binary64) (*.f64 #s(literal -5/64 binary64) (/.f64 (/.f64 #s(literal 1 binary64) x) x))))
(* -1 (* (pow x 4) (+ 21/512 (* 5/64 (/ 1 (pow x 2))))))
(*.f64 (*.f64 (*.f64 x x) (*.f64 x x)) (+.f64 #s(literal -21/512 binary64) (*.f64 #s(literal -5/64 binary64) (/.f64 (/.f64 #s(literal 1 binary64) x) x))))
(* -1 (* (pow x 4) (+ 21/512 (* 5/64 (/ 1 (pow x 2))))))
(*.f64 (*.f64 (*.f64 x x) (*.f64 x x)) (+.f64 #s(literal -21/512 binary64) (*.f64 #s(literal -5/64 binary64) (/.f64 (/.f64 #s(literal 1 binary64) x) x))))
(* -21/512 (pow x 4))
(*.f64 (*.f64 (*.f64 x x) (*.f64 x x)) #s(literal -21/512 binary64))
(* -1 (* (pow x 4) (+ 21/512 (* 5/64 (/ 1 (pow x 2))))))
(*.f64 (*.f64 (*.f64 x x) (*.f64 x x)) (+.f64 #s(literal -21/512 binary64) (*.f64 #s(literal -5/64 binary64) (/.f64 (/.f64 #s(literal 1 binary64) x) x))))
(* -1 (* (pow x 4) (+ 21/512 (* 5/64 (/ 1 (pow x 2))))))
(*.f64 (*.f64 (*.f64 x x) (*.f64 x x)) (+.f64 #s(literal -21/512 binary64) (*.f64 #s(literal -5/64 binary64) (/.f64 (/.f64 #s(literal 1 binary64) x) x))))
(* -1 (* (pow x 4) (+ 21/512 (* 5/64 (/ 1 (pow x 2))))))
(*.f64 (*.f64 (*.f64 x x) (*.f64 x x)) (+.f64 #s(literal -21/512 binary64) (*.f64 #s(literal -5/64 binary64) (/.f64 (/.f64 #s(literal 1 binary64) x) x))))
(* -5/64 x)
(*.f64 x #s(literal -5/64 binary64))
(* x (- (* -21/512 (pow x 2)) 5/64))
(*.f64 x (+.f64 #s(literal -5/64 binary64) (*.f64 (*.f64 x x) #s(literal -21/512 binary64))))
(* x (- (* -21/512 (pow x 2)) 5/64))
(*.f64 x (+.f64 #s(literal -5/64 binary64) (*.f64 (*.f64 x x) #s(literal -21/512 binary64))))
(* x (- (* -21/512 (pow x 2)) 5/64))
(*.f64 x (+.f64 #s(literal -5/64 binary64) (*.f64 (*.f64 x x) #s(literal -21/512 binary64))))
(* -21/512 (pow x 3))
(*.f64 (*.f64 x (*.f64 x x)) #s(literal -21/512 binary64))
(* -1 (* (pow x 3) (+ 21/512 (* 5/64 (/ 1 (pow x 2))))))
(*.f64 (*.f64 x (*.f64 x x)) (+.f64 #s(literal -21/512 binary64) (*.f64 #s(literal -5/64 binary64) (/.f64 (/.f64 #s(literal 1 binary64) x) x))))
(* -1 (* (pow x 3) (+ 21/512 (* 5/64 (/ 1 (pow x 2))))))
(*.f64 (*.f64 x (*.f64 x x)) (+.f64 #s(literal -21/512 binary64) (*.f64 #s(literal -5/64 binary64) (/.f64 (/.f64 #s(literal 1 binary64) x) x))))
(* -1 (* (pow x 3) (+ 21/512 (* 5/64 (/ 1 (pow x 2))))))
(*.f64 (*.f64 x (*.f64 x x)) (+.f64 #s(literal -21/512 binary64) (*.f64 #s(literal -5/64 binary64) (/.f64 (/.f64 #s(literal 1 binary64) x) x))))
(* -21/512 (pow x 3))
(*.f64 (*.f64 x (*.f64 x x)) #s(literal -21/512 binary64))
(* -1 (* (pow x 3) (+ 21/512 (* 5/64 (/ 1 (pow x 2))))))
(*.f64 (*.f64 x (*.f64 x x)) (+.f64 #s(literal -21/512 binary64) (*.f64 #s(literal -5/64 binary64) (/.f64 (/.f64 #s(literal 1 binary64) x) x))))
(* -1 (* (pow x 3) (+ 21/512 (* 5/64 (/ 1 (pow x 2))))))
(*.f64 (*.f64 x (*.f64 x x)) (+.f64 #s(literal -21/512 binary64) (*.f64 #s(literal -5/64 binary64) (/.f64 (/.f64 #s(literal 1 binary64) x) x))))
(* -1 (* (pow x 3) (+ 21/512 (* 5/64 (/ 1 (pow x 2))))))
(*.f64 (*.f64 x (*.f64 x x)) (+.f64 #s(literal -21/512 binary64) (*.f64 #s(literal -5/64 binary64) (/.f64 (/.f64 #s(literal 1 binary64) x) x))))

eval147.0ms (1.5%)

Compiler

Compiled 34535 to 2570 computations (92.6% saved)

prune100.0ms (1%)

