2isqrt (example 3.6)

Time bar (total: 6.8s)

start0.0ms (0%)

Memory
0.0MiB live, 0.0MiB allocated

analyze2.0ms (0%)

Memory
3.0MiB live, 3.0MiB allocated
Algorithm
search
Search
ProbabilityValidUnknownPreconditionInfiniteDomainCan'tIter
0%0%25%75%0%0%0%0
0%0%25%75%0%0%0%1
50%12.5%12.5%75%0%0%0%2
75%18.7%6.2%75%0%0%0%3
87.5%21.9%3.1%75%0%0%0%4
93.8%23.4%1.6%75%0%0%0%5
96.9%24.2%0.8%75%0%0%0%6
98.4%24.6%0.4%75%0%0%0%7
99.2%24.8%0.2%75%0%0%0%8
99.6%24.9%0.1%75%0%0%0%9
99.8%24.9%0%75%0%0%0%10
99.9%25%0%75%0%0%0%11
100%25%0%75%0%0%0%12
Compiler

Compiled 19 to 13 computations (31.6% saved)

sample2.2s (32.3%)

Memory
101.9MiB live, 1 829.7MiB allocated
Samples
1.2s6 448×1valid
438.0ms1 685×2valid
9.0ms123×0valid
Precisions
Click to see histograms. Total time spent on operations: 1.4s
ival-sqrt: 383.0ms (26.8% of total)
ival-div: 332.0ms (23.2% of total)
adjust: 324.0ms (22.6% of total)
const: 120.0ms (8.4% of total)
ival-add: 102.0ms (7.1% of total)
ival-sub: 77.0ms (5.4% of total)
ival-<: 48.0ms (3.4% of total)
ival->: 23.0ms (1.6% of total)
ival-and: 12.0ms (0.8% of total)
exact: 7.0ms (0.5% of total)
ival-assert: 3.0ms (0.2% of total)
Bogosity

explain153.0ms (2.2%)

Memory
10.2MiB live, 196.3MiB allocated
FPErrors
Click to see full error table
Ground TruthOverpredictionsExampleUnderpredictionsExampleSubexpression
1760-0-(-.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 x)) (/.f64 #s(literal 1 binary64) (sqrt.f64 (+.f64 x #s(literal 1 binary64)))))
00-0-(+.f64 x #s(literal 1 binary64))
00-0-(sqrt.f64 x)
00-0-(/.f64 #s(literal 1 binary64) (sqrt.f64 x))
00-0-(/.f64 #s(literal 1 binary64) (sqrt.f64 (+.f64 x #s(literal 1 binary64))))
00-0-#s(literal 1 binary64)
00-0-(sqrt.f64 (+.f64 x #s(literal 1 binary64)))
00-0-x
Explanations
Click to see full explanations table
OperatorSubexpressionExplanationCount
-.f64(-.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 x)) (/.f64 #s(literal 1 binary64) (sqrt.f64 (+.f64 x #s(literal 1 binary64)))))cancellation1760
Confusion
Predicted +Predicted -
+1760
-080
Precision
1.0
Recall
1.0
Confusion?
Predicted +Predicted MaybePredicted -
+17600
-0080
Precision?
1.0
Recall?
1.0
Freqs
test
numberfreq
080
1176
Total Confusion?
Predicted +Predicted MaybePredicted -
+100
-000
Precision?
1.0
Recall?
1.0
Samples
63.0ms424×1valid
18.0ms82×2valid
0.0ms0valid
Compiler

Compiled 79 to 28 computations (64.6% saved)

Precisions
Click to see histograms. Total time spent on operations: 60.0ms
ival-sqrt: 19.0ms (31.6% of total)
adjust: 15.0ms (24.9% of total)
ival-div: 14.0ms (23.2% of total)
ival-add: 6.0ms (10% of total)
ival-sub: 5.0ms (8.3% of total)
ival-assert: 0.0ms (0% of total)
ival-true: 0.0ms (0% of total)
exact: 0.0ms (0% of total)

preprocess88.0ms (1.3%)

Memory
-33.5MiB live, 17.6MiB allocated
Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
01027
11327
0811
01411
11711
01711
Stop Event
iter limit
saturated
iter limit
saturated
Calls
Call 1
Inputs
(-.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 x)) (/.f64 #s(literal 1 binary64) (sqrt.f64 (+.f64 x #s(literal 1 binary64)))))
Outputs
(-.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 x)) (/.f64 #s(literal 1 binary64) (sqrt.f64 (+.f64 x #s(literal 1 binary64)))))
Compiler

Compiled 11 to 8 computations (27.3% saved)

eval0.0ms (0%)

Memory
0.1MiB live, 0.1MiB allocated
Compiler

Compiled 0 to 1 computations (-∞% saved)

prune0.0ms (0%)

Memory
0.7MiB live, 0.7MiB allocated
Alt Table
Click to see full alt table
StatusAccuracyProgram
37.3%
(-.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 x)) (/.f64 #s(literal 1 binary64) (sqrt.f64 (+.f64 x #s(literal 1 binary64)))))
Compiler

Compiled 11 to 8 computations (27.3% saved)

simplify3.0ms (0%)

Memory
3.8MiB live, 3.8MiB allocated
Algorithm
egg-herbie
Localize:

Found 4 expressions of interest:

NewMetricScoreProgram
cost-diff0
(/.f64 #s(literal 1 binary64) (sqrt.f64 (+.f64 x #s(literal 1 binary64))))
cost-diff0
(sqrt.f64 x)
cost-diff0
(/.f64 #s(literal 1 binary64) (sqrt.f64 x))
cost-diff0
(-.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 x)) (/.f64 #s(literal 1 binary64) (sqrt.f64 (+.f64 x #s(literal 1 binary64)))))
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
0832
01432
11732
01732
Stop Event
iter limit
saturated
iter limit
Calls
Call 1
Inputs
(-.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 x)) (/.f64 #s(literal 1 binary64) (sqrt.f64 (+.f64 x #s(literal 1 binary64)))))
(/.f64 #s(literal 1 binary64) (sqrt.f64 x))
#s(literal 1 binary64)
(sqrt.f64 x)
x
(/.f64 #s(literal 1 binary64) (sqrt.f64 (+.f64 x #s(literal 1 binary64))))
(sqrt.f64 (+.f64 x #s(literal 1 binary64)))
(+.f64 x #s(literal 1 binary64))
Outputs
(-.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 x)) (/.f64 #s(literal 1 binary64) (sqrt.f64 (+.f64 x #s(literal 1 binary64)))))
(/.f64 #s(literal 1 binary64) (sqrt.f64 x))
#s(literal 1 binary64)
(sqrt.f64 x)
x
(/.f64 #s(literal 1 binary64) (sqrt.f64 (+.f64 x #s(literal 1 binary64))))
(sqrt.f64 (+.f64 x #s(literal 1 binary64)))
(+.f64 x #s(literal 1 binary64))

localize54.0ms (0.8%)

Memory
14.8MiB live, 63.7MiB allocated
Localize:

Found 4 expressions of interest:

NewMetricScoreProgram
accuracy0.0
(sqrt.f64 x)
accuracy0.25390625
(/.f64 #s(literal 1 binary64) (sqrt.f64 (+.f64 x #s(literal 1 binary64))))
accuracy0.25390625
(/.f64 #s(literal 1 binary64) (sqrt.f64 x))
accuracy40.095069924531046
(-.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 x)) (/.f64 #s(literal 1 binary64) (sqrt.f64 (+.f64 x #s(literal 1 binary64)))))
Samples
37.0ms212×1valid
9.0ms41×2valid
0.0ms0valid
Compiler

Compiled 34 to 10 computations (70.6% saved)

Precisions
Click to see histograms. Total time spent on operations: 35.0ms
ival-sqrt: 15.0ms (43% of total)
adjust: 8.0ms (22.9% of total)
ival-div: 7.0ms (20.1% of total)
ival-add: 3.0ms (8.6% of total)
ival-sub: 2.0ms (5.7% of total)
ival-assert: 0.0ms (0% of total)
ival-true: 0.0ms (0% of total)
exact: 0.0ms (0% of total)

series5.0ms (0.1%)

Memory
8.4MiB live, 8.4MiB allocated
Counts
4 → 25
Calls
Call 1
Inputs
(-.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 x)) (/.f64 #s(literal 1 binary64) (sqrt.f64 (+.f64 x #s(literal 1 binary64)))))
(/.f64 #s(literal 1 binary64) (sqrt.f64 x))
(sqrt.f64 x)
(/.f64 #s(literal 1 binary64) (sqrt.f64 (+.f64 x #s(literal 1 binary64))))
Outputs
(sqrt (/ 1 x))
(/ (+ (sqrt x) (* -1 x)) x)
(/ (+ (sqrt x) (* x (- (* 1/2 x) 1))) x)
(/ (+ (sqrt x) (* x (- (* x (+ 1/2 (* -3/8 x))) 1))) x)
(sqrt x)
1
(+ 1 (* -1/2 x))
(+ 1 (* x (- (* 3/8 x) 1/2)))
(+ 1 (* x (- (* x (+ 3/8 (* -5/16 x))) 1/2)))
(* 1/2 (sqrt (/ 1 (pow x 3))))
(/ (- (* -1/2 (sqrt (/ 1 x))) (* -1/2 (sqrt x))) (pow x 2))
(/ (- (* 1/2 (* (sqrt (/ 1 (pow x 3))) (+ 1 (* 1/4 x)))) (+ (* -1/2 (sqrt x)) (* 1/2 (sqrt (/ 1 x))))) (pow x 2))
(/ (- (* -1/2 (* (sqrt (/ 1 (pow x 5))) (+ 1 (* 1/2 x)))) (+ (* -1/2 (sqrt x)) (+ (* -1/2 (* (sqrt (/ 1 (pow x 3))) (+ 1 (* 1/4 x)))) (* 1/2 (sqrt (/ 1 x)))))) (pow x 2))
(+ (sqrt (/ 1 x)) (* -1/2 (sqrt (/ 1 (pow x 3)))))
(+ (sqrt (/ 1 x)) (+ (* -1/2 (sqrt (/ 1 (pow x 3)))) (* 1/2 (sqrt (/ 1 (pow x 5))))))
(+ (sqrt (/ 1 x)) (+ (* -1/2 (sqrt (/ 1 (pow x 3)))) (+ (* -1/2 (* (sqrt (/ 1 (pow x 7))) (+ 1 (* 1/4 x)))) (* 1/2 (sqrt (/ 1 (pow x 5)))))))
(- (sqrt (/ 1 x)) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)))
(- (+ (sqrt (/ 1 x)) (* 1/2 (sqrt (/ 1 (pow x 3))))) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)))
(- (+ (sqrt (/ 1 x)) (* -1/2 (sqrt (/ 1 (pow x 5))))) (+ (* -1/2 (sqrt (/ 1 (pow x 3)))) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))))
(- (+ (sqrt (/ 1 x)) (* -1 (/ (- (* -1/2 (* (sqrt (/ 1 x)) (+ 1 (* -1/4 (/ x (pow (sqrt -1) 2)))))) (* -1/2 (sqrt x))) (pow x 3)))) (+ (* -1/2 (sqrt (/ 1 (pow x 3)))) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))))
(* -1 (* (sqrt x) (pow (sqrt -1) 2)))
(* (sqrt (/ 1 x)) (pow (sqrt -1) 2))
(+ (* -1/2 (sqrt (/ 1 (pow x 3)))) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)))
(+ (* -1/2 (sqrt (/ 1 (pow x 3)))) (+ (* 1/2 (sqrt (/ 1 (pow x 5)))) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))))
(+ (* -1 (/ (+ (* -1/2 (sqrt x)) (* 1/2 (* (sqrt (/ 1 x)) (+ 1 (* -1/4 (/ x (pow (sqrt -1) 2))))))) (pow x 3))) (+ (* -1/2 (sqrt (/ 1 (pow x 3)))) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))))
Calls

3 calls:

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

simplify139.0ms (2%)

Memory
-7.4MiB live, 222.1MiB allocated
Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
0114457
1333395
21237369
36312369
08119348
Stop Event
iter limit
node limit
Counts
25 → 25
Calls
Call 1
Inputs
(sqrt (/ 1 x))
(/ (+ (sqrt x) (* -1 x)) x)
(/ (+ (sqrt x) (* x (- (* 1/2 x) 1))) x)
(/ (+ (sqrt x) (* x (- (* x (+ 1/2 (* -3/8 x))) 1))) x)
(sqrt x)
1
(+ 1 (* -1/2 x))
(+ 1 (* x (- (* 3/8 x) 1/2)))
(+ 1 (* x (- (* x (+ 3/8 (* -5/16 x))) 1/2)))
(* 1/2 (sqrt (/ 1 (pow x 3))))
(/ (- (* -1/2 (sqrt (/ 1 x))) (* -1/2 (sqrt x))) (pow x 2))
(/ (- (* 1/2 (* (sqrt (/ 1 (pow x 3))) (+ 1 (* 1/4 x)))) (+ (* -1/2 (sqrt x)) (* 1/2 (sqrt (/ 1 x))))) (pow x 2))
(/ (- (* -1/2 (* (sqrt (/ 1 (pow x 5))) (+ 1 (* 1/2 x)))) (+ (* -1/2 (sqrt x)) (+ (* -1/2 (* (sqrt (/ 1 (pow x 3))) (+ 1 (* 1/4 x)))) (* 1/2 (sqrt (/ 1 x)))))) (pow x 2))
(+ (sqrt (/ 1 x)) (* -1/2 (sqrt (/ 1 (pow x 3)))))
(+ (sqrt (/ 1 x)) (+ (* -1/2 (sqrt (/ 1 (pow x 3)))) (* 1/2 (sqrt (/ 1 (pow x 5))))))
(+ (sqrt (/ 1 x)) (+ (* -1/2 (sqrt (/ 1 (pow x 3)))) (+ (* -1/2 (* (sqrt (/ 1 (pow x 7))) (+ 1 (* 1/4 x)))) (* 1/2 (sqrt (/ 1 (pow x 5)))))))
(- (sqrt (/ 1 x)) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)))
(- (+ (sqrt (/ 1 x)) (* 1/2 (sqrt (/ 1 (pow x 3))))) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)))
(- (+ (sqrt (/ 1 x)) (* -1/2 (sqrt (/ 1 (pow x 5))))) (+ (* -1/2 (sqrt (/ 1 (pow x 3)))) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))))
(- (+ (sqrt (/ 1 x)) (* -1 (/ (- (* -1/2 (* (sqrt (/ 1 x)) (+ 1 (* -1/4 (/ x (pow (sqrt -1) 2)))))) (* -1/2 (sqrt x))) (pow x 3)))) (+ (* -1/2 (sqrt (/ 1 (pow x 3)))) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))))
(* -1 (* (sqrt x) (pow (sqrt -1) 2)))
(* (sqrt (/ 1 x)) (pow (sqrt -1) 2))
(+ (* -1/2 (sqrt (/ 1 (pow x 3)))) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)))
(+ (* -1/2 (sqrt (/ 1 (pow x 3)))) (+ (* 1/2 (sqrt (/ 1 (pow x 5)))) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))))
(+ (* -1 (/ (+ (* -1/2 (sqrt x)) (* 1/2 (* (sqrt (/ 1 x)) (+ 1 (* -1/4 (/ x (pow (sqrt -1) 2))))))) (pow x 3))) (+ (* -1/2 (sqrt (/ 1 (pow x 3)))) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))))
Outputs
(sqrt (/ 1 x))
(sqrt.f64 (/.f64 #s(literal 1 binary64) x))
(/ (+ (sqrt x) (* -1 x)) x)
(/.f64 (-.f64 (sqrt.f64 x) x) x)
(/ (+ (sqrt x) (* x (- (* 1/2 x) 1))) x)
(/.f64 (fma.f64 (-.f64 (*.f64 #s(literal 1/2 binary64) x) #s(literal 1 binary64)) x (sqrt.f64 x)) x)
(/ (+ (sqrt x) (* x (- (* x (+ 1/2 (* -3/8 x))) 1))) x)
(/.f64 (fma.f64 (-.f64 (*.f64 (fma.f64 #s(literal -3/8 binary64) x #s(literal 1/2 binary64)) x) #s(literal 1 binary64)) x (sqrt.f64 x)) x)
(sqrt x)
(sqrt.f64 x)
1
#s(literal 1 binary64)
(+ 1 (* -1/2 x))
(fma.f64 #s(literal -1/2 binary64) x #s(literal 1 binary64))
(+ 1 (* x (- (* 3/8 x) 1/2)))
(fma.f64 (-.f64 (*.f64 #s(literal 3/8 binary64) x) #s(literal 1/2 binary64)) x #s(literal 1 binary64))
(+ 1 (* x (- (* x (+ 3/8 (* -5/16 x))) 1/2)))
(fma.f64 (-.f64 (*.f64 (fma.f64 #s(literal -5/16 binary64) x #s(literal 3/8 binary64)) x) #s(literal 1/2 binary64)) x #s(literal 1 binary64))
(* 1/2 (sqrt (/ 1 (pow x 3))))
(*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 3 binary64)))) #s(literal 1/2 binary64))
(/ (- (* -1/2 (sqrt (/ 1 x))) (* -1/2 (sqrt x))) (pow x 2))
(*.f64 (/.f64 (-.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) (sqrt.f64 x)) (*.f64 x x)) #s(literal -1/2 binary64))
(/ (- (* 1/2 (* (sqrt (/ 1 (pow x 3))) (+ 1 (* 1/4 x)))) (+ (* -1/2 (sqrt x)) (* 1/2 (sqrt (/ 1 x))))) (pow x 2))
(/.f64 (fma.f64 #s(literal 1/2 binary64) (fma.f64 (fma.f64 #s(literal 1/4 binary64) x #s(literal 1 binary64)) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 3 binary64)))) (sqrt.f64 x)) (*.f64 #s(literal -1/2 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) x)))) (*.f64 x x))
(/ (- (* -1/2 (* (sqrt (/ 1 (pow x 5))) (+ 1 (* 1/2 x)))) (+ (* -1/2 (sqrt x)) (+ (* -1/2 (* (sqrt (/ 1 (pow x 3))) (+ 1 (* 1/4 x)))) (* 1/2 (sqrt (/ 1 x)))))) (pow x 2))
(/.f64 (*.f64 #s(literal -1/2 binary64) (-.f64 (fma.f64 (fma.f64 #s(literal 1/2 binary64) x #s(literal 1 binary64)) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 5 binary64)))) (neg.f64 (sqrt.f64 x))) (fma.f64 (fma.f64 #s(literal 1/4 binary64) x #s(literal 1 binary64)) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 3 binary64)))) (neg.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)))))) (*.f64 x x))
(+ (sqrt (/ 1 x)) (* -1/2 (sqrt (/ 1 (pow x 3)))))
(fma.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 3 binary64)))) #s(literal -1/2 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) x)))
(+ (sqrt (/ 1 x)) (+ (* -1/2 (sqrt (/ 1 (pow x 3)))) (* 1/2 (sqrt (/ 1 (pow x 5))))))
(fma.f64 (-.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 3 binary64)))) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 5 binary64))))) #s(literal -1/2 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) x)))
(+ (sqrt (/ 1 x)) (+ (* -1/2 (sqrt (/ 1 (pow x 3)))) (+ (* -1/2 (* (sqrt (/ 1 (pow x 7))) (+ 1 (* 1/4 x)))) (* 1/2 (sqrt (/ 1 (pow x 5)))))))
(fma.f64 #s(literal -1/2 binary64) (-.f64 (fma.f64 (fma.f64 #s(literal 1/4 binary64) x #s(literal 1 binary64)) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 7 binary64)))) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 3 binary64))))) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 5 binary64))))) (sqrt.f64 (/.f64 #s(literal 1 binary64) x)))
(- (sqrt (/ 1 x)) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)))
(*.f64 #s(literal 2 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) x)))
(- (+ (sqrt (/ 1 x)) (* 1/2 (sqrt (/ 1 (pow x 3))))) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)))
(fma.f64 #s(literal 2 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 3 binary64)))) #s(literal 1/2 binary64)))
(- (+ (sqrt (/ 1 x)) (* -1/2 (sqrt (/ 1 (pow x 5))))) (+ (* -1/2 (sqrt (/ 1 (pow x 3)))) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))))
(fma.f64 #s(literal -1/2 binary64) (-.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 5 binary64)))) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 3 binary64))))) (*.f64 #s(literal 2 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) x))))
(- (+ (sqrt (/ 1 x)) (* -1 (/ (- (* -1/2 (* (sqrt (/ 1 x)) (+ 1 (* -1/4 (/ x (pow (sqrt -1) 2)))))) (* -1/2 (sqrt x))) (pow x 3)))) (+ (* -1/2 (sqrt (/ 1 (pow x 3)))) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))))
(fma.f64 (/.f64 #s(literal -1/2 binary64) (pow.f64 x #s(literal 3 binary64))) (-.f64 (sqrt.f64 x) (*.f64 (fma.f64 #s(literal 1/4 binary64) x #s(literal 1 binary64)) (sqrt.f64 (/.f64 #s(literal 1 binary64) x)))) (fma.f64 #s(literal 2 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 3 binary64)))) #s(literal 1/2 binary64))))
(* -1 (* (sqrt x) (pow (sqrt -1) 2)))
(sqrt.f64 x)
(* (sqrt (/ 1 x)) (pow (sqrt -1) 2))
(neg.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)))
(+ (* -1/2 (sqrt (/ 1 (pow x 3)))) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)))
(fma.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 3 binary64)))) #s(literal -1/2 binary64) (neg.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x))))
(+ (* -1/2 (sqrt (/ 1 (pow x 3)))) (+ (* 1/2 (sqrt (/ 1 (pow x 5)))) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))))
(fma.f64 (-.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 3 binary64)))) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 5 binary64))))) #s(literal -1/2 binary64) (neg.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x))))
(+ (* -1 (/ (+ (* -1/2 (sqrt x)) (* 1/2 (* (sqrt (/ 1 x)) (+ 1 (* -1/4 (/ x (pow (sqrt -1) 2))))))) (pow x 3))) (+ (* -1/2 (sqrt (/ 1 (pow x 3)))) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))))
(fma.f64 #s(literal -1/2 binary64) (+.f64 (/.f64 (-.f64 (*.f64 (fma.f64 #s(literal 1/4 binary64) x #s(literal 1 binary64)) (sqrt.f64 (/.f64 #s(literal 1 binary64) x))) (sqrt.f64 x)) (pow.f64 x #s(literal 3 binary64))) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 3 binary64))))) (neg.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x))))