Pruning

13 alts after pruning (5 fresh and 8 done)

PrunedKeptTotal
New108731090
Fresh022
Picked325
Done066
Total1090131103
Accuracy
100.0%
Counts
1103 → 13
Alt Table
Click to see full alt table
StatusAccuracyProgram
7.7%
(/.f64 (/.f64 (-.f64 (*.f64 (-.f64 #s(literal 1 binary64) (*.f64 x x)) (+.f64 #s(literal 1 binary64) (*.f64 x (+.f64 x #s(literal 1 binary64))))) (*.f64 (-.f64 #s(literal 1 binary64) x) (-.f64 #s(literal 1 binary64) (*.f64 x (*.f64 x x))))) (*.f64 (-.f64 #s(literal 1 binary64) x) (+.f64 #s(literal 1 binary64) (*.f64 x (+.f64 x #s(literal 1 binary64)))))) (+.f64 #s(literal 2 binary64) (*.f64 (*.f64 x x) (+.f64 #s(literal -1/4 binary64) (*.f64 x (*.f64 x (+.f64 #s(literal -5/64 binary64) (*.f64 (*.f64 x x) #s(literal -21/512 binary64)))))))))
7.7%
(/.f64 (/.f64 (-.f64 (*.f64 (+.f64 #s(literal 1 binary64) (*.f64 x (*.f64 x x))) (+.f64 #s(literal 1 binary64) (*.f64 x (+.f64 x #s(literal 1 binary64))))) (*.f64 (+.f64 #s(literal 1 binary64) (*.f64 x (+.f64 x #s(literal -1 binary64)))) (-.f64 #s(literal 1 binary64) (*.f64 x (*.f64 x x))))) (*.f64 (+.f64 #s(literal 1 binary64) (*.f64 x (+.f64 x #s(literal -1 binary64)))) (+.f64 #s(literal 1 binary64) (*.f64 x (+.f64 x #s(literal 1 binary64)))))) (+.f64 #s(literal 2 binary64) (*.f64 (*.f64 x x) (+.f64 #s(literal -1/4 binary64) (*.f64 x (*.f64 x (+.f64 #s(literal -5/64 binary64) (*.f64 (*.f64 x x) #s(literal -21/512 binary64)))))))))
7.8%
(/.f64 (+.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (+.f64 x (+.f64 x #s(literal -1 binary64)))))) (+.f64 #s(literal 2 binary64) (*.f64 (*.f64 x x) (+.f64 #s(literal -1/4 binary64) (*.f64 x (*.f64 x (+.f64 #s(literal -5/64 binary64) (*.f64 (*.f64 x x) #s(literal -21/512 binary64)))))))))
7.8%
(/.f64 (+.f64 #s(literal 1 binary64) (-.f64 x (-.f64 #s(literal 1 binary64) x))) (+.f64 #s(literal 2 binary64) (*.f64 (*.f64 x x) (+.f64 #s(literal -1/4 binary64) (*.f64 x (*.f64 x (+.f64 #s(literal -5/64 binary64) (*.f64 (*.f64 x x) #s(literal -21/512 binary64)))))))))
100.0%
(/.f64 (*.f64 x #s(literal 2 binary64)) (+.f64 (sqrt.f64 (+.f64 x #s(literal 1 binary64))) (sqrt.f64 (-.f64 #s(literal 1 binary64) x))))
99.9%
(/.f64 (*.f64 x #s(literal 2 binary64)) (+.f64 #s(literal 2 binary64) (*.f64 (*.f64 x x) (+.f64 #s(literal -1/4 binary64) (*.f64 (*.f64 x x) #s(literal -5/64 binary64))))))
99.9%
(/.f64 (*.f64 x #s(literal 2 binary64)) (+.f64 #s(literal 2 binary64) (*.f64 (*.f64 x x) (+.f64 #s(literal -1/4 binary64) (*.f64 x (*.f64 x (+.f64 #s(literal -5/64 binary64) (*.f64 (*.f64 x x) #s(literal -21/512 binary64)))))))))
7.7%
(-.f64 (sqrt.f64 (+.f64 #s(literal 1 binary64) x)) (sqrt.f64 (-.f64 #s(literal 1 binary64) x)))
99.9%
(+.f64 (*.f64 (+.f64 #s(literal 1/8 binary64) (*.f64 (*.f64 x x) #s(literal 7/128 binary64))) (*.f64 x (*.f64 x x))) x)
99.8%
(*.f64 (/.f64 #s(literal 2 binary64) (+.f64 #s(literal 2 binary64) (*.f64 x (*.f64 x #s(literal -1/4 binary64))))) x)
99.9%
(*.f64 x (+.f64 #s(literal 1 binary64) (*.f64 (*.f64 x x) (+.f64 #s(literal 1/8 binary64) (*.f64 x (*.f64 x (+.f64 #s(literal 7/128 binary64) (*.f64 (*.f64 x x) #s(literal 33/1024 binary64)))))))))
99.8%
(*.f64 x (+.f64 #s(literal 1 binary64) (*.f64 #s(literal 1/8 binary64) (*.f64 x x))))
99.5%
x
Compiler

Compiled 914 to 303 computations (66.8% saved)

regimes17.0ms (0.2%)