rewrite143.0ms (2.1%)

Memory
-12.3MiB live, 227.1MiB allocated
Iterations

Useful iterations: 3 (0.0ms)

IterNodesCost
0823
01423
15919
241619
3567917
0879117
Stop Event
iter limit
node limit
iter limit
Counts
4 → 261
Calls
Call 1
Inputs
(-.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 x)) (/.f64 #s(literal 1 binary64) (sqrt.f64 (+.f64 x #s(literal 1 binary64)))))
(/.f64 #s(literal 1 binary64) (sqrt.f64 x))
(sqrt.f64 x)
(/.f64 #s(literal 1 binary64) (sqrt.f64 (+.f64 x #s(literal 1 binary64))))
Outputs
(*.f64 (/.f64 (-.f64 (pow.f64 x #s(literal -1 binary64)) (exp.f64 (neg.f64 (log1p.f64 x)))) (/.f64 (-.f64 (sqrt.f64 (+.f64 x #s(literal 1 binary64))) (sqrt.f64 x)) (sqrt.f64 x))) (sqrt.f64 (+.f64 x #s(literal 1 binary64))))
(*.f64 (/.f64 (-.f64 (pow.f64 x #s(literal -1 binary64)) (exp.f64 (neg.f64 (log1p.f64 x)))) (neg.f64 (-.f64 (sqrt.f64 (+.f64 x #s(literal 1 binary64))) (sqrt.f64 x)))) (neg.f64 (hypot.f64 (sqrt.f64 x) x)))
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(/.f64 #s(literal 1 binary64) (sqrt.f64 x))
(neg.f64 (pow.f64 x #s(literal -1/2 binary64)))
(sqrt.f64 (pow.f64 x #s(literal -1 binary64)))
(-.f64 (cosh.f64 (log.f64 (sqrt.f64 x))) (sinh.f64 (log.f64 (sqrt.f64 x))))
(fabs.f64 (pow.f64 x #s(literal -1/2 binary64)))
(+.f64 (cosh.f64 (*.f64 (log.f64 x) #s(literal -1/2 binary64))) (sinh.f64 (*.f64 (log.f64 x) #s(literal -1/2 binary64))))
(+.f64 (cosh.f64 (log.f64 (sqrt.f64 x))) (sinh.f64 (*.f64 #s(literal -1/2 binary64) (log.f64 x))))
(exp.f64 (*.f64 (*.f64 (log.f64 (sqrt.f64 x)) #s(literal -1/2 binary64)) #s(literal 2 binary64)))
(exp.f64 (*.f64 (*.f64 (log.f64 (sqrt.f64 x)) #s(literal 2 binary64)) #s(literal -1/2 binary64)))
(exp.f64 (*.f64 (*.f64 (log.f64 x) #s(literal -1/2 binary64)) #s(literal 1 binary64)))
(exp.f64 (*.f64 (*.f64 (log.f64 x) #s(literal 1/4 binary64)) #s(literal -2 binary64)))
(exp.f64 (*.f64 (*.f64 #s(literal -1/4 binary64) (log.f64 x)) #s(literal 2 binary64)))
(exp.f64 (*.f64 (*.f64 #s(literal -1/2 binary64) (log.f64 x)) #s(literal 1 binary64)))
(exp.f64 (*.f64 (*.f64 #s(literal 1/4 binary64) (log.f64 x)) #s(literal -2 binary64)))
(exp.f64 (*.f64 (log.f64 x) #s(literal -1/2 binary64)))
(exp.f64 (*.f64 #s(literal -1/2 binary64) (log.f64 x)))
(*.f64 (neg.f64 (pow.f64 x #s(literal 1/4 binary64))) (neg.f64 (pow.f64 x #s(literal 1/4 binary64))))
(*.f64 (fabs.f64 (pow.f64 x #s(literal 1/4 binary64))) (fabs.f64 (pow.f64 x #s(literal 1/4 binary64))))
(*.f64 (pow.f64 x #s(literal 1/4 binary64)) (pow.f64 x #s(literal 1/4 binary64)))
(*.f64 (neg.f64 (sqrt.f64 x)) #s(literal -1 binary64))
(*.f64 #s(literal -1 binary64) (neg.f64 (sqrt.f64 x)))
(*.f64 (sqrt.f64 x) #s(literal 1 binary64))
(*.f64 #s(literal 1 binary64) (sqrt.f64 x))
(pow.f64 (neg.f64 (pow.f64 x #s(literal 1/4 binary64))) #s(literal 2 binary64))
(pow.f64 (fabs.f64 (pow.f64 x #s(literal 1/4 binary64))) #s(literal 2 binary64))
(pow.f64 (pow.f64 x #s(literal 1/4 binary64)) #s(literal 2 binary64))
(pow.f64 (neg.f64 x) #s(literal 1/2 binary64))
(pow.f64 (*.f64 x x) #s(literal 1/4 binary64))
(pow.f64 (neg.f64 (sqrt.f64 x)) #s(literal 1 binary64))
(pow.f64 (sqrt.f64 x) #s(literal 1 binary64))
(pow.f64 x #s(literal 1/2 binary64))
(neg.f64 (neg.f64 (sqrt.f64 x)))
(sqrt.f64 x)
(+.f64 (cosh.f64 (log.f64 (sqrt.f64 x))) (sinh.f64 (log.f64 (sqrt.f64 x))))
(exp.f64 (*.f64 (*.f64 (log.f64 x) #s(literal 1/4 binary64)) #s(literal 2 binary64)))
(exp.f64 (*.f64 (*.f64 (log.f64 x) #s(literal 2 binary64)) #s(literal 1/4 binary64)))
(exp.f64 (*.f64 (*.f64 (log.f64 (sqrt.f64 x)) #s(literal 2 binary64)) #s(literal 1/2 binary64)))
(exp.f64 (*.f64 (*.f64 #s(literal 1/4 binary64) (log.f64 x)) #s(literal 2 binary64)))
(exp.f64 (*.f64 (*.f64 #s(literal 2 binary64) (log.f64 x)) #s(literal 1/4 binary64)))
(exp.f64 (log.f64 (sqrt.f64 x)))
(*.f64 (pow.f64 (sinh.f64 (acosh.f64 x)) #s(literal -1 binary64)) (sqrt.f64 (-.f64 x #s(literal 1 binary64))))
(*.f64 (cos.f64 (atan.f64 (pow.f64 x #s(literal 3/2 binary64)))) (sqrt.f64 (fma.f64 x x (-.f64 #s(literal 1 binary64) x))))
(*.f64 (/.f64 #s(literal -1 binary64) (sinh.f64 (acosh.f64 x))) (sqrt.f64 (-.f64 x #s(literal 1 binary64))))
(*.f64 (/.f64 #s(literal -1 binary64) (cosh.f64 (asinh.f64 (pow.f64 x #s(literal 3/2 binary64))))) (sqrt.f64 (fma.f64 x x (-.f64 #s(literal 1 binary64) x))))
(*.f64 (*.f64 #s(literal -1 binary64) (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)))
(*.f64 (neg.f64 (pow.f64 (+.f64 x #s(literal 1 binary64)) #s(literal -1/4 binary64))) (neg.f64 (pow.f64 (+.f64 x #s(literal 1 binary64)) #s(literal -1/4 binary64))))
(*.f64 (neg.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)))
(*.f64 (fabs.f64 (pow.f64 (+.f64 x #s(literal 1 binary64)) #s(literal -1/4 binary64))) (fabs.f64 (pow.f64 (+.f64 x #s(literal 1 binary64)) #s(literal -1/4 binary64))))
(*.f64 (pow.f64 (+.f64 x #s(literal 1 binary64)) #s(literal -1/4 binary64)) (*.f64 (pow.f64 (+.f64 x #s(literal 1 binary64)) #s(literal -1/4 binary64)) #s(literal -1 binary64)))
(*.f64 (pow.f64 (+.f64 x #s(literal 1 binary64)) #s(literal -1/4 binary64)) (neg.f64 (pow.f64 (+.f64 x #s(literal 1 binary64)) #s(literal -1/4 binary64))))
(*.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)))
(*.f64 #s(literal -1 binary64) (cos.f64 (atan.f64 (sqrt.f64 x))))
(*.f64 (cos.f64 (atan.f64 (sqrt.f64 x))) #s(literal -1 binary64))
(*.f64 (cos.f64 (atan.f64 (sqrt.f64 x))) #s(literal 1 binary64))
(*.f64 #s(literal 1 binary64) (cos.f64 (atan.f64 (sqrt.f64 x))))
(pow.f64 (neg.f64 (pow.f64 (+.f64 x #s(literal 1 binary64)) #s(literal -1/4 binary64))) #s(literal 2 binary64))
(pow.f64 (fabs.f64 (neg.f64 (sqrt.f64 (+.f64 x #s(literal 1 binary64))))) #s(literal -1 binary64))
(pow.f64 (fabs.f64 (sqrt.f64 (+.f64 x #s(literal 1 binary64)))) #s(literal -1 binary64))
(pow.f64 (fabs.f64 (pow.f64 (+.f64 x #s(literal 1 binary64)) #s(literal -1/4 binary64))) #s(literal 2 binary64))
(pow.f64 (pow.f64 (+.f64 x #s(literal 1 binary64)) #s(literal 2 binary64)) #s(literal -1/4 binary64))
(pow.f64 (pow.f64 (+.f64 x #s(literal 1 binary64)) #s(literal -1/4 binary64)) #s(literal 2 binary64))
(pow.f64 (pow.f64 (+.f64 x #s(literal 1 binary64)) #s(literal 1/4 binary64)) #s(literal -2 binary64))
(pow.f64 (exp.f64 (neg.f64 (log1p.f64 x))) #s(literal 1/2 binary64))
(pow.f64 (neg.f64 (sqrt.f64 (+.f64 x #s(literal 1 binary64)))) #s(literal -1 binary64))
(pow.f64 (cos.f64 (atan.f64 (sqrt.f64 x))) #s(literal 1 binary64))
(pow.f64 (sqrt.f64 (+.f64 x #s(literal 1 binary64))) #s(literal -1 binary64))
(pow.f64 (+.f64 x #s(literal 1 binary64)) #s(literal -1/2 binary64))
(/.f64 (/.f64 #s(literal -1 binary64) (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)))
(/.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)))
(/.f64 #s(literal -1 binary64) (neg.f64 (sqrt.f64 (+.f64 x #s(literal 1 binary64)))))
(/.f64 #s(literal -1 binary64) (sqrt.f64 (+.f64 x #s(literal 1 binary64))))
(/.f64 (cos.f64 (atan.f64 (sqrt.f64 x))) #s(literal 1 binary64))
(/.f64 #s(literal 1 binary64) (fabs.f64 (neg.f64 (sqrt.f64 (+.f64 x #s(literal 1 binary64))))))
(/.f64 #s(literal 1 binary64) (fabs.f64 (sqrt.f64 (+.f64 x #s(literal 1 binary64)))))
(/.f64 #s(literal 1 binary64) (neg.f64 (sqrt.f64 (+.f64 x #s(literal 1 binary64)))))
(/.f64 #s(literal 1 binary64) (sqrt.f64 (+.f64 x #s(literal 1 binary64))))
(neg.f64 (cos.f64 (atan.f64 (sqrt.f64 x))))
(sqrt.f64 (exp.f64 (neg.f64 (log1p.f64 x))))
(-.f64 (cosh.f64 (*.f64 #s(literal -1/2 binary64) (log1p.f64 x))) (sinh.f64 (*.f64 (log1p.f64 x) #s(literal 1/2 binary64))))
(fabs.f64 (cos.f64 (atan.f64 (sqrt.f64 x))))
(cos.f64 (atan.f64 (fabs.f64 (neg.f64 (sqrt.f64 x)))))
(cos.f64 (atan.f64 (fabs.f64 (sqrt.f64 x))))
(cos.f64 (atan.f64 (neg.f64 (sqrt.f64 x))))
(cos.f64 (atan.f64 (sqrt.f64 x)))
(+.f64 (cosh.f64 (*.f64 (log1p.f64 x) #s(literal -1/2 binary64))) (sinh.f64 (*.f64 (log1p.f64 x) #s(literal -1/2 binary64))))
(+.f64 (cosh.f64 (*.f64 #s(literal -1/2 binary64) (log1p.f64 x))) (sinh.f64 (*.f64 #s(literal -1/2 binary64) (log1p.f64 x))))
(exp.f64 (*.f64 (*.f64 (*.f64 (log1p.f64 x) #s(literal 1/2 binary64)) #s(literal -1/2 binary64)) #s(literal 2 binary64)))
(exp.f64 (*.f64 (*.f64 (*.f64 (log1p.f64 x) #s(literal 1/2 binary64)) #s(literal 2 binary64)) #s(literal -1/2 binary64)))
(exp.f64 (*.f64 (*.f64 (log1p.f64 x) #s(literal -1/2 binary64)) #s(literal 1 binary64)))
(exp.f64 (*.f64 (*.f64 (log1p.f64 x) #s(literal 1/4 binary64)) #s(literal -2 binary64)))
(exp.f64 (*.f64 (*.f64 #s(literal -1/4 binary64) (log1p.f64 x)) #s(literal 2 binary64)))
(exp.f64 (*.f64 (*.f64 #s(literal -1/2 binary64) (log1p.f64 x)) #s(literal 1 binary64)))
(exp.f64 (*.f64 (*.f64 #s(literal 1/4 binary64) (log1p.f64 x)) #s(literal -2 binary64)))
(exp.f64 (*.f64 (log1p.f64 x) #s(literal -1/2 binary64)))
(exp.f64 (*.f64 #s(literal -1/2 binary64) (log1p.f64 x)))

eval47.0ms (0.7%)

Memory
28.1MiB live, 80.4MiB allocated
Compiler

Compiled 5 466 to 776 computations (85.8% saved)

prune16.0ms (0.2%)

Memory
-18.9MiB live, 25.5MiB allocated
Pruning

9 alts after pruning (8 fresh and 1 done)

PrunedKeptTotal
New2778285
Fresh000
Picked011
Done000
Total2779286
Accuracy
83.7%
Counts
286 → 9
Alt Table
Click to see full alt table
StatusAccuracyProgram
37.4%
(/.f64 (/.f64 (-.f64 (sqrt.f64 (+.f64 x #s(literal 1 binary64))) (sqrt.f64 x)) (sqrt.f64 (+.f64 x #s(literal 1 binary64)))) (sqrt.f64 x))
37.4%
(/.f64 (/.f64 (-.f64 (sqrt.f64 (+.f64 x #s(literal 1 binary64))) (sqrt.f64 x)) (sqrt.f64 x)) (sqrt.f64 (+.f64 x #s(literal 1 binary64))))
36.1%
(/.f64 (-.f64 (pow.f64 (/.f64 (pow.f64 x #s(literal -1 binary64)) (-.f64 (pow.f64 x #s(literal -1/2 binary64)) (cos.f64 (atan.f64 (sqrt.f64 x))))) #s(literal 2 binary64)) (pow.f64 (/.f64 (exp.f64 (neg.f64 (log1p.f64 x))) (-.f64 (pow.f64 x #s(literal -1/2 binary64)) (cos.f64 (atan.f64 (sqrt.f64 x))))) #s(literal 2 binary64))) (-.f64 (pow.f64 x #s(literal -1/2 binary64)) (cos.f64 (atan.f64 (sqrt.f64 x)))))
38.3%
(/.f64 (-.f64 (+.f64 x #s(literal 1 binary64)) x) (*.f64 (+.f64 (sqrt.f64 (+.f64 x #s(literal 1 binary64))) (sqrt.f64 x)) (hypot.f64 (sqrt.f64 x) x)))
37.4%
(/.f64 (-.f64 (sqrt.f64 (+.f64 x #s(literal 1 binary64))) (sqrt.f64 x)) (hypot.f64 (sqrt.f64 x) x))
37.3%
(-.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 x)) (/.f64 #s(literal 1 binary64) (sqrt.f64 (+.f64 x #s(literal 1 binary64)))))
82.1%
#s(approx (- (/ 1 (sqrt x)) (/ 1 (sqrt (+ x 1)))) (*.f64 (/.f64 (-.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) (sqrt.f64 x)) (*.f64 x x)) #s(literal -1/2 binary64)))
65.2%
#s(approx (- (/ 1 (sqrt x)) (/ 1 (sqrt (+ x 1)))) (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 3 binary64)))) #s(literal 1/2 binary64)))
5.5%
#s(approx (- (/ 1 (sqrt x)) (/ 1 (sqrt (+ x 1)))) (sqrt.f64 (/.f64 #s(literal 1 binary64) x)))
Compiler

Compiled 331 to 206 computations (37.8% saved)

simplify258.0ms (3.8%)

Memory
-16.4MiB live, 249.6MiB allocated
Algorithm
egg-herbie
Localize:

Found 19 expressions of interest:

NewMetricScoreProgram
cost-diff0
(/.f64 (pow.f64 x #s(literal -1 binary64)) (-.f64 (pow.f64 x #s(literal -1/2 binary64)) (cos.f64 (atan.f64 (sqrt.f64 x)))))
cost-diff0
(pow.f64 (/.f64 (pow.f64 x #s(literal -1 binary64)) (-.f64 (pow.f64 x #s(literal -1/2 binary64)) (cos.f64 (atan.f64 (sqrt.f64 x))))) #s(literal 2 binary64))
cost-diff1
(-.f64 (pow.f64 (/.f64 (pow.f64 x #s(literal -1 binary64)) (-.f64 (pow.f64 x #s(literal -1/2 binary64)) (cos.f64 (atan.f64 (sqrt.f64 x))))) #s(literal 2 binary64)) (pow.f64 (/.f64 (exp.f64 (neg.f64 (log1p.f64 x))) (-.f64 (pow.f64 x #s(literal -1/2 binary64)) (cos.f64 (atan.f64 (sqrt.f64 x))))) #s(literal 2 binary64)))
cost-diff6
(/.f64 (-.f64 (pow.f64 (/.f64 (pow.f64 x #s(literal -1 binary64)) (-.f64 (pow.f64 x #s(literal -1/2 binary64)) (cos.f64 (atan.f64 (sqrt.f64 x))))) #s(literal 2 binary64)) (pow.f64 (/.f64 (exp.f64 (neg.f64 (log1p.f64 x))) (-.f64 (pow.f64 x #s(literal -1/2 binary64)) (cos.f64 (atan.f64 (sqrt.f64 x))))) #s(literal 2 binary64))) (-.f64 (pow.f64 x #s(literal -1/2 binary64)) (cos.f64 (atan.f64 (sqrt.f64 x)))))
cost-diff0
(+.f64 x #s(literal 1 binary64))
cost-diff0
(sqrt.f64 (+.f64 x #s(literal 1 binary64)))
cost-diff0
(-.f64 (sqrt.f64 (+.f64 x #s(literal 1 binary64))) (sqrt.f64 x))
cost-diff0
(/.f64 (-.f64 (sqrt.f64 (+.f64 x #s(literal 1 binary64))) (sqrt.f64 x)) (hypot.f64 (sqrt.f64 x) x))
cost-diff0
(sqrt.f64 (+.f64 x #s(literal 1 binary64)))
cost-diff0
(-.f64 (sqrt.f64 (+.f64 x #s(literal 1 binary64))) (sqrt.f64 x))
cost-diff1
(/.f64 (/.f64 (-.f64 (sqrt.f64 (+.f64 x #s(literal 1 binary64))) (sqrt.f64 x)) (sqrt.f64 (+.f64 x #s(literal 1 binary64)))) (sqrt.f64 x))
cost-diff3
(/.f64 (-.f64 (sqrt.f64 (+.f64 x #s(literal 1 binary64))) (sqrt.f64 x)) (sqrt.f64 (+.f64 x #s(literal 1 binary64))))
cost-diff0
(/.f64 #s(literal 1 binary64) x)
cost-diff0
(sqrt.f64 (/.f64 #s(literal 1 binary64) x))
cost-diff0
#s(approx (- (/ 1 (sqrt x)) (/ 1 (sqrt (+ x 1)))) (sqrt.f64 (/.f64 #s(literal 1 binary64) x)))
cost-diff0
(-.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) (sqrt.f64 x))
cost-diff0
(/.f64 (-.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) (sqrt.f64 x)) (*.f64 x x))
cost-diff0
(*.f64 (/.f64 (-.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) (sqrt.f64 x)) (*.f64 x x)) #s(literal -1/2 binary64))
cost-diff0
#s(approx (- (/ 1 (sqrt x)) (/ 1 (sqrt (+ x 1)))) (*.f64 (/.f64 (-.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) (sqrt.f64 x)) (*.f64 x x)) #s(literal -1/2 binary64)))
Iterations

Useful iterations: 4 (0.0ms)

IterNodesCost
041334
072334
1125328
2277328
3917327
43161319
08357319
Stop Event
iter limit
node limit
iter limit
Calls
Call 1
Inputs
#s(approx (- (/ 1 (sqrt x)) (/ 1 (sqrt (+ x 1)))) (*.f64 (/.f64 (-.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) (sqrt.f64 x)) (*.f64 x x)) #s(literal -1/2 binary64)))
(*.f64 (/.f64 (-.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) (sqrt.f64 x)) (*.f64 x x)) #s(literal -1/2 binary64))
(/.f64 (-.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) (sqrt.f64 x)) (*.f64 x x))
(-.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) (sqrt.f64 x))
(sqrt.f64 (/.f64 #s(literal 1 binary64) x))
(/.f64 #s(literal 1 binary64) x)
#s(literal 1 binary64)
x
(sqrt.f64 x)
(*.f64 x x)
#s(literal -1/2 binary64)
#s(approx (- (/ 1 (sqrt x)) (/ 1 (sqrt (+ x 1)))) (sqrt.f64 (/.f64 #s(literal 1 binary64) x)))
(sqrt.f64 (/.f64 #s(literal 1 binary64) x))
(/.f64 #s(literal 1 binary64) x)
#s(literal 1 binary64)
x
(/.f64 (/.f64 (-.f64 (sqrt.f64 (+.f64 x #s(literal 1 binary64))) (sqrt.f64 x)) (sqrt.f64 (+.f64 x #s(literal 1 binary64)))) (sqrt.f64 x))
(/.f64 (-.f64 (sqrt.f64 (+.f64 x #s(literal 1 binary64))) (sqrt.f64 x)) (sqrt.f64 (+.f64 x #s(literal 1 binary64))))
(-.f64 (sqrt.f64 (+.f64 x #s(literal 1 binary64))) (sqrt.f64 x))
(sqrt.f64 (+.f64 x #s(literal 1 binary64)))
(+.f64 x #s(literal 1 binary64))
x
#s(literal 1 binary64)
(sqrt.f64 x)
(/.f64 (-.f64 (sqrt.f64 (+.f64 x #s(literal 1 binary64))) (sqrt.f64 x)) (hypot.f64 (sqrt.f64 x) x))
(-.f64 (sqrt.f64 (+.f64 x #s(literal 1 binary64))) (sqrt.f64 x))
(sqrt.f64 (+.f64 x #s(literal 1 binary64)))
(+.f64 x #s(literal 1 binary64))
x
#s(literal 1 binary64)
(sqrt.f64 x)
(hypot.f64 (sqrt.f64 x) x)
(/.f64 (-.f64 (pow.f64 (/.f64 (pow.f64 x #s(literal -1 binary64)) (-.f64 (pow.f64 x #s(literal -1/2 binary64)) (cos.f64 (atan.f64 (sqrt.f64 x))))) #s(literal 2 binary64)) (pow.f64 (/.f64 (exp.f64 (neg.f64 (log1p.f64 x))) (-.f64 (pow.f64 x #s(literal -1/2 binary64)) (cos.f64 (atan.f64 (sqrt.f64 x))))) #s(literal 2 binary64))) (-.f64 (pow.f64 x #s(literal -1/2 binary64)) (cos.f64 (atan.f64 (sqrt.f64 x)))))
(-.f64 (pow.f64 (/.f64 (pow.f64 x #s(literal -1 binary64)) (-.f64 (pow.f64 x #s(literal -1/2 binary64)) (cos.f64 (atan.f64 (sqrt.f64 x))))) #s(literal 2 binary64)) (pow.f64 (/.f64 (exp.f64 (neg.f64 (log1p.f64 x))) (-.f64 (pow.f64 x #s(literal -1/2 binary64)) (cos.f64 (atan.f64 (sqrt.f64 x))))) #s(literal 2 binary64)))
(pow.f64 (/.f64 (pow.f64 x #s(literal -1 binary64)) (-.f64 (pow.f64 x #s(literal -1/2 binary64)) (cos.f64 (atan.f64 (sqrt.f64 x))))) #s(literal 2 binary64))
(/.f64 (pow.f64 x #s(literal -1 binary64)) (-.f64 (pow.f64 x #s(literal -1/2 binary64)) (cos.f64 (atan.f64 (sqrt.f64 x)))))
(pow.f64 x #s(literal -1 binary64))
x
#s(literal -1 binary64)
(-.f64 (pow.f64 x #s(literal -1/2 binary64)) (cos.f64 (atan.f64 (sqrt.f64 x))))
(pow.f64 x #s(literal -1/2 binary64))
#s(literal -1/2 binary64)
(cos.f64 (atan.f64 (sqrt.f64 x)))
(atan.f64 (sqrt.f64 x))
(sqrt.f64 x)
#s(literal 2 binary64)
(pow.f64 (/.f64 (exp.f64 (neg.f64 (log1p.f64 x))) (-.f64 (pow.f64 x #s(literal -1/2 binary64)) (cos.f64 (atan.f64 (sqrt.f64 x))))) #s(literal 2 binary64))
(/.f64 (exp.f64 (neg.f64 (log1p.f64 x))) (-.f64 (pow.f64 x #s(literal -1/2 binary64)) (cos.f64 (atan.f64 (sqrt.f64 x)))))
(exp.f64 (neg.f64 (log1p.f64 x)))
(neg.f64 (log1p.f64 x))
(log1p.f64 x)
Outputs
#s(approx (- (/ 1 (sqrt x)) (/ 1 (sqrt (+ x 1)))) (*.f64 (/.f64 (-.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) (sqrt.f64 x)) (*.f64 x x)) #s(literal -1/2 binary64)))
#s(approx (- (/ 1 (sqrt x)) (/ 1 (sqrt (+ x 1)))) (*.f64 (/.f64 (/.f64 #s(literal -1/2 binary64) x) x) (-.f64 (sqrt.f64 (pow.f64 x #s(literal -1 binary64))) (sqrt.f64 x))))
(*.f64 (/.f64 (-.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) (sqrt.f64 x)) (*.f64 x x)) #s(literal -1/2 binary64))
(*.f64 (/.f64 (/.f64 #s(literal -1/2 binary64) x) x) (-.f64 (sqrt.f64 (pow.f64 x #s(literal -1 binary64))) (sqrt.f64 x)))
(/.f64 (-.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) (sqrt.f64 x)) (*.f64 x x))
(/.f64 (-.f64 (sqrt.f64 (pow.f64 x #s(literal -1 binary64))) (sqrt.f64 x)) (*.f64 x x))
(-.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) (sqrt.f64 x))
(-.f64 (sqrt.f64 (pow.f64 x #s(literal -1 binary64))) (sqrt.f64 x))
(sqrt.f64 (/.f64 #s(literal 1 binary64) x))
(sqrt.f64 (pow.f64 x #s(literal -1 binary64)))
(/.f64 #s(literal 1 binary64) x)
(pow.f64 x #s(literal -1 binary64))
#s(literal 1 binary64)
x
(sqrt.f64 x)
(*.f64 x x)
#s(literal -1/2 binary64)
#s(approx (- (/ 1 (sqrt x)) (/ 1 (sqrt (+ x 1)))) (sqrt.f64 (/.f64 #s(literal 1 binary64) x)))
#s(approx (- (/ 1 (sqrt x)) (/ 1 (sqrt (+ x 1)))) (sqrt.f64 (pow.f64 x #s(literal -1 binary64))))
(sqrt.f64 (/.f64 #s(literal 1 binary64) x))
(sqrt.f64 (pow.f64 x #s(literal -1 binary64)))
(/.f64 #s(literal 1 binary64) x)
(pow.f64 x #s(literal -1 binary64))
#s(literal 1 binary64)
x
(/.f64 (/.f64 (-.f64 (sqrt.f64 (+.f64 x #s(literal 1 binary64))) (sqrt.f64 x)) (sqrt.f64 (+.f64 x #s(literal 1 binary64)))) (sqrt.f64 x))
(-.f64 (/.f64 (sqrt.f64 x) x) (/.f64 #s(literal 1 binary64) (sqrt.f64 (+.f64 x #s(literal 1 binary64)))))
(/.f64 (-.f64 (sqrt.f64 (+.f64 x #s(literal 1 binary64))) (sqrt.f64 x)) (sqrt.f64 (+.f64 x #s(literal 1 binary64))))
(-.f64 #s(literal 1 binary64) (/.f64 (sqrt.f64 x) (sqrt.f64 (+.f64 x #s(literal 1 binary64)))))
(-.f64 (sqrt.f64 (+.f64 x #s(literal 1 binary64))) (sqrt.f64 x))
(sqrt.f64 (+.f64 x #s(literal 1 binary64)))
(+.f64 x #s(literal 1 binary64))
x
#s(literal 1 binary64)
(sqrt.f64 x)
(/.f64 (-.f64 (sqrt.f64 (+.f64 x #s(literal 1 binary64))) (sqrt.f64 x)) (hypot.f64 (sqrt.f64 x) x))
(-.f64 (sqrt.f64 (+.f64 x #s(literal 1 binary64))) (sqrt.f64 x))
(sqrt.f64 (+.f64 x #s(literal 1 binary64)))
(+.f64 x #s(literal 1 binary64))
x
#s(literal 1 binary64)
(sqrt.f64 x)
(hypot.f64 (sqrt.f64 x) x)
(/.f64 (-.f64 (pow.f64 (/.f64 (pow.f64 x #s(literal -1 binary64)) (-.f64 (pow.f64 x #s(literal -1/2 binary64)) (cos.f64 (atan.f64 (sqrt.f64 x))))) #s(literal 2 binary64)) (pow.f64 (/.f64 (exp.f64 (neg.f64 (log1p.f64 x))) (-.f64 (pow.f64 x #s(literal -1/2 binary64)) (cos.f64 (atan.f64 (sqrt.f64 x))))) #s(literal 2 binary64))) (-.f64 (pow.f64 x #s(literal -1/2 binary64)) (cos.f64 (atan.f64 (sqrt.f64 x)))))
(-.f64 (/.f64 (pow.f64 x #s(literal -2 binary64)) (pow.f64 (-.f64 (pow.f64 x #s(literal -1/2 binary64)) (cos.f64 (atan.f64 (sqrt.f64 x)))) #s(literal 3 binary64))) (/.f64 (exp.f64 (neg.f64 (*.f64 (log1p.f64 x) #s(literal 2 binary64)))) (pow.f64 (-.f64 (pow.f64 x #s(literal -1/2 binary64)) (cos.f64 (atan.f64 (sqrt.f64 x)))) #s(literal 3 binary64))))
(-.f64 (pow.f64 (/.f64 (pow.f64 x #s(literal -1 binary64)) (-.f64 (pow.f64 x #s(literal -1/2 binary64)) (cos.f64 (atan.f64 (sqrt.f64 x))))) #s(literal 2 binary64)) (pow.f64 (/.f64 (exp.f64 (neg.f64 (log1p.f64 x))) (-.f64 (pow.f64 x #s(literal -1/2 binary64)) (cos.f64 (atan.f64 (sqrt.f64 x))))) #s(literal 2 binary64)))
(/.f64 (/.f64 (+.f64 (neg.f64 (exp.f64 (neg.f64 (*.f64 (log1p.f64 x) #s(literal 2 binary64))))) (pow.f64 x #s(literal -2 binary64))) (-.f64 (pow.f64 x #s(literal -1/2 binary64)) (cos.f64 (atan.f64 (sqrt.f64 x))))) (-.f64 (pow.f64 x #s(literal -1/2 binary64)) (cos.f64 (atan.f64 (sqrt.f64 x)))))
(pow.f64 (/.f64 (pow.f64 x #s(literal -1 binary64)) (-.f64 (pow.f64 x #s(literal -1/2 binary64)) (cos.f64 (atan.f64 (sqrt.f64 x))))) #s(literal 2 binary64))
(/.f64 (pow.f64 x #s(literal -1 binary64)) (-.f64 (pow.f64 x #s(literal -1/2 binary64)) (cos.f64 (atan.f64 (sqrt.f64 x)))))
(pow.f64 x #s(literal -1 binary64))
x
#s(literal -1 binary64)
(-.f64 (pow.f64 x #s(literal -1/2 binary64)) (cos.f64 (atan.f64 (sqrt.f64 x))))
(pow.f64 x #s(literal -1/2 binary64))
#s(literal -1/2 binary64)
(cos.f64 (atan.f64 (sqrt.f64 x)))
(atan.f64 (sqrt.f64 x))
(sqrt.f64 x)
#s(literal 2 binary64)
(pow.f64 (/.f64 (exp.f64 (neg.f64 (log1p.f64 x))) (-.f64 (pow.f64 x #s(literal -1/2 binary64)) (cos.f64 (atan.f64 (sqrt.f64 x))))) #s(literal 2 binary64))
(/.f64 (exp.f64 (neg.f64 (log1p.f64 x))) (-.f64 (pow.f64 x #s(literal -1/2 binary64)) (cos.f64 (atan.f64 (sqrt.f64 x)))))
(exp.f64 (neg.f64 (log1p.f64 x)))
(neg.f64 (log1p.f64 x))
(log1p.f64 x)

localize468.0ms (6.9%)