Counts
22 → 1
Calls
Call 1
Inputs
x
(*.f64 x (+.f64 #s(literal 1 binary64) (*.f64 #s(literal 1/8 binary64) (*.f64 x x))))
(*.f64 (/.f64 #s(literal 2 binary64) (+.f64 #s(literal 2 binary64) (*.f64 x (*.f64 x #s(literal -1/4 binary64))))) x)
(/.f64 (*.f64 x #s(literal 2 binary64)) (+.f64 #s(literal 2 binary64) (*.f64 (*.f64 x x) #s(literal -1/4 binary64))))
(*.f64 x (+.f64 #s(literal 1 binary64) (*.f64 (*.f64 x x) (+.f64 #s(literal 1/8 binary64) (*.f64 (*.f64 x x) #s(literal 7/128 binary64))))))
(+.f64 (*.f64 (+.f64 #s(literal 1/8 binary64) (*.f64 (*.f64 x x) #s(literal 7/128 binary64))) (*.f64 x (*.f64 x x))) x)
(/.f64 (*.f64 x #s(literal 2 binary64)) (+.f64 #s(literal 2 binary64) (*.f64 (*.f64 x x) (+.f64 #s(literal -1/4 binary64) (*.f64 (*.f64 x x) #s(literal -5/64 binary64))))))
(*.f64 x (+.f64 #s(literal 1 binary64) (*.f64 (*.f64 x x) (+.f64 #s(literal 1/8 binary64) (*.f64 x (*.f64 x (+.f64 #s(literal 7/128 binary64) (*.f64 (*.f64 x x) #s(literal 33/1024 binary64)))))))))
(/.f64 (*.f64 x #s(literal 2 binary64)) (+.f64 #s(literal 2 binary64) (*.f64 (*.f64 x x) (+.f64 #s(literal -1/4 binary64) (*.f64 x (*.f64 x (+.f64 #s(literal -5/64 binary64) (*.f64 (*.f64 x x) #s(literal -21/512 binary64)))))))))
(*.f64 x (+.f64 (+.f64 #s(literal 1 binary64) (*.f64 (*.f64 x x) #s(literal 1/8 binary64))) (*.f64 (*.f64 x x) (*.f64 (*.f64 x x) (+.f64 #s(literal 7/128 binary64) (*.f64 (*.f64 x x) #s(literal 33/1024 binary64)))))))
(/.f64 (+.f64 #s(literal 1 binary64) (-.f64 x (-.f64 #s(literal 1 binary64) x))) (+.f64 #s(literal 2 binary64) (*.f64 (*.f64 x x) (+.f64 #s(literal -1/4 binary64) (*.f64 x (*.f64 x (+.f64 #s(literal -5/64 binary64) (*.f64 (*.f64 x x) #s(literal -21/512 binary64)))))))))
(/.f64 (+.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (+.f64 x (+.f64 x #s(literal -1 binary64)))))) (+.f64 #s(literal 2 binary64) (*.f64 (*.f64 x x) (+.f64 #s(literal -1/4 binary64) (*.f64 x (*.f64 x (+.f64 #s(literal -5/64 binary64) (*.f64 (*.f64 x x) #s(literal -21/512 binary64)))))))))
(/.f64 (+.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (/.f64 (+.f64 x (-.f64 #s(literal 1 binary64) x)) (*.f64 (+.f64 x (-.f64 #s(literal 1 binary64) x)) (-.f64 x (-.f64 #s(literal 1 binary64) x)))))) (+.f64 #s(literal 2 binary64) (*.f64 (*.f64 x x) (+.f64 #s(literal -1/4 binary64) (*.f64 x (*.f64 x (+.f64 #s(literal -5/64 binary64) (*.f64 (*.f64 x x) #s(literal -21/512 binary64)))))))))
(/.f64 (/.f64 (-.f64 (*.f64 (-.f64 #s(literal 1 binary64) (*.f64 x x)) (+.f64 #s(literal 1 binary64) (*.f64 x (+.f64 x #s(literal 1 binary64))))) (*.f64 (-.f64 #s(literal 1 binary64) x) (-.f64 #s(literal 1 binary64) (*.f64 x (*.f64 x x))))) (*.f64 (-.f64 #s(literal 1 binary64) x) (+.f64 #s(literal 1 binary64) (*.f64 x (+.f64 x #s(literal 1 binary64)))))) (+.f64 #s(literal 2 binary64) (*.f64 (*.f64 x x) (+.f64 #s(literal -1/4 binary64) (*.f64 x (*.f64 x (+.f64 #s(literal -5/64 binary64) (*.f64 (*.f64 x x) #s(literal -21/512 binary64)))))))))