Memory
8.5MiB live, 620.3MiB allocated
Localize:

Found 19 expressions of interest:

NewMetricScoreProgram
accuracy19.506566503198414
(/.f64 (pow.f64 x #s(literal -1 binary64)) (-.f64 (pow.f64 x #s(literal -1/2 binary64)) (cos.f64 (atan.f64 (sqrt.f64 x)))))
accuracy40.095069924531046
(-.f64 (pow.f64 x #s(literal -1/2 binary64)) (cos.f64 (atan.f64 (sqrt.f64 x))))
accuracy56.490183012307604
(cos.f64 (atan.f64 (sqrt.f64 x)))
accuracy60.14437560801474
(-.f64 (pow.f64 (/.f64 (pow.f64 x #s(literal -1 binary64)) (-.f64 (pow.f64 x #s(literal -1/2 binary64)) (cos.f64 (atan.f64 (sqrt.f64 x))))) #s(literal 2 binary64)) (pow.f64 (/.f64 (exp.f64 (neg.f64 (log1p.f64 x))) (-.f64 (pow.f64 x #s(literal -1/2 binary64)) (cos.f64 (atan.f64 (sqrt.f64 x))))) #s(literal 2 binary64)))
accuracy0.0
(sqrt.f64 (+.f64 x #s(literal 1 binary64)))
accuracy0.0
(sqrt.f64 x)
accuracy0.1640625
(/.f64 (-.f64 (sqrt.f64 (+.f64 x #s(literal 1 binary64))) (sqrt.f64 x)) (hypot.f64 (sqrt.f64 x) x))
accuracy60.18462999946927
(-.f64 (sqrt.f64 (+.f64 x #s(literal 1 binary64))) (sqrt.f64 x))
accuracy0.0
(sqrt.f64 x)
accuracy0.25390625
(/.f64 (/.f64 (-.f64 (sqrt.f64 (+.f64 x #s(literal 1 binary64))) (sqrt.f64 x)) (sqrt.f64 (+.f64 x #s(literal 1 binary64)))) (sqrt.f64 x))
accuracy0.33822250976844204
(/.f64 (-.f64 (sqrt.f64 (+.f64 x #s(literal 1 binary64))) (sqrt.f64 x)) (sqrt.f64 (+.f64 x #s(literal 1 binary64))))
accuracy60.18462999946927
(-.f64 (sqrt.f64 (+.f64 x #s(literal 1 binary64))) (sqrt.f64 x))
accuracy0.0
(/.f64 #s(literal 1 binary64) x)
accuracy0.15234375
(sqrt.f64 (/.f64 #s(literal 1 binary64) x))
accuracy60.464192040049284
#s(approx (- (/ 1 (sqrt x)) (/ 1 (sqrt (+ x 1)))) (sqrt.f64 (/.f64 #s(literal 1 binary64) x)))
accuracy0.015625
(-.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) (sqrt.f64 x))
accuracy0.15234375
(sqrt.f64 (/.f64 #s(literal 1 binary64) x))
accuracy0.9167017926041685
#s(approx (- (/ 1 (sqrt x)) (/ 1 (sqrt (+ x 1)))) (*.f64 (/.f64 (-.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) (sqrt.f64 x)) (*.f64 x x)) #s(literal -1/2 binary64)))
accuracy10.569011443006001
(/.f64 (-.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) (sqrt.f64 x)) (*.f64 x x))
Samples
230.0ms98×2valid
194.0ms157×1valid
0.0ms0valid
Compiler

Compiled 343 to 38 computations (88.9% saved)

Precisions
Click to see histograms. Total time spent on operations: 379.0ms
ival-pow: 100.0ms (26.4% of total)
ival-cos: 59.0ms (15.6% of total)
adjust: 51.0ms (13.5% of total)
ival-div: 37.0ms (9.8% of total)
ival-atan: 34.0ms (9% of total)
ival-exp: 17.0ms (4.5% of total)
ival-log1p: 17.0ms (4.5% of total)
ival-hypot: 14.0ms (3.7% of total)
ival-sub: 13.0ms (3.4% of total)
ival-pow2: 12.0ms (3.2% of total)
ival-sqrt: 12.0ms (3.2% of total)
ival-mult: 6.0ms (1.6% of total)
ival-neg: 3.0ms (0.8% of total)
ival-add: 3.0ms (0.8% of total)
exact: 1.0ms (0.3% of total)
ival-true: 0.0ms (0% of total)
ival-assert: 0.0ms (0% of total)

series54.0ms (0.8%)

Memory
-2.5MiB live, 59.8MiB allocated
Counts
20 → 117
Calls
Call 1
Inputs
#s(approx (- (/ 1 (sqrt x)) (/ 1 (sqrt (+ x 1)))) (*.f64 (/.f64 (-.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) (sqrt.f64 x)) (*.f64 x x)) #s(literal -1/2 binary64)))
(*.f64 (/.f64 (-.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) (sqrt.f64 x)) (*.f64 x x)) #s(literal -1/2 binary64))
(/.f64 (-.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) (sqrt.f64 x)) (*.f64 x x))
(-.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) (sqrt.f64 x))
#s(approx (- (/ 1 (sqrt x)) (/ 1 (sqrt (+ x 1)))) (sqrt.f64 (/.f64 #s(literal 1 binary64) x)))
(sqrt.f64 (/.f64 #s(literal 1 binary64) x))
(/.f64 #s(literal 1 binary64) x)
(/.f64 (-.f64 (sqrt.f64 (+.f64 x #s(literal 1 binary64))) (sqrt.f64 x)) (sqrt.f64 (+.f64 x #s(literal 1 binary64))))
(/.f64 (/.f64 (-.f64 (sqrt.f64 (+.f64 x #s(literal 1 binary64))) (sqrt.f64 x)) (sqrt.f64 (+.f64 x #s(literal 1 binary64)))) (sqrt.f64 x))
(-.f64 (sqrt.f64 (+.f64 x #s(literal 1 binary64))) (sqrt.f64 x))
(sqrt.f64 (+.f64 x #s(literal 1 binary64)))
(/.f64 (-.f64 (sqrt.f64 (+.f64 x #s(literal 1 binary64))) (sqrt.f64 x)) (hypot.f64 (sqrt.f64 x) x))
(+.f64 x #s(literal 1 binary64))
(/.f64 (-.f64 (pow.f64 (/.f64 (pow.f64 x #s(literal -1 binary64)) (-.f64 (pow.f64 x #s(literal -1/2 binary64)) (cos.f64 (atan.f64 (sqrt.f64 x))))) #s(literal 2 binary64)) (pow.f64 (/.f64 (exp.f64 (neg.f64 (log1p.f64 x))) (-.f64 (pow.f64 x #s(literal -1/2 binary64)) (cos.f64 (atan.f64 (sqrt.f64 x))))) #s(literal 2 binary64))) (-.f64 (pow.f64 x #s(literal -1/2 binary64)) (cos.f64 (atan.f64 (sqrt.f64 x)))))
(-.f64 (pow.f64 (/.f64 (pow.f64 x #s(literal -1 binary64)) (-.f64 (pow.f64 x #s(literal -1/2 binary64)) (cos.f64 (atan.f64 (sqrt.f64 x))))) #s(literal 2 binary64)) (pow.f64 (/.f64 (exp.f64 (neg.f64 (log1p.f64 x))) (-.f64 (pow.f64 x #s(literal -1/2 binary64)) (cos.f64 (atan.f64 (sqrt.f64 x))))) #s(literal 2 binary64)))
(pow.f64 (/.f64 (pow.f64 x #s(literal -1 binary64)) (-.f64 (pow.f64 x #s(literal -1/2 binary64)) (cos.f64 (atan.f64 (sqrt.f64 x))))) #s(literal 2 binary64))
(/.f64 (pow.f64 x #s(literal -1 binary64)) (-.f64 (pow.f64 x #s(literal -1/2 binary64)) (cos.f64 (atan.f64 (sqrt.f64 x)))))
(sqrt.f64 x)
(cos.f64 (atan.f64 (sqrt.f64 x)))
(-.f64 (pow.f64 x #s(literal -1/2 binary64)) (cos.f64 (atan.f64 (sqrt.f64 x))))
Outputs
(sqrt (/ 1 x))
(/ (+ (sqrt x) (* -1 x)) x)
(/ (+ (sqrt x) (* x (- (* 1/2 x) 1))) x)
(/ (+ (sqrt x) (* x (- (* x (+ 1/2 (* -3/8 x))) 1))) x)
(* -1/2 (sqrt (/ 1 (pow x 5))))
(/ (+ (* -1/2 (sqrt x)) (* 1/2 (sqrt (pow x 3)))) (pow x 3))
(sqrt (/ 1 (pow x 5)))
(/ (+ (sqrt x) (* -1 (sqrt (pow x 3)))) (pow x 3))
(/ (+ (sqrt x) (* -1 (sqrt (pow x 3)))) x)
(/ 1 x)
(- 1 (sqrt x))
(- (+ 1 (* x (+ 1/2 (* -1/2 (- 1 (sqrt x)))))) (sqrt x))
(- (+ 1 (* x (+ 1/2 (+ (* -1/2 (- 1 (sqrt x))) (* x (- (* 3/8 (- 1 (sqrt x))) 3/8)))))) (sqrt x))
(- (+ 1 (* x (+ 1/2 (+ (* -1/2 (- 1 (sqrt x))) (* x (- (+ (* 3/8 (- 1 (sqrt x))) (* x (+ 5/16 (* -5/16 (- 1 (sqrt x)))))) 3/8)))))) (sqrt x))
(* (sqrt (/ 1 x)) (- 1 (sqrt x)))
(/ (+ (* 1/2 (sqrt (pow x 3))) (* (sqrt x) (- 1 (sqrt x)))) x)
(/ (+ (* x (+ (* 1/2 (sqrt x)) (* x (+ (* -1/2 (* (sqrt (/ 1 x)) (- 1 (sqrt x)))) (* -1/8 (sqrt x)))))) (* (sqrt x) (- 1 (sqrt x)))) x)
(/ (+ (* x (+ (* 1/2 (sqrt x)) (* x (+ (* -1/2 (* (sqrt (/ 1 x)) (- 1 (sqrt x)))) (+ (* -1/8 (sqrt x)) (* x (+ (* -1/4 (sqrt (/ 1 x))) (+ (* 1/16 (sqrt x)) (* 1/2 (* (sqrt (/ 1 x)) (- 1 (sqrt x)))))))))))) (* (sqrt x) (- 1 (sqrt x)))) x)
(- (+ 1 (* 1/2 x)) (sqrt x))
(- (+ 1 (* x (+ 1/2 (* -1/8 x)))) (sqrt x))
(- (+ 1 (* x (+ 1/2 (* x (- (* 1/16 x) 1/8))))) (sqrt x))
1
(+ 1 (* 1/2 x))
(+ 1 (* x (+ 1/2 (* -1/8 x))))
(+ 1 (* x (+ 1/2 (* x (- (* 1/16 x) 1/8)))))
(+ 1 x)
(* x (+ (sqrt (/ 1 (pow x 3))) (* x (- (* 2 (/ (cos (atan (sqrt x))) (pow x 2))) (* -1 (/ (cos (atan (sqrt x))) (pow x 2)))))))
(* x (+ (sqrt (/ 1 (pow x 3))) (* x (- (+ (* 2 (/ (cos (atan (sqrt x))) (pow x 2))) (* x (- (* -1 (* (sqrt (/ 1 x)) (+ (* -4 (/ (pow (cos (atan (sqrt x))) 2) (pow x 2))) (+ (/ 1 x) (/ (pow (cos (atan (sqrt x))) 2) (pow x 2)))))) (* -1 (* (sqrt (/ 1 x)) (* (cos (atan (sqrt x))) (- (* 2 (/ (cos (atan (sqrt x))) (pow x 2))) (* -1 (/ (cos (atan (sqrt x))) (pow x 2)))))))))) (* -1 (/ (cos (atan (sqrt x))) (pow x 2)))))))
(* x (+ (sqrt (/ 1 (pow x 3))) (* x (- (+ (* 2 (/ (cos (atan (sqrt x))) (pow x 2))) (* x (- (+ (* -1 (* (sqrt (/ 1 x)) (+ (* -4 (/ (pow (cos (atan (sqrt x))) 2) (pow x 2))) (+ (/ 1 x) (/ (pow (cos (atan (sqrt x))) 2) (pow x 2)))))) (* x (- (* (sqrt (/ 1 x)) (- (+ (* -2 (* (sqrt (/ 1 (pow x 3))) (cos (atan (sqrt x))))) (* 2 (/ 1 x))) (+ (* 2 (* (sqrt (/ 1 x)) (* (cos (atan (sqrt x))) (+ (* -4 (/ (pow (cos (atan (sqrt x))) 2) (pow x 2))) (/ (pow (cos (atan (sqrt x))) 2) (pow x 2)))))) (* 2 (* (sqrt (/ 1 (pow x 5))) (pow (cos (atan (sqrt x))) 3)))))) (* -1 (* (sqrt (/ 1 x)) (* (cos (atan (sqrt x))) (- (* -1 (* (sqrt (/ 1 x)) (+ (* -4 (/ (pow (cos (atan (sqrt x))) 2) (pow x 2))) (+ (/ 1 x) (/ (pow (cos (atan (sqrt x))) 2) (pow x 2)))))) (* -1 (* (sqrt (/ 1 x)) (* (cos (atan (sqrt x))) (- (* 2 (/ (cos (atan (sqrt x))) (pow x 2))) (* -1 (/ (cos (atan (sqrt x))) (pow x 2)))))))))))))) (* -1 (* (sqrt (/ 1 x)) (* (cos (atan (sqrt x))) (- (* 2 (/ (cos (atan (sqrt x))) (pow x 2))) (* -1 (/ (cos (atan (sqrt x))) (pow x 2)))))))))) (* -1 (/ (cos (atan (sqrt x))) (pow x 2)))))))
(+ (* 2 (* (sqrt (/ 1 x)) (cos (atan (sqrt x))))) (/ 1 x))
(+ (* x (- (* -1 (* x (+ (* -4 (/ (pow (cos (atan (sqrt x))) 2) (pow x 2))) (+ (/ 1 x) (/ (pow (cos (atan (sqrt x))) 2) (pow x 2)))))) (* -2 (* (sqrt (/ 1 (pow x 3))) (cos (atan (sqrt x))))))) (/ 1 x))
(+ (* x (- (* x (- (* x (- (+ (* -2 (* (sqrt (/ 1 (pow x 3))) (cos (atan (sqrt x))))) (* 2 (/ 1 x))) (+ (* 2 (* (sqrt (/ 1 x)) (* (cos (atan (sqrt x))) (+ (* -4 (/ (pow (cos (atan (sqrt x))) 2) (pow x 2))) (/ (pow (cos (atan (sqrt x))) 2) (pow x 2)))))) (* 2 (* (sqrt (/ 1 (pow x 5))) (pow (cos (atan (sqrt x))) 3)))))) (+ (* -4 (/ (pow (cos (atan (sqrt x))) 2) (pow x 2))) (+ (/ 1 x) (/ (pow (cos (atan (sqrt x))) 2) (pow x 2)))))) (* -2 (* (sqrt (/ 1 (pow x 3))) (cos (atan (sqrt x))))))) (/ 1 x))
(+ (* x (- (* -1 (* x (+ (* -4 (/ (pow (cos (atan (sqrt x))) 2) (pow x 2))) (/ (pow (cos (atan (sqrt x))) 2) (pow x 2))))) (* -2 (* (sqrt (/ 1 (pow x 3))) (cos (atan (sqrt x))))))) (/ 1 x))
(+ (* x (- (* x (- (* -1 (* x (+ (* 2 (* (sqrt (/ 1 x)) (* (cos (atan (sqrt x))) (+ (* -4 (/ (pow (cos (atan (sqrt x))) 2) (pow x 2))) (/ (pow (cos (atan (sqrt x))) 2) (pow x 2)))))) (* 2 (* (sqrt (/ 1 (pow x 5))) (pow (cos (atan (sqrt x))) 3)))))) (+ (* -4 (/ (pow (cos (atan (sqrt x))) 2) (pow x 2))) (/ (pow (cos (atan (sqrt x))) 2) (pow x 2))))) (* -2 (* (sqrt (/ 1 (pow x 3))) (cos (atan (sqrt x))))))) (/ 1 x))
(+ (cos (atan (sqrt x))) (sqrt (/ 1 x)))
(+ (sqrt (/ 1 x)) (* x (- (* (sqrt (/ 1 x)) (pow (cos (atan (sqrt x))) 2)) (* -1 (/ (cos (atan (sqrt x))) x)))))
(+ (sqrt (/ 1 x)) (* x (- (* x (- (/ (pow (cos (atan (sqrt x))) 3) x) (* -1 (* (sqrt (/ 1 (pow x 3))) (pow (cos (atan (sqrt x))) 2))))) (* -1 (/ (cos (atan (sqrt x))) x)))))
(sqrt x)
(cos (atan (sqrt x)))
(/ (+ (sqrt x) (* -1 (* x (cos (atan (sqrt x)))))) x)
(* 1/2 (sqrt (/ 1 (pow x 3))))
(/ (- (* -1/2 (sqrt (/ 1 x))) (* -1/2 (sqrt x))) (pow x 2))
(/ (- (* 1/2 (* (sqrt (/ 1 (pow x 3))) (+ 1 (* 1/4 x)))) (+ (* -1/2 (sqrt x)) (* 1/2 (sqrt (/ 1 x))))) (pow x 2))
(/ (- (* -1/2 (* (sqrt (/ 1 (pow x 5))) (+ 1 (* 1/2 x)))) (+ (* -1/2 (sqrt x)) (+ (* -1/2 (* (sqrt (/ 1 (pow x 3))) (+ 1 (* 1/4 x)))) (* 1/2 (sqrt (/ 1 x)))))) (pow x 2))
(/ (+ (* -1/2 (sqrt (/ 1 (pow x 3)))) (* 1/2 (sqrt (/ 1 x)))) x)
(* -1 (sqrt (/ 1 (pow x 3))))
(/ (+ (sqrt (/ 1 (pow x 3))) (* -1 (sqrt (/ 1 x)))) x)
(* -1 (sqrt x))
(* x (- (sqrt (/ 1 (pow x 3))) (sqrt (/ 1 x))))
(/ 1/2 x)
(/ (+ 1/2 (* -1 (/ (+ (* 1/8 x) (* 1/4 x)) (pow x 2)))) x)
(/ (- (+ 1/2 (* 1/4 (/ 1 (pow x 2)))) (+ (/ 1/8 x) (/ 1/4 x))) x)
(/ (- (+ 1/2 (+ (* -1/4 (/ (+ 1 (* 1/4 x)) (pow x 3))) (* 3/8 (/ 1 (pow x 2))))) (+ (/ 1/8 x) (/ 1/4 x))) x)
(/ (+ (* -1/4 (sqrt (/ 1 x))) (* 1/2 (sqrt x))) (pow x 2))
(/ (+ (* -1/4 (sqrt (/ 1 x))) (+ (* -1/8 (sqrt (/ 1 x))) (+ (* 3/16 (sqrt (/ 1 (pow x 3)))) (* 1/2 (sqrt x))))) (pow x 2))
(/ (+ (* -1/4 (sqrt (/ 1 x))) (+ (* -5/32 (sqrt (/ 1 (pow x 5)))) (+ (* -1/8 (sqrt (/ 1 x))) (+ (* 1/16 (sqrt (/ 1 (pow x 3)))) (+ (* 3/16 (sqrt (/ 1 (pow x 3)))) (* 1/2 (sqrt x))))))) (pow x 2))
(* 1/2 (sqrt (/ 1 x)))
(/ (+ (* -1/8 (sqrt (/ 1 x))) (* 1/2 (sqrt x))) x)
(/ (+ (* -1/8 (sqrt (/ 1 x))) (+ (* 1/16 (sqrt (/ 1 (pow x 3)))) (* 1/2 (sqrt x)))) x)
(/ (+ (* -1/8 (sqrt (/ 1 x))) (+ (* -5/128 (sqrt (/ 1 (pow x 5)))) (+ (* 1/16 (sqrt (/ 1 (pow x 3)))) (* 1/2 (sqrt x))))) 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))))))))
x
(* x (+ 1 (/ 1 x)))
(* -1 (/ (pow (exp (neg (* -1 (log (/ 1 x))))) 2) (pow (- (sqrt (/ 1 x)) (cos (atan (sqrt x)))) 3)))
(+ (* -1 (/ (pow (exp (neg (* -1 (log (/ 1 x))))) 2) (pow (- (sqrt (/ 1 x)) (cos (atan (sqrt x)))) 3))) (* 2 (/ (pow (exp (neg (* -1 (log (/ 1 x))))) 2) (* x (pow (- (sqrt (/ 1 x)) (cos (atan (sqrt x)))) 3)))))
(- (+ (* -1 (/ (pow (exp (neg (* -1 (log (/ 1 x))))) 2) (pow (- (sqrt (/ 1 x)) (cos (atan (sqrt x)))) 3))) (+ (* 2 (/ (pow (exp (neg (* -1 (log (/ 1 x))))) 2) (* x (pow (- (sqrt (/ 1 x)) (cos (atan (sqrt x)))) 3)))) (/ 1 (* (pow x 2) (pow (- (sqrt (/ 1 x)) (cos (atan (sqrt x)))) 3))))) (+ (* 2 (/ (pow (exp (neg (* -1 (log (/ 1 x))))) 2) (* (pow x 2) (pow (- (sqrt (/ 1 x)) (cos (atan (sqrt x)))) 3)))) (/ (pow (exp (neg (* -1 (log (/ 1 x))))) 2) (* (pow x 2) (pow (- (sqrt (/ 1 x)) (cos (atan (sqrt x)))) 3)))))
(- (+ (* -1 (/ (pow (exp (neg (* -1 (log (/ 1 x))))) 2) (pow (- (sqrt (/ 1 x)) (cos (atan (sqrt x)))) 3))) (+ (* 2 (/ (pow (exp (neg (* -1 (log (/ 1 x))))) 2) (* x (pow (- (sqrt (/ 1 x)) (cos (atan (sqrt x)))) 3)))) (+ (* 4 (/ (pow (exp (neg (* -1 (log (/ 1 x))))) 2) (* (pow x 3) (pow (- (sqrt (/ 1 x)) (cos (atan (sqrt x)))) 3)))) (/ 1 (* (pow x 2) (pow (- (sqrt (/ 1 x)) (cos (atan (sqrt x)))) 3)))))) (+ (* 2 (/ (pow (exp (neg (* -1 (log (/ 1 x))))) 2) (* (pow x 2) (pow (- (sqrt (/ 1 x)) (cos (atan (sqrt x)))) 3)))) (/ (pow (exp (neg (* -1 (log (/ 1 x))))) 2) (* (pow x 2) (pow (- (sqrt (/ 1 x)) (cos (atan (sqrt x)))) 3)))))
(* -1 (/ (pow (exp (neg (* -1 (log (/ 1 x))))) 2) (pow (- (sqrt (/ 1 x)) (cos (atan (sqrt x)))) 2)))
(- (* 2 (/ (pow (exp (neg (* -1 (log (/ 1 x))))) 2) (* x (pow (- (sqrt (/ 1 x)) (cos (atan (sqrt x)))) 2)))) (/ (pow (exp (neg (* -1 (log (/ 1 x))))) 2) (pow (- (sqrt (/ 1 x)) (cos (atan (sqrt x)))) 2)))
(- (/ 1 (* (pow x 2) (pow (- (sqrt (/ 1 x)) (cos (atan (sqrt x)))) 2))) (+ (* -2 (/ (pow (exp (neg (* -1 (log (/ 1 x))))) 2) (* x (pow (- (sqrt (/ 1 x)) (cos (atan (sqrt x)))) 2)))) (+ (* 2 (/ (pow (exp (neg (* -1 (log (/ 1 x))))) 2) (* (pow x 2) (pow (- (sqrt (/ 1 x)) (cos (atan (sqrt x)))) 2)))) (+ (/ (pow (exp (neg (* -1 (log (/ 1 x))))) 2) (* (pow x 2) (pow (- (sqrt (/ 1 x)) (cos (atan (sqrt x)))) 2))) (/ (pow (exp (neg (* -1 (log (/ 1 x))))) 2) (pow (- (sqrt (/ 1 x)) (cos (atan (sqrt x)))) 2))))))
(- (+ (* 4 (/ (pow (exp (neg (* -1 (log (/ 1 x))))) 2) (* (pow x 3) (pow (- (sqrt (/ 1 x)) (cos (atan (sqrt x)))) 2)))) (/ 1 (* (pow x 2) (pow (- (sqrt (/ 1 x)) (cos (atan (sqrt x)))) 2)))) (+ (* -2 (/ (pow (exp (neg (* -1 (log (/ 1 x))))) 2) (* x (pow (- (sqrt (/ 1 x)) (cos (atan (sqrt x)))) 2)))) (+ (* 2 (/ (pow (exp (neg (* -1 (log (/ 1 x))))) 2) (* (pow x 2) (pow (- (sqrt (/ 1 x)) (cos (atan (sqrt x)))) 2)))) (+ (/ (pow (exp (neg (* -1 (log (/ 1 x))))) 2) (* (pow x 2) (pow (- (sqrt (/ 1 x)) (cos (atan (sqrt x)))) 2))) (/ (pow (exp (neg (* -1 (log (/ 1 x))))) 2) (pow (- (sqrt (/ 1 x)) (cos (atan (sqrt x)))) 2))))))
(/ 1 (* (pow x 2) (pow (- (sqrt (/ 1 x)) (cos (atan (sqrt x)))) 2)))
(/ 1 (* x (- (sqrt (/ 1 x)) (cos (atan (sqrt x))))))
(- (sqrt (/ 1 x)) (cos (atan (sqrt x))))
(- (sqrt (/ 1 x)) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)))
(- (+ (sqrt (/ 1 x)) (* 1/2 (sqrt (/ 1 (pow x 3))))) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)))
(- (+ (sqrt (/ 1 x)) (* -1/2 (sqrt (/ 1 (pow x 5))))) (+ (* -1/2 (sqrt (/ 1 (pow x 3)))) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))))
(- (+ (sqrt (/ 1 x)) (* -1 (/ (- (* -1/2 (* (sqrt (/ 1 x)) (+ 1 (* -1/4 (/ x (pow (sqrt -1) 2)))))) (* -1/2 (sqrt x))) (pow x 3)))) (+ (* -1/2 (sqrt (/ 1 (pow x 3)))) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))))
(* -1/2 (* (sqrt (/ 1 (pow x 3))) (pow (sqrt -1) 2)))
(* -1 (/ (+ (* 1/2 (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))) (* 1/2 (* (sqrt (/ 1 (pow x 3))) (pow (sqrt -1) 2)))) x))
(* (sqrt (/ 1 (pow x 3))) (pow (sqrt -1) 2))
(* -1 (/ (+ (* -1 (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))) (* -1 (* (sqrt (/ 1 (pow x 3))) (pow (sqrt -1) 2)))) x))
(* (sqrt x) (pow (sqrt -1) 2))
(* -1 (* x (- (* -1 (* (sqrt (/ 1 (pow x 3))) (pow (sqrt -1) 2))) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)))))
(* (sqrt (/ 1 x)) (pow (sqrt -1) 2))
(/ -1/2 x)
(* -1 (/ (+ 1/2 (* -1 (/ (+ (* -1/4 (/ x (pow (sqrt -1) 2))) (* -1/8 (/ x (pow (sqrt -1) 2)))) (pow x 2)))) x))
(* -1 (/ (+ 1/2 (* -1 (/ (+ (* -1/4 (/ x (pow (sqrt -1) 2))) (+ (* -1/8 (/ x (pow (sqrt -1) 2))) (* 1/4 (/ 1 (pow (sqrt -1) 2))))) (pow x 2)))) x))
(* -1 (/ (- (+ 1/2 (* -1 (/ (- (* -1 (/ (+ (* 1/8 (/ (pow x 2) (pow (sqrt -1) 4))) (* 1/4 (/ (* x (+ 1 (* -1/4 (/ x (pow (sqrt -1) 2))))) (pow (sqrt -1) 2)))) x)) (* -1/4 (/ x (pow (sqrt -1) 2)))) (pow x 3)))) (+ (/ -1/4 (* x (pow (sqrt -1) 2))) (/ -1/8 (* x (pow (sqrt -1) 2))))) x))
(/ (+ (* 1/4 (* (sqrt (/ 1 x)) (/ 1 (pow (sqrt -1) 2)))) (* 1/2 (sqrt x))) (pow x 2))
(/ (+ (* -1 (/ (+ (* -1 (/ (+ (* -1/4 (* (sqrt x) (/ (+ 1 (* 1/4 (/ 1 (pow (sqrt -1) 2)))) (pow (sqrt -1) 2)))) (* -1/8 (* (sqrt (pow x 3)) (/ 1 (pow (sqrt -1) 2))))) x)) (* -1/4 (* (sqrt x) (/ 1 (pow (sqrt -1) 2))))) x)) (* 1/2 (sqrt x))) (pow x 2))
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(* -1/2 (sqrt (/ 1 x)))
(* -1 (/ (+ (* -1/8 (* (sqrt (/ 1 x)) (/ 1 (pow (sqrt -1) 2)))) (* 1/2 (sqrt x))) x))
(* -1 (/ (+ (* -1/8 (* (sqrt (/ 1 x)) (/ 1 (pow (sqrt -1) 2)))) (+ (* 1/16 (* (sqrt (/ 1 (pow x 3))) (/ 1 (pow (sqrt -1) 4)))) (* 1/2 (sqrt x)))) x))
(* -1 (/ (+ (* -1/8 (* (sqrt (/ 1 x)) (/ 1 (pow (sqrt -1) 2)))) (+ (* -5/128 (* (sqrt (/ 1 (pow x 5))) (/ 1 (pow (sqrt -1) 6)))) (+ (* 1/16 (* (sqrt (/ 1 (pow x 3))) (/ 1 (pow (sqrt -1) 4)))) (* 1/2 (sqrt x))))) x))
(* -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)))))))
(/ (+ (* 1/4 (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))) (* 1/2 (sqrt x))) (pow x 2))
(/ (+ (* -1 (/ (+ (* -1 (/ (+ (* -1/4 (* (sqrt x) (+ (* -1 (pow (sqrt -1) 4)) (* 1/4 (pow (sqrt -1) 4))))) (* -1/8 (* (sqrt (pow x 3)) (/ 1 (pow (sqrt -1) 2))))) x)) (* -1/4 (* (sqrt x) (pow (sqrt -1) 2)))) x)) (* 1/2 (sqrt x))) (pow x 2))
(/ (+ (* -1 (/ (+ (* -1 (/ (+ (* -1 (/ (+ (* -1/4 (* (sqrt x) (+ (* 1/2 (* (pow (sqrt -1) 2) (+ (* -1 (pow (sqrt -1) 4)) (* 1/4 (pow (sqrt -1) 4))))) (pow (sqrt -1) 6)))) (* 1/16 (sqrt (pow x 3)))) x)) (+ (* -1/4 (* (sqrt x) (+ (* -1 (pow (sqrt -1) 4)) (* 1/4 (pow (sqrt -1) 4))))) (* -1/8 (* (sqrt (pow x 3)) (/ 1 (pow (sqrt -1) 2)))))) x)) (* -1/4 (* (sqrt x) (pow (sqrt -1) 2)))) x)) (* 1/2 (sqrt x))) (pow x 2))
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(+ (* -1 (/ (pow (exp (neg (+ (log -1) (* -1 (log (/ -1 x)))))) 2) (pow (- (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)) (cos (atan (* (sqrt x) (pow (sqrt -1) 2))))) 3))) (* 2 (/ (pow (exp (neg (+ (log -1) (* -1 (log (/ -1 x)))))) 2) (* x (pow (- (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)) (cos (atan (* (sqrt x) (pow (sqrt -1) 2))))) 3)))))
(+ (* -1 (/ (+ (* -2 (/ (pow (exp (neg (+ (log -1) (* -1 (log (/ -1 x)))))) 2) (pow (- (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)) (cos (atan (* (sqrt x) (pow (sqrt -1) 2))))) 3))) (* -1 (/ (- (/ 1 (pow (- (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)) (cos (atan (* (sqrt x) (pow (sqrt -1) 2))))) 3)) (+ (* 2 (/ (pow (exp (neg (+ (log -1) (* -1 (log (/ -1 x)))))) 2) (pow (- (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)) (cos (atan (* (sqrt x) (pow (sqrt -1) 2))))) 3))) (/ (pow (exp (neg (+ (log -1) (* -1 (log (/ -1 x)))))) 2) (pow (- (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)) (cos (atan (* (sqrt x) (pow (sqrt -1) 2))))) 3)))) x))) x)) (* -1 (/ (pow (exp (neg (+ (log -1) (* -1 (log (/ -1 x)))))) 2) (pow (- (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)) (cos (atan (* (sqrt x) (pow (sqrt -1) 2))))) 3))))
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(- (* -1 (/ (- (* -1 (/ (- (+ (* 4 (/ (pow (exp (neg (+ (log -1) (* -1 (log (/ -1 x)))))) 2) (* x (pow (- (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)) (cos (atan (* (sqrt x) (pow (sqrt -1) 2))))) 2)))) (/ 1 (pow (- (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)) (cos (atan (* (sqrt x) (pow (sqrt -1) 2))))) 2))) (+ (* 2 (/ (pow (exp (neg (+ (log -1) (* -1 (log (/ -1 x)))))) 2) (pow (- (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)) (cos (atan (* (sqrt x) (pow (sqrt -1) 2))))) 2))) (/ (pow (exp (neg (+ (log -1) (* -1 (log (/ -1 x)))))) 2) (pow (- (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)) (cos (atan (* (sqrt x) (pow (sqrt -1) 2))))) 2)))) x)) (* 2 (/ (pow (exp (neg (+ (log -1) (* -1 (log (/ -1 x)))))) 2) (pow (- (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)) (cos (atan (* (sqrt x) (pow (sqrt -1) 2))))) 2)))) x)) (/ (pow (exp (neg (+ (log -1) (* -1 (log (/ -1 x)))))) 2) (pow (- (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)) (cos (atan (* (sqrt x) (pow (sqrt -1) 2))))) 2)))
(/ 1 (* (pow x 2) (pow (- (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)) (cos (atan (* (sqrt x) (pow (sqrt -1) 2))))) 2)))
(/ 1 (* x (- (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)) (cos (atan (* (sqrt x) (pow (sqrt -1) 2)))))))
(cos (atan (* (sqrt x) (pow (sqrt -1) 2))))
(- (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)) (cos (atan (* (sqrt x) (pow (sqrt -1) 2)))))
Calls