(/.f64 (/.f64 (-.f64 (*.f64 (+.f64 #s(literal 1 binary64) (*.f64 x (*.f64 x x))) (+.f64 #s(literal 1 binary64) (*.f64 x (+.f64 x #s(literal 1 binary64))))) (*.f64 (+.f64 #s(literal 1 binary64) (*.f64 x (+.f64 x #s(literal -1 binary64)))) (-.f64 #s(literal 1 binary64) (*.f64 x (*.f64 x x))))) (*.f64 (+.f64 #s(literal 1 binary64) (*.f64 x (+.f64 x #s(literal -1 binary64)))) (+.f64 #s(literal 1 binary64) (*.f64 x (+.f64 x #s(literal 1 binary64)))))) (+.f64 #s(literal 2 binary64) (*.f64 (*.f64 x x) (+.f64 #s(literal -1/4 binary64) (*.f64 x (*.f64 x (+.f64 #s(literal -5/64 binary64) (*.f64 (*.f64 x x) #s(literal -21/512 binary64)))))))))
(-.f64 (sqrt.f64 (+.f64 #s(literal 1 binary64) x)) (sqrt.f64 (-.f64 #s(literal 1 binary64) x)))
(/.f64 (*.f64 x #s(literal 2 binary64)) (+.f64 (sqrt.f64 (+.f64 x #s(literal 1 binary64))) (sqrt.f64 (-.f64 #s(literal 1 binary64) x))))
(/.f64 (*.f64 x #s(literal 2 binary64)) (+.f64 (pow.f64 (+.f64 #s(literal 1 binary64) x) #s(literal 1/2 binary64)) (sqrt.f64 (-.f64 #s(literal 1 binary64) x))))
(/.f64 (*.f64 x #s(literal 2 binary64)) (+.f64 (pow.f64 (+.f64 #s(literal 1 binary64) x) #s(literal 1/2 binary64)) (pow.f64 (-.f64 #s(literal 1 binary64) x) #s(literal 1/2 binary64))))
(/.f64 (+.f64 #s(literal 1 binary64) (-.f64 x (-.f64 #s(literal 1 binary64) x))) (+.f64 (pow.f64 (+.f64 #s(literal 1 binary64) x) #s(literal 1/2 binary64)) (pow.f64 (-.f64 #s(literal 1 binary64) x) #s(literal 1/2 binary64))))
(*.f64 (/.f64 #s(literal 1 binary64) (+.f64 (pow.f64 (+.f64 #s(literal 1 binary64) x) #s(literal 1/2 binary64)) (pow.f64 (-.f64 #s(literal 1 binary64) x) #s(literal 1/2 binary64)))) (+.f64 #s(literal 1 binary64) (-.f64 x (-.f64 #s(literal 1 binary64) x))))
(/.f64 (-.f64 (*.f64 (/.f64 (pow.f64 (+.f64 #s(literal 1 binary64) x) #s(literal 3/2 binary64)) (+.f64 (sqrt.f64 (*.f64 (+.f64 #s(literal 1 binary64) x) (-.f64 #s(literal 1 binary64) x))) (+.f64 #s(literal 1 binary64) (+.f64 x (-.f64 #s(literal 1 binary64) x))))) (/.f64 (pow.f64 (+.f64 #s(literal 1 binary64) x) #s(literal 3/2 binary64)) (+.f64 (sqrt.f64 (*.f64 (+.f64 #s(literal 1 binary64) x) (-.f64 #s(literal 1 binary64) x))) (+.f64 #s(literal 1 binary64) (+.f64 x (-.f64 #s(literal 1 binary64) x)))))) (*.f64 (/.f64 (pow.f64 (-.f64 #s(literal 1 binary64) x) #s(literal 3/2 binary64)) (+.f64 (sqrt.f64 (*.f64 (+.f64 #s(literal 1 binary64) x) (-.f64 #s(literal 1 binary64) x))) (+.f64 #s(literal 1 binary64) (+.f64 x (-.f64 #s(literal 1 binary64) x))))) (/.f64 (pow.f64 (-.f64 #s(literal 1 binary64) x) #s(literal 3/2 binary64)) (+.f64 (sqrt.f64 (*.f64 (+.f64 #s(literal 1 binary64) x) (-.f64 #s(literal 1 binary64) x))) (+.f64 #s(literal 1 binary64) (+.f64 x (-.f64 #s(literal 1 binary64) x))))))) (+.f64 (/.f64 (pow.f64 (+.f64 #s(literal 1 binary64) x) #s(literal 3/2 binary64)) (+.f64 (sqrt.f64 (*.f64 (+.f64 #s(literal 1 binary64) x) (-.f64 #s(literal 1 binary64) x))) (+.f64 #s(literal 1 binary64) (+.f64 x (-.f64 #s(literal 1 binary64) x))))) (/.f64 (pow.f64 (-.f64 #s(literal 1 binary64) x) #s(literal 3/2 binary64)) (+.f64 (sqrt.f64 (*.f64 (+.f64 #s(literal 1 binary64) x) (-.f64 #s(literal 1 binary64) x))) (+.f64 #s(literal 1 binary64) (+.f64 x (-.f64 #s(literal 1 binary64) x)))))))
Outputs
(/.f64 (*.f64 x #s(literal 2 binary64)) (+.f64 (sqrt.f64 (+.f64 x #s(literal 1 binary64))) (sqrt.f64 (-.f64 #s(literal 1 binary64) x))))
Calls