3 calls:

TimeVariablePointExpression
27.0ms
x
@inf
((- (/ 1 (sqrt x)) (/ 1 (sqrt (+ x 1)))) (* (/ (- (sqrt (/ 1 x)) (sqrt x)) (* x x)) -1/2) (/ (- (sqrt (/ 1 x)) (sqrt x)) (* x x)) (- (sqrt (/ 1 x)) (sqrt x)) (- (/ 1 (sqrt x)) (/ 1 (sqrt (+ x 1)))) (sqrt (/ 1 x)) (/ 1 x) (/ (- (sqrt (+ x 1)) (sqrt x)) (sqrt (+ x 1))) (/ (/ (- (sqrt (+ x 1)) (sqrt x)) (sqrt (+ x 1))) (sqrt x)) (- (sqrt (+ x 1)) (sqrt x)) (sqrt (+ x 1)) (/ (- (sqrt (+ x 1)) (sqrt x)) (sqrt (+ (* (sqrt x) (sqrt x)) (* x x)))) (+ x 1) (/ (- (pow (/ (pow x -1) (- (pow x -1/2) (cos (atan (sqrt x))))) 2) (pow (/ (exp (neg (log (+ 1 x)))) (- (pow x -1/2) (cos (atan (sqrt x))))) 2)) (- (pow x -1/2) (cos (atan (sqrt x))))) (- (pow (/ (pow x -1) (- (pow x -1/2) (cos (atan (sqrt x))))) 2) (pow (/ (exp (neg (log (+ 1 x)))) (- (pow x -1/2) (cos (atan (sqrt x))))) 2)) (pow (/ (pow x -1) (- (pow x -1/2) (cos (atan (sqrt x))))) 2) (/ (pow x -1) (- (pow x -1/2) (cos (atan (sqrt x))))) (sqrt x) (cos (atan (sqrt x))) (- (pow x -1/2) (cos (atan (sqrt x)))))
16.0ms
x
@-inf
((- (/ 1 (sqrt x)) (/ 1 (sqrt (+ x 1)))) (* (/ (- (sqrt (/ 1 x)) (sqrt x)) (* x x)) -1/2) (/ (- (sqrt (/ 1 x)) (sqrt x)) (* x x)) (- (sqrt (/ 1 x)) (sqrt x)) (- (/ 1 (sqrt x)) (/ 1 (sqrt (+ x 1)))) (sqrt (/ 1 x)) (/ 1 x) (/ (- (sqrt (+ x 1)) (sqrt x)) (sqrt (+ x 1))) (/ (/ (- (sqrt (+ x 1)) (sqrt x)) (sqrt (+ x 1))) (sqrt x)) (- (sqrt (+ x 1)) (sqrt x)) (sqrt (+ x 1)) (/ (- (sqrt (+ x 1)) (sqrt x)) (sqrt (+ (* (sqrt x) (sqrt x)) (* x x)))) (+ x 1) (/ (- (pow (/ (pow x -1) (- (pow x -1/2) (cos (atan (sqrt x))))) 2) (pow (/ (exp (neg (log (+ 1 x)))) (- (pow x -1/2) (cos (atan (sqrt x))))) 2)) (- (pow x -1/2) (cos (atan (sqrt x))))) (- (pow (/ (pow x -1) (- (pow x -1/2) (cos (atan (sqrt x))))) 2) (pow (/ (exp (neg (log (+ 1 x)))) (- (pow x -1/2) (cos (atan (sqrt x))))) 2)) (pow (/ (pow x -1) (- (pow x -1/2) (cos (atan (sqrt x))))) 2) (/ (pow x -1) (- (pow x -1/2) (cos (atan (sqrt x))))) (sqrt x) (cos (atan (sqrt x))) (- (pow x -1/2) (cos (atan (sqrt x)))))
7.0ms
x
@0
((- (/ 1 (sqrt x)) (/ 1 (sqrt (+ x 1)))) (* (/ (- (sqrt (/ 1 x)) (sqrt x)) (* x x)) -1/2) (/ (- (sqrt (/ 1 x)) (sqrt x)) (* x x)) (- (sqrt (/ 1 x)) (sqrt x)) (- (/ 1 (sqrt x)) (/ 1 (sqrt (+ x 1)))) (sqrt (/ 1 x)) (/ 1 x) (/ (- (sqrt (+ x 1)) (sqrt x)) (sqrt (+ x 1))) (/ (/ (- (sqrt (+ x 1)) (sqrt x)) (sqrt (+ x 1))) (sqrt x)) (- (sqrt (+ x 1)) (sqrt x)) (sqrt (+ x 1)) (/ (- (sqrt (+ x 1)) (sqrt x)) (sqrt (+ (* (sqrt x) (sqrt x)) (* x x)))) (+ x 1) (/ (- (pow (/ (pow x -1) (- (pow x -1/2) (cos (atan (sqrt x))))) 2) (pow (/ (exp (neg (log (+ 1 x)))) (- (pow x -1/2) (cos (atan (sqrt x))))) 2)) (- (pow x -1/2) (cos (atan (sqrt x))))) (- (pow (/ (pow x -1) (- (pow x -1/2) (cos (atan (sqrt x))))) 2) (pow (/ (exp (neg (log (+ 1 x)))) (- (pow x -1/2) (cos (atan (sqrt x))))) 2)) (pow (/ (pow x -1) (- (pow x -1/2) (cos (atan (sqrt x))))) 2) (/ (pow x -1) (- (pow x -1/2) (cos (atan (sqrt x))))) (sqrt x) (cos (atan (sqrt x))) (- (pow x -1/2) (cos (atan (sqrt x)))))

simplify155.0ms (2.3%)

Memory
0.9MiB live, 133.6MiB allocated
Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
06113964
120383206
086853068
Stop Event
iter limit
node limit
Counts
117 → 116
Calls
Call 1
Inputs
(sqrt (/ 1 x))
(/ (+ (sqrt x) (* -1 x)) x)
(/ (+ (sqrt x) (* x (- (* 1/2 x) 1))) x)
(/ (+ (sqrt x) (* x (- (* x (+ 1/2 (* -3/8 x))) 1))) x)
(* -1/2 (sqrt (/ 1 (pow x 5))))
(/ (+ (* -1/2 (sqrt x)) (* 1/2 (sqrt (pow x 3)))) (pow x 3))
(sqrt (/ 1 (pow x 5)))
(/ (+ (sqrt x) (* -1 (sqrt (pow x 3)))) (pow x 3))
(/ (+ (sqrt x) (* -1 (sqrt (pow x 3)))) x)
(/ 1 x)
(- 1 (sqrt x))
(- (+ 1 (* x (+ 1/2 (* -1/2 (- 1 (sqrt x)))))) (sqrt x))
(- (+ 1 (* x (+ 1/2 (+ (* -1/2 (- 1 (sqrt x))) (* x (- (* 3/8 (- 1 (sqrt x))) 3/8)))))) (sqrt x))
(- (+ 1 (* x (+ 1/2 (+ (* -1/2 (- 1 (sqrt x))) (* x (- (+ (* 3/8 (- 1 (sqrt x))) (* x (+ 5/16 (* -5/16 (- 1 (sqrt x)))))) 3/8)))))) (sqrt x))
(* (sqrt (/ 1 x)) (- 1 (sqrt x)))
(/ (+ (* 1/2 (sqrt (pow x 3))) (* (sqrt x) (- 1 (sqrt x)))) x)
(/ (+ (* x (+ (* 1/2 (sqrt x)) (* x (+ (* -1/2 (* (sqrt (/ 1 x)) (- 1 (sqrt x)))) (* -1/8 (sqrt x)))))) (* (sqrt x) (- 1 (sqrt x)))) x)
(/ (+ (* x (+ (* 1/2 (sqrt x)) (* x (+ (* -1/2 (* (sqrt (/ 1 x)) (- 1 (sqrt x)))) (+ (* -1/8 (sqrt x)) (* x (+ (* -1/4 (sqrt (/ 1 x))) (+ (* 1/16 (sqrt x)) (* 1/2 (* (sqrt (/ 1 x)) (- 1 (sqrt x)))))))))))) (* (sqrt x) (- 1 (sqrt x)))) x)
(- (+ 1 (* 1/2 x)) (sqrt x))
(- (+ 1 (* x (+ 1/2 (* -1/8 x)))) (sqrt x))
(- (+ 1 (* x (+ 1/2 (* x (- (* 1/16 x) 1/8))))) (sqrt x))
1
(+ 1 (* 1/2 x))
(+ 1 (* x (+ 1/2 (* -1/8 x))))
(+ 1 (* x (+ 1/2 (* x (- (* 1/16 x) 1/8)))))
(+ 1 x)
(* x (+ (sqrt (/ 1 (pow x 3))) (* x (- (* 2 (/ (cos (atan (sqrt x))) (pow x 2))) (* -1 (/ (cos (atan (sqrt x))) (pow x 2)))))))
(* x (+ (sqrt (/ 1 (pow x 3))) (* x (- (+ (* 2 (/ (cos (atan (sqrt x))) (pow x 2))) (* x (- (* -1 (* (sqrt (/ 1 x)) (+ (* -4 (/ (pow (cos (atan (sqrt x))) 2) (pow x 2))) (+ (/ 1 x) (/ (pow (cos (atan (sqrt x))) 2) (pow x 2)))))) (* -1 (* (sqrt (/ 1 x)) (* (cos (atan (sqrt x))) (- (* 2 (/ (cos (atan (sqrt x))) (pow x 2))) (* -1 (/ (cos (atan (sqrt x))) (pow x 2)))))))))) (* -1 (/ (cos (atan (sqrt x))) (pow x 2)))))))
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(+ (* 2 (* (sqrt (/ 1 x)) (cos (atan (sqrt x))))) (/ 1 x))
(+ (* x (- (* -1 (* x (+ (* -4 (/ (pow (cos (atan (sqrt x))) 2) (pow x 2))) (+ (/ 1 x) (/ (pow (cos (atan (sqrt x))) 2) (pow x 2)))))) (* -2 (* (sqrt (/ 1 (pow x 3))) (cos (atan (sqrt x))))))) (/ 1 x))
(+ (* x (- (* x (- (* x (- (+ (* -2 (* (sqrt (/ 1 (pow x 3))) (cos (atan (sqrt x))))) (* 2 (/ 1 x))) (+ (* 2 (* (sqrt (/ 1 x)) (* (cos (atan (sqrt x))) (+ (* -4 (/ (pow (cos (atan (sqrt x))) 2) (pow x 2))) (/ (pow (cos (atan (sqrt x))) 2) (pow x 2)))))) (* 2 (* (sqrt (/ 1 (pow x 5))) (pow (cos (atan (sqrt x))) 3)))))) (+ (* -4 (/ (pow (cos (atan (sqrt x))) 2) (pow x 2))) (+ (/ 1 x) (/ (pow (cos (atan (sqrt x))) 2) (pow x 2)))))) (* -2 (* (sqrt (/ 1 (pow x 3))) (cos (atan (sqrt x))))))) (/ 1 x))
(+ (* x (- (* -1 (* x (+ (* -4 (/ (pow (cos (atan (sqrt x))) 2) (pow x 2))) (/ (pow (cos (atan (sqrt x))) 2) (pow x 2))))) (* -2 (* (sqrt (/ 1 (pow x 3))) (cos (atan (sqrt x))))))) (/ 1 x))
(+ (* x (- (* x (- (* -1 (* x (+ (* 2 (* (sqrt (/ 1 x)) (* (cos (atan (sqrt x))) (+ (* -4 (/ (pow (cos (atan (sqrt x))) 2) (pow x 2))) (/ (pow (cos (atan (sqrt x))) 2) (pow x 2)))))) (* 2 (* (sqrt (/ 1 (pow x 5))) (pow (cos (atan (sqrt x))) 3)))))) (+ (* -4 (/ (pow (cos (atan (sqrt x))) 2) (pow x 2))) (/ (pow (cos (atan (sqrt x))) 2) (pow x 2))))) (* -2 (* (sqrt (/ 1 (pow x 3))) (cos (atan (sqrt x))))))) (/ 1 x))
(+ (cos (atan (sqrt x))) (sqrt (/ 1 x)))
(+ (sqrt (/ 1 x)) (* x (- (* (sqrt (/ 1 x)) (pow (cos (atan (sqrt x))) 2)) (* -1 (/ (cos (atan (sqrt x))) x)))))
(+ (sqrt (/ 1 x)) (* x (- (* x (- (/ (pow (cos (atan (sqrt x))) 3) x) (* -1 (* (sqrt (/ 1 (pow x 3))) (pow (cos (atan (sqrt x))) 2))))) (* -1 (/ (cos (atan (sqrt x))) x)))))
(sqrt x)
(cos (atan (sqrt x)))
(/ (+ (sqrt x) (* -1 (* x (cos (atan (sqrt x)))))) x)
(* 1/2 (sqrt (/ 1 (pow x 3))))
(/ (- (* -1/2 (sqrt (/ 1 x))) (* -1/2 (sqrt x))) (pow x 2))
(/ (- (* 1/2 (* (sqrt (/ 1 (pow x 3))) (+ 1 (* 1/4 x)))) (+ (* -1/2 (sqrt x)) (* 1/2 (sqrt (/ 1 x))))) (pow x 2))
(/ (- (* -1/2 (* (sqrt (/ 1 (pow x 5))) (+ 1 (* 1/2 x)))) (+ (* -1/2 (sqrt x)) (+ (* -1/2 (* (sqrt (/ 1 (pow x 3))) (+ 1 (* 1/4 x)))) (* 1/2 (sqrt (/ 1 x)))))) (pow x 2))
(/ (+ (* -1/2 (sqrt (/ 1 (pow x 3)))) (* 1/2 (sqrt (/ 1 x)))) x)
(* -1 (sqrt (/ 1 (pow x 3))))
(/ (+ (sqrt (/ 1 (pow x 3))) (* -1 (sqrt (/ 1 x)))) x)
(* -1 (sqrt x))
(* x (- (sqrt (/ 1 (pow x 3))) (sqrt (/ 1 x))))
(/ 1/2 x)
(/ (+ 1/2 (* -1 (/ (+ (* 1/8 x) (* 1/4 x)) (pow x 2)))) x)
(/ (- (+ 1/2 (* 1/4 (/ 1 (pow x 2)))) (+ (/ 1/8 x) (/ 1/4 x))) x)
(/ (- (+ 1/2 (+ (* -1/4 (/ (+ 1 (* 1/4 x)) (pow x 3))) (* 3/8 (/ 1 (pow x 2))))) (+ (/ 1/8 x) (/ 1/4 x))) x)
(/ (+ (* -1/4 (sqrt (/ 1 x))) (* 1/2 (sqrt x))) (pow x 2))
(/ (+ (* -1/4 (sqrt (/ 1 x))) (+ (* -1/8 (sqrt (/ 1 x))) (+ (* 3/16 (sqrt (/ 1 (pow x 3)))) (* 1/2 (sqrt x))))) (pow x 2))
(/ (+ (* -1/4 (sqrt (/ 1 x))) (+ (* -5/32 (sqrt (/ 1 (pow x 5)))) (+ (* -1/8 (sqrt (/ 1 x))) (+ (* 1/16 (sqrt (/ 1 (pow x 3)))) (+ (* 3/16 (sqrt (/ 1 (pow x 3)))) (* 1/2 (sqrt x))))))) (pow x 2))
(* 1/2 (sqrt (/ 1 x)))
(/ (+ (* -1/8 (sqrt (/ 1 x))) (* 1/2 (sqrt x))) x)
(/ (+ (* -1/8 (sqrt (/ 1 x))) (+ (* 1/16 (sqrt (/ 1 (pow x 3)))) (* 1/2 (sqrt x)))) x)
(/ (+ (* -1/8 (sqrt (/ 1 x))) (+ (* -5/128 (sqrt (/ 1 (pow x 5)))) (+ (* 1/16 (sqrt (/ 1 (pow x 3)))) (* 1/2 (sqrt x))))) 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))))))))
x
(* x (+ 1 (/ 1 x)))
(* -1 (/ (pow (exp (neg (* -1 (log (/ 1 x))))) 2) (pow (- (sqrt (/ 1 x)) (cos (atan (sqrt x)))) 3)))
(+ (* -1 (/ (pow (exp (neg (* -1 (log (/ 1 x))))) 2) (pow (- (sqrt (/ 1 x)) (cos (atan (sqrt x)))) 3))) (* 2 (/ (pow (exp (neg (* -1 (log (/ 1 x))))) 2) (* x (pow (- (sqrt (/ 1 x)) (cos (atan (sqrt x)))) 3)))))
(- (+ (* -1 (/ (pow (exp (neg (* -1 (log (/ 1 x))))) 2) (pow (- (sqrt (/ 1 x)) (cos (atan (sqrt x)))) 3))) (+ (* 2 (/ (pow (exp (neg (* -1 (log (/ 1 x))))) 2) (* x (pow (- (sqrt (/ 1 x)) (cos (atan (sqrt x)))) 3)))) (/ 1 (* (pow x 2) (pow (- (sqrt (/ 1 x)) (cos (atan (sqrt x)))) 3))))) (+ (* 2 (/ (pow (exp (neg (* -1 (log (/ 1 x))))) 2) (* (pow x 2) (pow (- (sqrt (/ 1 x)) (cos (atan (sqrt x)))) 3)))) (/ (pow (exp (neg (* -1 (log (/ 1 x))))) 2) (* (pow x 2) (pow (- (sqrt (/ 1 x)) (cos (atan (sqrt x)))) 3)))))
(- (+ (* -1 (/ (pow (exp (neg (* -1 (log (/ 1 x))))) 2) (pow (- (sqrt (/ 1 x)) (cos (atan (sqrt x)))) 3))) (+ (* 2 (/ (pow (exp (neg (* -1 (log (/ 1 x))))) 2) (* x (pow (- (sqrt (/ 1 x)) (cos (atan (sqrt x)))) 3)))) (+ (* 4 (/ (pow (exp (neg (* -1 (log (/ 1 x))))) 2) (* (pow x 3) (pow (- (sqrt (/ 1 x)) (cos (atan (sqrt x)))) 3)))) (/ 1 (* (pow x 2) (pow (- (sqrt (/ 1 x)) (cos (atan (sqrt x)))) 3)))))) (+ (* 2 (/ (pow (exp (neg (* -1 (log (/ 1 x))))) 2) (* (pow x 2) (pow (- (sqrt (/ 1 x)) (cos (atan (sqrt x)))) 3)))) (/ (pow (exp (neg (* -1 (log (/ 1 x))))) 2) (* (pow x 2) (pow (- (sqrt (/ 1 x)) (cos (atan (sqrt x)))) 3)))))
(* -1 (/ (pow (exp (neg (* -1 (log (/ 1 x))))) 2) (pow (- (sqrt (/ 1 x)) (cos (atan (sqrt x)))) 2)))
(- (* 2 (/ (pow (exp (neg (* -1 (log (/ 1 x))))) 2) (* x (pow (- (sqrt (/ 1 x)) (cos (atan (sqrt x)))) 2)))) (/ (pow (exp (neg (* -1 (log (/ 1 x))))) 2) (pow (- (sqrt (/ 1 x)) (cos (atan (sqrt x)))) 2)))
(- (/ 1 (* (pow x 2) (pow (- (sqrt (/ 1 x)) (cos (atan (sqrt x)))) 2))) (+ (* -2 (/ (pow (exp (neg (* -1 (log (/ 1 x))))) 2) (* x (pow (- (sqrt (/ 1 x)) (cos (atan (sqrt x)))) 2)))) (+ (* 2 (/ (pow (exp (neg (* -1 (log (/ 1 x))))) 2) (* (pow x 2) (pow (- (sqrt (/ 1 x)) (cos (atan (sqrt x)))) 2)))) (+ (/ (pow (exp (neg (* -1 (log (/ 1 x))))) 2) (* (pow x 2) (pow (- (sqrt (/ 1 x)) (cos (atan (sqrt x)))) 2))) (/ (pow (exp (neg (* -1 (log (/ 1 x))))) 2) (pow (- (sqrt (/ 1 x)) (cos (atan (sqrt x)))) 2))))))
(- (+ (* 4 (/ (pow (exp (neg (* -1 (log (/ 1 x))))) 2) (* (pow x 3) (pow (- (sqrt (/ 1 x)) (cos (atan (sqrt x)))) 2)))) (/ 1 (* (pow x 2) (pow (- (sqrt (/ 1 x)) (cos (atan (sqrt x)))) 2)))) (+ (* -2 (/ (pow (exp (neg (* -1 (log (/ 1 x))))) 2) (* x (pow (- (sqrt (/ 1 x)) (cos (atan (sqrt x)))) 2)))) (+ (* 2 (/ (pow (exp (neg (* -1 (log (/ 1 x))))) 2) (* (pow x 2) (pow (- (sqrt (/ 1 x)) (cos (atan (sqrt x)))) 2)))) (+ (/ (pow (exp (neg (* -1 (log (/ 1 x))))) 2) (* (pow x 2) (pow (- (sqrt (/ 1 x)) (cos (atan (sqrt x)))) 2))) (/ (pow (exp (neg (* -1 (log (/ 1 x))))) 2) (pow (- (sqrt (/ 1 x)) (cos (atan (sqrt x)))) 2))))))
(/ 1 (* (pow x 2) (pow (- (sqrt (/ 1 x)) (cos (atan (sqrt x)))) 2)))
(/ 1 (* x (- (sqrt (/ 1 x)) (cos (atan (sqrt x))))))
(- (sqrt (/ 1 x)) (cos (atan (sqrt x))))
(- (sqrt (/ 1 x)) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)))
(- (+ (sqrt (/ 1 x)) (* 1/2 (sqrt (/ 1 (pow x 3))))) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)))
(- (+ (sqrt (/ 1 x)) (* -1/2 (sqrt (/ 1 (pow x 5))))) (+ (* -1/2 (sqrt (/ 1 (pow x 3)))) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))))
(- (+ (sqrt (/ 1 x)) (* -1 (/ (- (* -1/2 (* (sqrt (/ 1 x)) (+ 1 (* -1/4 (/ x (pow (sqrt -1) 2)))))) (* -1/2 (sqrt x))) (pow x 3)))) (+ (* -1/2 (sqrt (/ 1 (pow x 3)))) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))))
(* -1/2 (* (sqrt (/ 1 (pow x 3))) (pow (sqrt -1) 2)))
(* -1 (/ (+ (* 1/2 (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))) (* 1/2 (* (sqrt (/ 1 (pow x 3))) (pow (sqrt -1) 2)))) x))
(* (sqrt (/ 1 (pow x 3))) (pow (sqrt -1) 2))
(* -1 (/ (+ (* -1 (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))) (* -1 (* (sqrt (/ 1 (pow x 3))) (pow (sqrt -1) 2)))) x))
(* (sqrt x) (pow (sqrt -1) 2))
(* -1 (* x (- (* -1 (* (sqrt (/ 1 (pow x 3))) (pow (sqrt -1) 2))) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)))))
(* (sqrt (/ 1 x)) (pow (sqrt -1) 2))
(/ -1/2 x)
(* -1 (/ (+ 1/2 (* -1 (/ (+ (* -1/4 (/ x (pow (sqrt -1) 2))) (* -1/8 (/ x (pow (sqrt -1) 2)))) (pow x 2)))) x))
(* -1 (/ (+ 1/2 (* -1 (/ (+ (* -1/4 (/ x (pow (sqrt -1) 2))) (+ (* -1/8 (/ x (pow (sqrt -1) 2))) (* 1/4 (/ 1 (pow (sqrt -1) 2))))) (pow x 2)))) x))
(* -1 (/ (- (+ 1/2 (* -1 (/ (- (* -1 (/ (+ (* 1/8 (/ (pow x 2) (pow (sqrt -1) 4))) (* 1/4 (/ (* x (+ 1 (* -1/4 (/ x (pow (sqrt -1) 2))))) (pow (sqrt -1) 2)))) x)) (* -1/4 (/ x (pow (sqrt -1) 2)))) (pow x 3)))) (+ (/ -1/4 (* x (pow (sqrt -1) 2))) (/ -1/8 (* x (pow (sqrt -1) 2))))) x))
(/ (+ (* 1/4 (* (sqrt (/ 1 x)) (/ 1 (pow (sqrt -1) 2)))) (* 1/2 (sqrt x))) (pow x 2))
(/ (+ (* -1 (/ (+ (* -1 (/ (+ (* -1/4 (* (sqrt x) (/ (+ 1 (* 1/4 (/ 1 (pow (sqrt -1) 2)))) (pow (sqrt -1) 2)))) (* -1/8 (* (sqrt (pow x 3)) (/ 1 (pow (sqrt -1) 2))))) x)) (* -1/4 (* (sqrt x) (/ 1 (pow (sqrt -1) 2))))) x)) (* 1/2 (sqrt x))) (pow x 2))
(/ (+ (* -1 (/ (+ (* -1 (/ (+ (* -1 (/ (+ (* -1/4 (* (sqrt x) (/ (+ 1 (* 1/2 (/ (+ 1 (* 1/4 (/ 1 (pow (sqrt -1) 2)))) (pow (sqrt -1) 2)))) (pow (sqrt -1) 2)))) (* 1/16 (* (sqrt (pow x 3)) (/ 1 (pow (sqrt -1) 4))))) x)) (+ (* -1/4 (* (sqrt x) (/ (+ 1 (* 1/4 (/ 1 (pow (sqrt -1) 2)))) (pow (sqrt -1) 2)))) (* -1/8 (* (sqrt (pow x 3)) (/ 1 (pow (sqrt -1) 2)))))) x)) (* -1/4 (* (sqrt x) (/ 1 (pow (sqrt -1) 2))))) x)) (* 1/2 (sqrt x))) (pow x 2))
(* -1/2 (sqrt (/ 1 x)))
(* -1 (/ (+ (* -1/8 (* (sqrt (/ 1 x)) (/ 1 (pow (sqrt -1) 2)))) (* 1/2 (sqrt x))) x))
(* -1 (/ (+ (* -1/8 (* (sqrt (/ 1 x)) (/ 1 (pow (sqrt -1) 2)))) (+ (* 1/16 (* (sqrt (/ 1 (pow x 3))) (/ 1 (pow (sqrt -1) 4)))) (* 1/2 (sqrt x)))) x))
(* -1 (/ (+ (* -1/8 (* (sqrt (/ 1 x)) (/ 1 (pow (sqrt -1) 2)))) (+ (* -5/128 (* (sqrt (/ 1 (pow x 5))) (/ 1 (pow (sqrt -1) 6)))) (+ (* 1/16 (* (sqrt (/ 1 (pow x 3))) (/ 1 (pow (sqrt -1) 4)))) (* 1/2 (sqrt x))))) x))
(* -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)))))))
(/ (+ (* 1/4 (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))) (* 1/2 (sqrt x))) (pow x 2))
(/ (+ (* -1 (/ (+ (* -1 (/ (+ (* -1/4 (* (sqrt x) (+ (* -1 (pow (sqrt -1) 4)) (* 1/4 (pow (sqrt -1) 4))))) (* -1/8 (* (sqrt (pow x 3)) (/ 1 (pow (sqrt -1) 2))))) x)) (* -1/4 (* (sqrt x) (pow (sqrt -1) 2)))) x)) (* 1/2 (sqrt x))) (pow x 2))
(/ (+ (* -1 (/ (+ (* -1 (/ (+ (* -1 (/ (+ (* -1/4 (* (sqrt x) (+ (* 1/2 (* (pow (sqrt -1) 2) (+ (* -1 (pow (sqrt -1) 4)) (* 1/4 (pow (sqrt -1) 4))))) (pow (sqrt -1) 6)))) (* 1/16 (sqrt (pow x 3)))) x)) (+ (* -1/4 (* (sqrt x) (+ (* -1 (pow (sqrt -1) 4)) (* 1/4 (pow (sqrt -1) 4))))) (* -1/8 (* (sqrt (pow x 3)) (/ 1 (pow (sqrt -1) 2)))))) x)) (* -1/4 (* (sqrt x) (pow (sqrt -1) 2)))) x)) (* 1/2 (sqrt x))) (pow x 2))
(* -1 (/ (pow (exp (neg (+ (log -1) (* -1 (log (/ -1 x)))))) 2) (pow (- (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)) (cos (atan (* (sqrt x) (pow (sqrt -1) 2))))) 3)))
(+ (* -1 (/ (pow (exp (neg (+ (log -1) (* -1 (log (/ -1 x)))))) 2) (pow (- (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)) (cos (atan (* (sqrt x) (pow (sqrt -1) 2))))) 3))) (* 2 (/ (pow (exp (neg (+ (log -1) (* -1 (log (/ -1 x)))))) 2) (* x (pow (- (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)) (cos (atan (* (sqrt x) (pow (sqrt -1) 2))))) 3)))))
(+ (* -1 (/ (+ (* -2 (/ (pow (exp (neg (+ (log -1) (* -1 (log (/ -1 x)))))) 2) (pow (- (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)) (cos (atan (* (sqrt x) (pow (sqrt -1) 2))))) 3))) (* -1 (/ (- (/ 1 (pow (- (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)) (cos (atan (* (sqrt x) (pow (sqrt -1) 2))))) 3)) (+ (* 2 (/ (pow (exp (neg (+ (log -1) (* -1 (log (/ -1 x)))))) 2) (pow (- (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)) (cos (atan (* (sqrt x) (pow (sqrt -1) 2))))) 3))) (/ (pow (exp (neg (+ (log -1) (* -1 (log (/ -1 x)))))) 2) (pow (- (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)) (cos (atan (* (sqrt x) (pow (sqrt -1) 2))))) 3)))) x))) x)) (* -1 (/ (pow (exp (neg (+ (log -1) (* -1 (log (/ -1 x)))))) 2) (pow (- (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)) (cos (atan (* (sqrt x) (pow (sqrt -1) 2))))) 3))))
(+ (* -1 (/ (+ (* -2 (/ (pow (exp (neg (+ (log -1) (* -1 (log (/ -1 x)))))) 2) (pow (- (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)) (cos (atan (* (sqrt x) (pow (sqrt -1) 2))))) 3))) (* -1 (/ (- (+ (* 4 (/ (pow (exp (neg (+ (log -1) (* -1 (log (/ -1 x)))))) 2) (* x (pow (- (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)) (cos (atan (* (sqrt x) (pow (sqrt -1) 2))))) 3)))) (/ 1 (pow (- (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)) (cos (atan (* (sqrt x) (pow (sqrt -1) 2))))) 3))) (+ (* 2 (/ (pow (exp (neg (+ (log -1) (* -1 (log (/ -1 x)))))) 2) (pow (- (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)) (cos (atan (* (sqrt x) (pow (sqrt -1) 2))))) 3))) (/ (pow (exp (neg (+ (log -1) (* -1 (log (/ -1 x)))))) 2) (pow (- (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)) (cos (atan (* (sqrt x) (pow (sqrt -1) 2))))) 3)))) x))) x)) (* -1 (/ (pow (exp (neg (+ (log -1) (* -1 (log (/ -1 x)))))) 2) (pow (- (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)) (cos (atan (* (sqrt x) (pow (sqrt -1) 2))))) 3))))
(* -1 (/ (pow (exp (neg (+ (log -1) (* -1 (log (/ -1 x)))))) 2) (pow (- (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)) (cos (atan (* (sqrt x) (pow (sqrt -1) 2))))) 2)))
(- (* 2 (/ (pow (exp (neg (+ (log -1) (* -1 (log (/ -1 x)))))) 2) (* x (pow (- (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)) (cos (atan (* (sqrt x) (pow (sqrt -1) 2))))) 2)))) (/ (pow (exp (neg (+ (log -1) (* -1 (log (/ -1 x)))))) 2) (pow (- (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)) (cos (atan (* (sqrt x) (pow (sqrt -1) 2))))) 2)))