2 calls:

7.0ms
(-.f64 (sqrt.f64 (+.f64 #s(literal 1 binary64) x)) (sqrt.f64 (-.f64 #s(literal 1 binary64) x)))
6.0ms
x
Results
AccuracySegmentsBranch
100.0%1x
100.0%1(-.f64 (sqrt.f64 (+.f64 #s(literal 1 binary64) x)) (sqrt.f64 (-.f64 #s(literal 1 binary64) x)))
Compiler

Compiled 12 to 8 computations (33.3% saved)

regimes10.0ms (0.1%)

Counts
16 → 1
Calls
Call 1
Inputs
x
(*.f64 x (+.f64 #s(literal 1 binary64) (*.f64 #s(literal 1/8 binary64) (*.f64 x x))))
(*.f64 (/.f64 #s(literal 2 binary64) (+.f64 #s(literal 2 binary64) (*.f64 x (*.f64 x #s(literal -1/4 binary64))))) x)
(/.f64 (*.f64 x #s(literal 2 binary64)) (+.f64 #s(literal 2 binary64) (*.f64 (*.f64 x x) #s(literal -1/4 binary64))))
(*.f64 x (+.f64 #s(literal 1 binary64) (*.f64 (*.f64 x x) (+.f64 #s(literal 1/8 binary64) (*.f64 (*.f64 x x) #s(literal 7/128 binary64))))))
(+.f64 (*.f64 (+.f64 #s(literal 1/8 binary64) (*.f64 (*.f64 x x) #s(literal 7/128 binary64))) (*.f64 x (*.f64 x x))) x)
(/.f64 (*.f64 x #s(literal 2 binary64)) (+.f64 #s(literal 2 binary64) (*.f64 (*.f64 x x) (+.f64 #s(literal -1/4 binary64) (*.f64 (*.f64 x x) #s(literal -5/64 binary64))))))
(*.f64 x (+.f64 #s(literal 1 binary64) (*.f64 (*.f64 x x) (+.f64 #s(literal 1/8 binary64) (*.f64 x (*.f64 x (+.f64 #s(literal 7/128 binary64) (*.f64 (*.f64 x x) #s(literal 33/1024 binary64)))))))))
(/.f64 (*.f64 x #s(literal 2 binary64)) (+.f64 #s(literal 2 binary64) (*.f64 (*.f64 x x) (+.f64 #s(literal -1/4 binary64) (*.f64 x (*.f64 x (+.f64 #s(literal -5/64 binary64) (*.f64 (*.f64 x x) #s(literal -21/512 binary64)))))))))
(*.f64 x (+.f64 (+.f64 #s(literal 1 binary64) (*.f64 (*.f64 x x) #s(literal 1/8 binary64))) (*.f64 (*.f64 x x) (*.f64 (*.f64 x x) (+.f64 #s(literal 7/128 binary64) (*.f64 (*.f64 x x) #s(literal 33/1024 binary64)))))))
(/.f64 (+.f64 #s(literal 1 binary64) (-.f64 x (-.f64 #s(literal 1 binary64) x))) (+.f64 #s(literal 2 binary64) (*.f64 (*.f64 x x) (+.f64 #s(literal -1/4 binary64) (*.f64 x (*.f64 x (+.f64 #s(literal -5/64 binary64) (*.f64 (*.f64 x x) #s(literal -21/512 binary64)))))))))
(/.f64 (+.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (+.f64 x (+.f64 x #s(literal -1 binary64)))))) (+.f64 #s(literal 2 binary64) (*.f64 (*.f64 x x) (+.f64 #s(literal -1/4 binary64) (*.f64 x (*.f64 x (+.f64 #s(literal -5/64 binary64) (*.f64 (*.f64 x x) #s(literal -21/512 binary64)))))))))
(/.f64 (+.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (/.f64 (+.f64 x (-.f64 #s(literal 1 binary64) x)) (*.f64 (+.f64 x (-.f64 #s(literal 1 binary64) x)) (-.f64 x (-.f64 #s(literal 1 binary64) x)))))) (+.f64 #s(literal 2 binary64) (*.f64 (*.f64 x x) (+.f64 #s(literal -1/4 binary64) (*.f64 x (*.f64 x (+.f64 #s(literal -5/64 binary64) (*.f64 (*.f64 x x) #s(literal -21/512 binary64)))))))))
(/.f64 (/.f64 (-.f64 (*.f64 (-.f64 #s(literal 1 binary64) (*.f64 x x)) (+.f64 #s(literal 1 binary64) (*.f64 x (+.f64 x #s(literal 1 binary64))))) (*.f64 (-.f64 #s(literal 1 binary64) x) (-.f64 #s(literal 1 binary64) (*.f64 x (*.f64 x x))))) (*.f64 (-.f64 #s(literal 1 binary64) x) (+.f64 #s(literal 1 binary64) (*.f64 x (+.f64 x #s(literal 1 binary64)))))) (+.f64 #s(literal 2 binary64) (*.f64 (*.f64 x x) (+.f64 #s(literal -1/4 binary64) (*.f64 x (*.f64 x (+.f64 #s(literal -5/64 binary64) (*.f64 (*.f64 x x) #s(literal -21/512 binary64)))))))))
(/.f64 (/.f64 (-.f64 (*.f64 (+.f64 #s(literal 1 binary64) (*.f64 x (*.f64 x x))) (+.f64 #s(literal 1 binary64) (*.f64 x (+.f64 x #s(literal 1 binary64))))) (*.f64 (+.f64 #s(literal 1 binary64) (*.f64 x (+.f64 x #s(literal -1 binary64)))) (-.f64 #s(literal 1 binary64) (*.f64 x (*.f64 x x))))) (*.f64 (+.f64 #s(literal 1 binary64) (*.f64 x (+.f64 x #s(literal -1 binary64)))) (+.f64 #s(literal 1 binary64) (*.f64 x (+.f64 x #s(literal 1 binary64)))))) (+.f64 #s(literal 2 binary64) (*.f64 (*.f64 x x) (+.f64 #s(literal -1/4 binary64) (*.f64 x (*.f64 x (+.f64 #s(literal -5/64 binary64) (*.f64 (*.f64 x x) #s(literal -21/512 binary64)))))))))
(-.f64 (sqrt.f64 (+.f64 #s(literal 1 binary64) x)) (sqrt.f64 (-.f64 #s(literal 1 binary64) x)))
Outputs
(/.f64 (*.f64 x #s(literal 2 binary64)) (+.f64 #s(literal 2 binary64) (*.f64 (*.f64 x x) (+.f64 #s(literal -1/4 binary64) (*.f64 x (*.f64 x (+.f64 #s(literal -5/64 binary64) (*.f64 (*.f64 x x) #s(literal -21/512 binary64)))))))))
Calls

2 calls:

5.0ms
x
4.0ms
(-.f64 (sqrt.f64 (+.f64 #s(literal 1 binary64) x)) (sqrt.f64 (-.f64 #s(literal 1 binary64) x)))
Results
AccuracySegmentsBranch
99.9%1x
99.9%1(-.f64 (sqrt.f64 (+.f64 #s(literal 1 binary64) x)) (sqrt.f64 (-.f64 #s(literal 1 binary64) x)))
Compiler

Compiled 12 to 8 computations (33.3% saved)

regimes3.0ms (0%)

Counts
8 → 1
Calls
Call 1
Inputs
x
(*.f64 x (+.f64 #s(literal 1 binary64) (*.f64 #s(literal 1/8 binary64) (*.f64 x x))))
(*.f64 (/.f64 #s(literal 2 binary64) (+.f64 #s(literal 2 binary64) (*.f64 x (*.f64 x #s(literal -1/4 binary64))))) x)
(/.f64 (*.f64 x #s(literal 2 binary64)) (+.f64 #s(literal 2 binary64) (*.f64 (*.f64 x x) #s(literal -1/4 binary64))))
(*.f64 x (+.f64 #s(literal 1 binary64) (*.f64 (*.f64 x x) (+.f64 #s(literal 1/8 binary64) (*.f64 (*.f64 x x) #s(literal 7/128 binary64))))))
(+.f64 (*.f64 (+.f64 #s(literal 1/8 binary64) (*.f64 (*.f64 x x) #s(literal 7/128 binary64))) (*.f64 x (*.f64 x x))) x)
(/.f64 (*.f64 x #s(literal 2 binary64)) (+.f64 #s(literal 2 binary64) (*.f64 (*.f64 x x) (+.f64 #s(literal -1/4 binary64) (*.f64 (*.f64 x x) #s(literal -5/64 binary64))))))
(*.f64 x (+.f64 #s(literal 1 binary64) (*.f64 (*.f64 x x) (+.f64 #s(literal 1/8 binary64) (*.f64 x (*.f64 x (+.f64 #s(literal 7/128 binary64) (*.f64 (*.f64 x x) #s(literal 33/1024 binary64)))))))))
Outputs
(*.f64 x (+.f64 #s(literal 1 binary64) (*.f64 (*.f64 x x) (+.f64 #s(literal 1/8 binary64) (*.f64 x (*.f64 x (+.f64 #s(literal 7/128 binary64) (*.f64 (*.f64 x x) #s(literal 33/1024 binary64)))))))))
Calls

1 calls:

3.0ms
x
Results
AccuracySegmentsBranch
99.9%1x
Compiler

Compiled 2 to 1 computations (50% saved)

regimes8.0ms (0.1%)

Counts
7 → 1
Calls
Call 1
Inputs
x
(*.f64 x (+.f64 #s(literal 1 binary64) (*.f64 #s(literal 1/8 binary64) (*.f64 x x))))
(*.f64 (/.f64 #s(literal 2 binary64) (+.f64 #s(literal 2 binary64) (*.f64 x (*.f64 x #s(literal -1/4 binary64))))) x)
(/.f64 (*.f64 x #s(literal 2 binary64)) (+.f64 #s(literal 2 binary64) (*.f64 (*.f64 x x) #s(literal -1/4 binary64))))
(*.f64 x (+.f64 #s(literal 1 binary64) (*.f64 (*.f64 x x) (+.f64 #s(literal 1/8 binary64) (*.f64 (*.f64 x x) #s(literal 7/128 binary64))))))
(+.f64 (*.f64 (+.f64 #s(literal 1/8 binary64) (*.f64 (*.f64 x x) #s(literal 7/128 binary64))) (*.f64 x (*.f64 x x))) x)
(/.f64 (*.f64 x #s(literal 2 binary64)) (+.f64 #s(literal 2 binary64) (*.f64 (*.f64 x x) (+.f64 #s(literal -1/4 binary64) (*.f64 (*.f64 x x) #s(literal -5/64 binary64))))))
Outputs
(/.f64 (*.f64 x #s(literal 2 binary64)) (+.f64 #s(literal 2 binary64) (*.f64 (*.f64 x x) (+.f64 #s(literal -1/4 binary64) (*.f64 (*.f64 x x) #s(literal -5/64 binary64))))))
Calls

1 calls:

7.0ms
x
Results
AccuracySegmentsBranch
99.9%1x
Compiler

Compiled 2 to 1 computations (50% saved)

regimes3.0ms (0%)

Counts
6 → 1
Calls
Call 1
Inputs
x
(*.f64 x (+.f64 #s(literal 1 binary64) (*.f64 #s(literal 1/8 binary64) (*.f64 x x))))
(*.f64 (/.f64 #s(literal 2 binary64) (+.f64 #s(literal 2 binary64) (*.f64 x (*.f64 x #s(literal -1/4 binary64))))) x)
(/.f64 (*.f64 x #s(literal 2 binary64)) (+.f64 #s(literal 2 binary64) (*.f64 (*.f64 x x) #s(literal -1/4 binary64))))
(*.f64 x (+.f64 #s(literal 1 binary64) (*.f64 (*.f64 x x) (+.f64 #s(literal 1/8 binary64) (*.f64 (*.f64 x x) #s(literal 7/128 binary64))))))
(+.f64 (*.f64 (+.f64 #s(literal 1/8 binary64) (*.f64 (*.f64 x x) #s(literal 7/128 binary64))) (*.f64 x (*.f64 x x))) x)
Outputs
(+.f64 (*.f64 (+.f64 #s(literal 1/8 binary64) (*.f64 (*.f64 x x) #s(literal 7/128 binary64))) (*.f64 x (*.f64 x x))) x)
Calls

1 calls:

2.0ms
x
Results
AccuracySegmentsBranch
99.9%1x
Compiler

Compiled 2 to 1 computations (50% saved)

regimes3.0ms (0%)

Counts
5 → 1
Calls
Call 1
Inputs
x
(*.f64 x (+.f64 #s(literal 1 binary64) (*.f64 #s(literal 1/8 binary64) (*.f64 x x))))
(*.f64 (/.f64 #s(literal 2 binary64) (+.f64 #s(literal 2 binary64) (*.f64 x (*.f64 x #s(literal -1/4 binary64))))) x)
(/.f64 (*.f64 x #s(literal 2 binary64)) (+.f64 #s(literal 2 binary64) (*.f64 (*.f64 x x) #s(literal -1/4 binary64))))
(*.f64 x (+.f64 #s(literal 1 binary64) (*.f64 (*.f64 x x) (+.f64 #s(literal 1/8 binary64) (*.f64 (*.f64 x x) #s(literal 7/128 binary64))))))
Outputs
(*.f64 x (+.f64 #s(literal 1 binary64) (*.f64 (*.f64 x x) (+.f64 #s(literal 1/8 binary64) (*.f64 (*.f64 x x) #s(literal 7/128 binary64))))))
Calls

1 calls:

2.0ms
x
Results
AccuracySegmentsBranch
99.9%1x
Compiler

Compiled 2 to 1 computations (50% saved)

regimes2.0ms (0%)

Counts
4 → 1
Calls
Call 1
Inputs
x
(*.f64 x (+.f64 #s(literal 1 binary64) (*.f64 #s(literal 1/8 binary64) (*.f64 x x))))
(*.f64 (/.f64 #s(literal 2 binary64) (+.f64 #s(literal 2 binary64) (*.f64 x (*.f64 x #s(literal -1/4 binary64))))) x)
(/.f64 (*.f64 x #s(literal 2 binary64)) (+.f64 #s(literal 2 binary64) (*.f64 (*.f64 x x) #s(literal -1/4 binary64))))
Outputs
(*.f64 (/.f64 #s(literal 2 binary64) (+.f64 #s(literal 2 binary64) (*.f64 x (*.f64 x #s(literal -1/4 binary64))))) x)
Calls

1 calls:

2.0ms
x
Results
AccuracySegmentsBranch
99.8%1x
Compiler

Compiled 2 to 1 computations (50% saved)

regimes2.0ms (0%)

Counts
2 → 1
Calls
Call 1
Inputs
x
(*.f64 x (+.f64 #s(literal 1 binary64) (*.f64 #s(literal 1/8 binary64) (*.f64 x x))))
Outputs
(*.f64 x (+.f64 #s(literal 1 binary64) (*.f64 #s(literal 1/8 binary64) (*.f64 x x))))
Calls

1 calls:

1.0ms
x
Results
AccuracySegmentsBranch
99.8%1x
Compiler

Compiled 2 to 1 computations (50% saved)

regimes1.0ms (0%)

Accuracy

Total 0.0b remaining (0%)

Threshold costs 0b (0%)

Counts
1 → 1
Calls
Call 1
Inputs
x
Outputs
x
Calls

1 calls:

1.0ms
x
Results
AccuracySegmentsBranch
99.5%1x
Compiler

Compiled 2 to 1 computations (50% saved)

simplify10.0ms (0.1%)

Algorithm
egg-herbie
Rules
46×*-commutative_binary64
34×+-commutative_binary64
sub-neg_binary64
1-exp_binary64
neg-sub0_binary64
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
054125
196125
2100125
3102125
4103125
Stop Event
saturated
Calls
Call 1
Inputs
(/.f64 (*.f64 x #s(literal 2 binary64)) (+.f64 (sqrt.f64 (+.f64 x #s(literal 1 binary64))) (sqrt.f64 (-.f64 #s(literal 1 binary64) x))))
(/.f64 (*.f64 x #s(literal 2 binary64)) (+.f64 #s(literal 2 binary64) (*.f64 (*.f64 x x) (+.f64 #s(literal -1/4 binary64) (*.f64 x (*.f64 x (+.f64 #s(literal -5/64 binary64) (*.f64 (*.f64 x x) #s(literal -21/512 binary64)))))))))
(*.f64 x (+.f64 #s(literal 1 binary64) (*.f64 (*.f64 x x) (+.f64 #s(literal 1/8 binary64) (*.f64 x (*.f64 x (+.f64 #s(literal 7/128 binary64) (*.f64 (*.f64 x x) #s(literal 33/1024 binary64)))))))))
(/.f64 (*.f64 x #s(literal 2 binary64)) (+.f64 #s(literal 2 binary64) (*.f64 (*.f64 x x) (+.f64 #s(literal -1/4 binary64) (*.f64 (*.f64 x x) #s(literal -5/64 binary64))))))
(+.f64 (*.f64 (+.f64 #s(literal 1/8 binary64) (*.f64 (*.f64 x x) #s(literal 7/128 binary64))) (*.f64 x (*.f64 x x))) x)
(*.f64 x (+.f64 #s(literal 1 binary64) (*.f64 (*.f64 x x) (+.f64 #s(literal 1/8 binary64) (*.f64 (*.f64 x x) #s(literal 7/128 binary64))))))
(*.f64 (/.f64 #s(literal 2 binary64) (+.f64 #s(literal 2 binary64) (*.f64 x (*.f64 x #s(literal -1/4 binary64))))) x)
(*.f64 x (+.f64 #s(literal 1 binary64) (*.f64 #s(literal 1/8 binary64) (*.f64 x x))))
x
Outputs
(/.f64 (*.f64 x #s(literal 2 binary64)) (+.f64 (sqrt.f64 (+.f64 x #s(literal 1 binary64))) (sqrt.f64 (-.f64 #s(literal 1 binary64) x))))
(/.f64 (*.f64 x #s(literal 2 binary64)) (+.f64 #s(literal 2 binary64) (*.f64 (*.f64 x x) (+.f64 #s(literal -1/4 binary64) (*.f64 x (*.f64 x (+.f64 #s(literal -5/64 binary64) (*.f64 (*.f64 x x) #s(literal -21/512 binary64)))))))))
(*.f64 x (+.f64 #s(literal 1 binary64) (*.f64 (*.f64 x x) (+.f64 #s(literal 1/8 binary64) (*.f64 x (*.f64 x (+.f64 #s(literal 7/128 binary64) (*.f64 (*.f64 x x) #s(literal 33/1024 binary64)))))))))
(/.f64 (*.f64 x #s(literal 2 binary64)) (+.f64 #s(literal 2 binary64) (*.f64 (*.f64 x x) (+.f64 #s(literal -1/4 binary64) (*.f64 (*.f64 x x) #s(literal -5/64 binary64))))))
(+.f64 (*.f64 (+.f64 #s(literal 1/8 binary64) (*.f64 (*.f64 x x) #s(literal 7/128 binary64))) (*.f64 x (*.f64 x x))) x)
(+.f64 x (*.f64 (+.f64 #s(literal 1/8 binary64) (*.f64 (*.f64 x x) #s(literal 7/128 binary64))) (*.f64 x (*.f64 x x))))
(*.f64 x (+.f64 #s(literal 1 binary64) (*.f64 (*.f64 x x) (+.f64 #s(literal 1/8 binary64) (*.f64 (*.f64 x x) #s(literal 7/128 binary64))))))
(*.f64 (/.f64 #s(literal 2 binary64) (+.f64 #s(literal 2 binary64) (*.f64 x (*.f64 x #s(literal -1/4 binary64))))) x)
(*.f64 x (/.f64 #s(literal 2 binary64) (+.f64 #s(literal 2 binary64) (*.f64 x (*.f64 x #s(literal -1/4 binary64))))))
(*.f64 x (+.f64 #s(literal 1 binary64) (*.f64 #s(literal 1/8 binary64) (*.f64 x x))))
(*.f64 x (+.f64 #s(literal 1 binary64) (*.f64 (*.f64 x x) #s(literal 1/8 binary64))))
x

soundness2.1s (20.9%)

Rules
5918×*-lowering-*.f32
5918×*-lowering-*.f64
5894×*-lowering-*.f32
5894×*-lowering-*.f64
4834×*-lowering-*.f32
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
04063523
113692939
253762894
080982894
03393050
111382475
245272386
081302386
031171
1238145
22376140
08486140
038257
1286187
22734183
08439183
0720
14620
238920
3620920
0843520
0161826
1528727
22050693
08755693
041202
1302179
22896176
08238176
Stop Event
fuel
iter limit
node limit
iter limit
node limit
iter limit
node limit
iter limit
node limit
iter limit
node limit
iter limit
node limit
iter limit
node limit
Compiler

Compiled 447 to 256 computations (42.7% saved)

preprocess67.0ms (0.7%)

Remove

(negabs x)

Compiler

Compiled 412 to 222 computations (46.1% saved)

end0.0ms (0%)

Profiling

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