(- (* -1 (/ (- (* -1 (/ (- (/ 1 (pow (- (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)) (cos (atan (* (sqrt x) (pow (sqrt -1) 2))))) 2)) (+ (* 2 (/ (pow (exp (neg (+ (log -1) (* -1 (log (/ -1 x)))))) 2) (pow (- (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)) (cos (atan (* (sqrt x) (pow (sqrt -1) 2))))) 2))) (/ (pow (exp (neg (+ (log -1) (* -1 (log (/ -1 x)))))) 2) (pow (- (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)) (cos (atan (* (sqrt x) (pow (sqrt -1) 2))))) 2)))) x)) (* 2 (/ (pow (exp (neg (+ (log -1) (* -1 (log (/ -1 x)))))) 2) (pow (- (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)) (cos (atan (* (sqrt x) (pow (sqrt -1) 2))))) 2)))) x)) (/ (pow (exp (neg (+ (log -1) (* -1 (log (/ -1 x)))))) 2) (pow (- (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)) (cos (atan (* (sqrt x) (pow (sqrt -1) 2))))) 2)))
(- (* -1 (/ (- (* -1 (/ (- (+ (* 4 (/ (pow (exp (neg (+ (log -1) (* -1 (log (/ -1 x)))))) 2) (* x (pow (- (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)) (cos (atan (* (sqrt x) (pow (sqrt -1) 2))))) 2)))) (/ 1 (pow (- (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)) (cos (atan (* (sqrt x) (pow (sqrt -1) 2))))) 2))) (+ (* 2 (/ (pow (exp (neg (+ (log -1) (* -1 (log (/ -1 x)))))) 2) (pow (- (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)) (cos (atan (* (sqrt x) (pow (sqrt -1) 2))))) 2))) (/ (pow (exp (neg (+ (log -1) (* -1 (log (/ -1 x)))))) 2) (pow (- (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)) (cos (atan (* (sqrt x) (pow (sqrt -1) 2))))) 2)))) x)) (* 2 (/ (pow (exp (neg (+ (log -1) (* -1 (log (/ -1 x)))))) 2) (pow (- (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)) (cos (atan (* (sqrt x) (pow (sqrt -1) 2))))) 2)))) x)) (/ (pow (exp (neg (+ (log -1) (* -1 (log (/ -1 x)))))) 2) (pow (- (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)) (cos (atan (* (sqrt x) (pow (sqrt -1) 2))))) 2)))
(/ 1 (* (pow x 2) (pow (- (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)) (cos (atan (* (sqrt x) (pow (sqrt -1) 2))))) 2)))
(/ 1 (* x (- (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)) (cos (atan (* (sqrt x) (pow (sqrt -1) 2)))))))
(cos (atan (* (sqrt x) (pow (sqrt -1) 2))))
(- (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)) (cos (atan (* (sqrt x) (pow (sqrt -1) 2)))))
Outputs
(sqrt (/ 1 x))
(sqrt.f64 (/.f64 #s(literal 1 binary64) x))
(/ (+ (sqrt x) (* -1 x)) x)
(/.f64 (-.f64 (sqrt.f64 x) x) x)
(/ (+ (sqrt x) (* x (- (* 1/2 x) 1))) x)
(/.f64 (fma.f64 (-.f64 (*.f64 #s(literal 1/2 binary64) x) #s(literal 1 binary64)) x (sqrt.f64 x)) x)
(/ (+ (sqrt x) (* x (- (* x (+ 1/2 (* -3/8 x))) 1))) x)
(/.f64 (fma.f64 (-.f64 (*.f64 (fma.f64 #s(literal -3/8 binary64) x #s(literal 1/2 binary64)) x) #s(literal 1 binary64)) x (sqrt.f64 x)) x)
(* -1/2 (sqrt (/ 1 (pow x 5))))
(*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 5 binary64)))) #s(literal -1/2 binary64))
(/ (+ (* -1/2 (sqrt x)) (* 1/2 (sqrt (pow x 3)))) (pow x 3))
(/.f64 (*.f64 #s(literal -1/2 binary64) (-.f64 (sqrt.f64 x) (sqrt.f64 (pow.f64 x #s(literal 3 binary64))))) (pow.f64 x #s(literal 3 binary64)))
(sqrt (/ 1 (pow x 5)))
(sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 5 binary64))))
(/ (+ (sqrt x) (* -1 (sqrt (pow x 3)))) (pow x 3))
(/.f64 (-.f64 (sqrt.f64 x) (sqrt.f64 (pow.f64 x #s(literal 3 binary64)))) (pow.f64 x #s(literal 3 binary64)))
(/ (+ (sqrt x) (* -1 (sqrt (pow x 3)))) x)
(/.f64 (-.f64 (sqrt.f64 x) (sqrt.f64 (pow.f64 x #s(literal 3 binary64)))) x)
(/ 1 x)
(/.f64 #s(literal 1 binary64) x)
(- 1 (sqrt x))
(-.f64 #s(literal 1 binary64) (sqrt.f64 x))
(- (+ 1 (* x (+ 1/2 (* -1/2 (- 1 (sqrt x)))))) (sqrt x))
(fma.f64 (fma.f64 (-.f64 #s(literal 1 binary64) (sqrt.f64 x)) #s(literal -1/2 binary64) #s(literal 1/2 binary64)) x (-.f64 #s(literal 1 binary64) (sqrt.f64 x)))
(- (+ 1 (* x (+ 1/2 (+ (* -1/2 (- 1 (sqrt x))) (* x (- (* 3/8 (- 1 (sqrt x))) 3/8)))))) (sqrt x))
(fma.f64 (fma.f64 (-.f64 (*.f64 #s(literal 3/8 binary64) (-.f64 #s(literal 1 binary64) (sqrt.f64 x))) #s(literal 3/8 binary64)) x (fma.f64 (-.f64 #s(literal 1 binary64) (sqrt.f64 x)) #s(literal -1/2 binary64) #s(literal 1/2 binary64))) x (-.f64 #s(literal 1 binary64) (sqrt.f64 x)))
(- (+ 1 (* x (+ 1/2 (+ (* -1/2 (- 1 (sqrt x))) (* x (- (+ (* 3/8 (- 1 (sqrt x))) (* x (+ 5/16 (* -5/16 (- 1 (sqrt x)))))) 3/8)))))) (sqrt x))
(fma.f64 (fma.f64 (fma.f64 (fma.f64 #s(literal -5/16 binary64) (-.f64 #s(literal 1 binary64) (sqrt.f64 x)) #s(literal 5/16 binary64)) x (-.f64 (*.f64 #s(literal 3/8 binary64) (-.f64 #s(literal 1 binary64) (sqrt.f64 x))) #s(literal 3/8 binary64))) x (fma.f64 (-.f64 #s(literal 1 binary64) (sqrt.f64 x)) #s(literal -1/2 binary64) #s(literal 1/2 binary64))) x (-.f64 #s(literal 1 binary64) (sqrt.f64 x)))
(* (sqrt (/ 1 x)) (- 1 (sqrt x)))
(*.f64 (-.f64 #s(literal 1 binary64) (sqrt.f64 x)) (sqrt.f64 (/.f64 #s(literal 1 binary64) x)))
(/ (+ (* 1/2 (sqrt (pow x 3))) (* (sqrt x) (- 1 (sqrt x)))) x)
(/.f64 (fma.f64 (sqrt.f64 (pow.f64 x #s(literal 3 binary64))) #s(literal 1/2 binary64) (*.f64 (-.f64 #s(literal 1 binary64) (sqrt.f64 x)) (sqrt.f64 x))) x)
(/ (+ (* x (+ (* 1/2 (sqrt x)) (* x (+ (* -1/2 (* (sqrt (/ 1 x)) (- 1 (sqrt x)))) (* -1/8 (sqrt x)))))) (* (sqrt x) (- 1 (sqrt x)))) x)
(/.f64 (fma.f64 (fma.f64 (fma.f64 #s(literal -1/8 binary64) (sqrt.f64 x) (*.f64 (*.f64 (-.f64 #s(literal 1 binary64) (sqrt.f64 x)) #s(literal -1/2 binary64)) (sqrt.f64 (/.f64 #s(literal 1 binary64) x)))) x (*.f64 #s(literal 1/2 binary64) (sqrt.f64 x))) x (*.f64 (-.f64 #s(literal 1 binary64) (sqrt.f64 x)) (sqrt.f64 x))) x)
(/ (+ (* x (+ (* 1/2 (sqrt x)) (* x (+ (* -1/2 (* (sqrt (/ 1 x)) (- 1 (sqrt x)))) (+ (* -1/8 (sqrt x)) (* x (+ (* -1/4 (sqrt (/ 1 x))) (+ (* 1/16 (sqrt x)) (* 1/2 (* (sqrt (/ 1 x)) (- 1 (sqrt x)))))))))))) (* (sqrt x) (- 1 (sqrt x)))) x)
(/.f64 (fma.f64 (fma.f64 (fma.f64 (fma.f64 (*.f64 (-.f64 #s(literal 1 binary64) (sqrt.f64 x)) #s(literal 1/2 binary64)) (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) (fma.f64 #s(literal -1/4 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) (*.f64 #s(literal 1/16 binary64) (sqrt.f64 x)))) x (fma.f64 #s(literal -1/8 binary64) (sqrt.f64 x) (*.f64 (*.f64 (-.f64 #s(literal 1 binary64) (sqrt.f64 x)) #s(literal -1/2 binary64)) (sqrt.f64 (/.f64 #s(literal 1 binary64) x))))) x (*.f64 #s(literal 1/2 binary64) (sqrt.f64 x))) x (*.f64 (-.f64 #s(literal 1 binary64) (sqrt.f64 x)) (sqrt.f64 x))) x)
(- (+ 1 (* 1/2 x)) (sqrt x))
(fma.f64 #s(literal 1/2 binary64) x (-.f64 #s(literal 1 binary64) (sqrt.f64 x)))
(- (+ 1 (* x (+ 1/2 (* -1/8 x)))) (sqrt x))
(fma.f64 (fma.f64 #s(literal -1/8 binary64) x #s(literal 1/2 binary64)) x (-.f64 #s(literal 1 binary64) (sqrt.f64 x)))
(- (+ 1 (* x (+ 1/2 (* x (- (* 1/16 x) 1/8))))) (sqrt x))
(fma.f64 (fma.f64 (-.f64 (*.f64 #s(literal 1/16 binary64) x) #s(literal 1/8 binary64)) x #s(literal 1/2 binary64)) x (-.f64 #s(literal 1 binary64) (sqrt.f64 x)))
1
#s(literal 1 binary64)
(+ 1 (* 1/2 x))
(fma.f64 #s(literal 1/2 binary64) x #s(literal 1 binary64))
(+ 1 (* x (+ 1/2 (* -1/8 x))))
(fma.f64 (fma.f64 #s(literal -1/8 binary64) x #s(literal 1/2 binary64)) x #s(literal 1 binary64))
(+ 1 (* x (+ 1/2 (* x (- (* 1/16 x) 1/8)))))
(fma.f64 (fma.f64 (-.f64 (*.f64 #s(literal 1/16 binary64) x) #s(literal 1/8 binary64)) x #s(literal 1/2 binary64)) x #s(literal 1 binary64))
(+ 1 x)
(+.f64 x #s(literal 1 binary64))
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(* -1 (/ (pow (exp (neg (+ (log -1) (* -1 (log (/ -1 x)))))) 2) (pow (- (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)) (cos (atan (* (sqrt x) (pow (sqrt -1) 2))))) 3)))
(/.f64 (neg.f64 (pow.f64 (exp.f64 (+.f64 (log.f64 (/.f64 #s(literal -1 binary64) x)) (neg.f64 (log.f64 #s(literal -1 binary64))))) #s(literal 2 binary64))) (pow.f64 (-.f64 (neg.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x))) (cos.f64 (atan.f64 (neg.f64 (sqrt.f64 x))))) #s(literal 3 binary64)))
(+ (* -1 (/ (pow (exp (neg (+ (log -1) (* -1 (log (/ -1 x)))))) 2) (pow (- (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)) (cos (atan (* (sqrt x) (pow (sqrt -1) 2))))) 3))) (* 2 (/ (pow (exp (neg (+ (log -1) (* -1 (log (/ -1 x)))))) 2) (* x (pow (- (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)) (cos (atan (* (sqrt x) (pow (sqrt -1) 2))))) 3)))))
(fma.f64 (/.f64 #s(literal 2 binary64) (pow.f64 (-.f64 (neg.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x))) (cos.f64 (atan.f64 (neg.f64 (sqrt.f64 x))))) #s(literal 3 binary64))) (/.f64 (pow.f64 (exp.f64 (+.f64 (log.f64 (/.f64 #s(literal -1 binary64) x)) (neg.f64 (log.f64 #s(literal -1 binary64))))) #s(literal 2 binary64)) x) (/.f64 (neg.f64 (pow.f64 (exp.f64 (+.f64 (log.f64 (/.f64 #s(literal -1 binary64) x)) (neg.f64 (log.f64 #s(literal -1 binary64))))) #s(literal 2 binary64))) (pow.f64 (-.f64 (neg.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x))) (cos.f64 (atan.f64 (neg.f64 (sqrt.f64 x))))) #s(literal 3 binary64))))
(+ (* -1 (/ (+ (* -2 (/ (pow (exp (neg (+ (log -1) (* -1 (log (/ -1 x)))))) 2) (pow (- (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)) (cos (atan (* (sqrt x) (pow (sqrt -1) 2))))) 3))) (* -1 (/ (- (/ 1 (pow (- (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)) (cos (atan (* (sqrt x) (pow (sqrt -1) 2))))) 3)) (+ (* 2 (/ (pow (exp (neg (+ (log -1) (* -1 (log (/ -1 x)))))) 2) (pow (- (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)) (cos (atan (* (sqrt x) (pow (sqrt -1) 2))))) 3))) (/ (pow (exp (neg (+ (log -1) (* -1 (log (/ -1 x)))))) 2) (pow (- (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)) (cos (atan (* (sqrt x) (pow (sqrt -1) 2))))) 3)))) x))) x)) (* -1 (/ (pow (exp (neg (+ (log -1) (* -1 (log (/ -1 x)))))) 2) (pow (- (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)) (cos (atan (* (sqrt x) (pow (sqrt -1) 2))))) 3))))
(neg.f64 (+.f64 (/.f64 (-.f64 (*.f64 (/.f64 (pow.f64 (exp.f64 (+.f64 (log.f64 (/.f64 #s(literal -1 binary64) x)) (neg.f64 (log.f64 #s(literal -1 binary64))))) #s(literal 2 binary64)) (pow.f64 (-.f64 (neg.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x))) (cos.f64 (atan.f64 (neg.f64 (sqrt.f64 x))))) #s(literal 3 binary64))) #s(literal -2 binary64)) (/.f64 (-.f64 (/.f64 #s(literal 1 binary64) (pow.f64 (-.f64 (neg.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x))) (cos.f64 (atan.f64 (neg.f64 (sqrt.f64 x))))) #s(literal 3 binary64))) (*.f64 (/.f64 (pow.f64 (exp.f64 (+.f64 (log.f64 (/.f64 #s(literal -1 binary64) x)) (neg.f64 (log.f64 #s(literal -1 binary64))))) #s(literal 2 binary64)) (pow.f64 (-.f64 (neg.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x))) (cos.f64 (atan.f64 (neg.f64 (sqrt.f64 x))))) #s(literal 3 binary64))) #s(literal 3 binary64))) x)) x) (/.f64 (pow.f64 (exp.f64 (+.f64 (log.f64 (/.f64 #s(literal -1 binary64) x)) (neg.f64 (log.f64 #s(literal -1 binary64))))) #s(literal 2 binary64)) (pow.f64 (-.f64 (neg.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x))) (cos.f64 (atan.f64 (neg.f64 (sqrt.f64 x))))) #s(literal 3 binary64)))))
(+ (* -1 (/ (+ (* -2 (/ (pow (exp (neg (+ (log -1) (* -1 (log (/ -1 x)))))) 2) (pow (- (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)) (cos (atan (* (sqrt x) (pow (sqrt -1) 2))))) 3))) (* -1 (/ (- (+ (* 4 (/ (pow (exp (neg (+ (log -1) (* -1 (log (/ -1 x)))))) 2) (* x (pow (- (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)) (cos (atan (* (sqrt x) (pow (sqrt -1) 2))))) 3)))) (/ 1 (pow (- (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)) (cos (atan (* (sqrt x) (pow (sqrt -1) 2))))) 3))) (+ (* 2 (/ (pow (exp (neg (+ (log -1) (* -1 (log (/ -1 x)))))) 2) (pow (- (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)) (cos (atan (* (sqrt x) (pow (sqrt -1) 2))))) 3))) (/ (pow (exp (neg (+ (log -1) (* -1 (log (/ -1 x)))))) 2) (pow (- (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)) (cos (atan (* (sqrt x) (pow (sqrt -1) 2))))) 3)))) x))) x)) (* -1 (/ (pow (exp (neg (+ (log -1) (* -1 (log (/ -1 x)))))) 2) (pow (- (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)) (cos (atan (* (sqrt x) (pow (sqrt -1) 2))))) 3))))
(neg.f64 (+.f64 (/.f64 (-.f64 (*.f64 (/.f64 (pow.f64 (exp.f64 (+.f64 (log.f64 (/.f64 #s(literal -1 binary64) x)) (neg.f64 (log.f64 #s(literal -1 binary64))))) #s(literal 2 binary64)) (pow.f64 (-.f64 (neg.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x))) (cos.f64 (atan.f64 (neg.f64 (sqrt.f64 x))))) #s(literal 3 binary64))) #s(literal -2 binary64)) (/.f64 (fma.f64 (/.f64 #s(literal 4 binary64) (pow.f64 (-.f64 (neg.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x))) (cos.f64 (atan.f64 (neg.f64 (sqrt.f64 x))))) #s(literal 3 binary64))) (/.f64 (pow.f64 (exp.f64 (+.f64 (log.f64 (/.f64 #s(literal -1 binary64) x)) (neg.f64 (log.f64 #s(literal -1 binary64))))) #s(literal 2 binary64)) x) (-.f64 (/.f64 #s(literal 1 binary64) (pow.f64 (-.f64 (neg.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x))) (cos.f64 (atan.f64 (neg.f64 (sqrt.f64 x))))) #s(literal 3 binary64))) (*.f64 (/.f64 (pow.f64 (exp.f64 (+.f64 (log.f64 (/.f64 #s(literal -1 binary64) x)) (neg.f64 (log.f64 #s(literal -1 binary64))))) #s(literal 2 binary64)) (pow.f64 (-.f64 (neg.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x))) (cos.f64 (atan.f64 (neg.f64 (sqrt.f64 x))))) #s(literal 3 binary64))) #s(literal 3 binary64)))) x)) x) (/.f64 (pow.f64 (exp.f64 (+.f64 (log.f64 (/.f64 #s(literal -1 binary64) x)) (neg.f64 (log.f64 #s(literal -1 binary64))))) #s(literal 2 binary64)) (pow.f64 (-.f64 (neg.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x))) (cos.f64 (atan.f64 (neg.f64 (sqrt.f64 x))))) #s(literal 3 binary64)))))
(* -1 (/ (pow (exp (neg (+ (log -1) (* -1 (log (/ -1 x)))))) 2) (pow (- (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)) (cos (atan (* (sqrt x) (pow (sqrt -1) 2))))) 2)))
(/.f64 (neg.f64 (pow.f64 (exp.f64 (+.f64 (log.f64 (/.f64 #s(literal -1 binary64) x)) (neg.f64 (log.f64 #s(literal -1 binary64))))) #s(literal 2 binary64))) (pow.f64 (-.f64 (neg.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x))) (cos.f64 (atan.f64 (neg.f64 (sqrt.f64 x))))) #s(literal 2 binary64)))
(- (* 2 (/ (pow (exp (neg (+ (log -1) (* -1 (log (/ -1 x)))))) 2) (* x (pow (- (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)) (cos (atan (* (sqrt x) (pow (sqrt -1) 2))))) 2)))) (/ (pow (exp (neg (+ (log -1) (* -1 (log (/ -1 x)))))) 2) (pow (- (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)) (cos (atan (* (sqrt x) (pow (sqrt -1) 2))))) 2)))
(-.f64 (*.f64 (/.f64 #s(literal 2 binary64) (pow.f64 (-.f64 (neg.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x))) (cos.f64 (atan.f64 (neg.f64 (sqrt.f64 x))))) #s(literal 2 binary64))) (/.f64 (pow.f64 (exp.f64 (+.f64 (log.f64 (/.f64 #s(literal -1 binary64) x)) (neg.f64 (log.f64 #s(literal -1 binary64))))) #s(literal 2 binary64)) x)) (/.f64 (pow.f64 (exp.f64 (+.f64 (log.f64 (/.f64 #s(literal -1 binary64) x)) (neg.f64 (log.f64 #s(literal -1 binary64))))) #s(literal 2 binary64)) (pow.f64 (-.f64 (neg.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x))) (cos.f64 (atan.f64 (neg.f64 (sqrt.f64 x))))) #s(literal 2 binary64))))
(- (* -1 (/ (- (* -1 (/ (- (/ 1 (pow (- (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)) (cos (atan (* (sqrt x) (pow (sqrt -1) 2))))) 2)) (+ (* 2 (/ (pow (exp (neg (+ (log -1) (* -1 (log (/ -1 x)))))) 2) (pow (- (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)) (cos (atan (* (sqrt x) (pow (sqrt -1) 2))))) 2))) (/ (pow (exp (neg (+ (log -1) (* -1 (log (/ -1 x)))))) 2) (pow (- (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)) (cos (atan (* (sqrt x) (pow (sqrt -1) 2))))) 2)))) x)) (* 2 (/ (pow (exp (neg (+ (log -1) (* -1 (log (/ -1 x)))))) 2) (pow (- (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)) (cos (atan (* (sqrt x) (pow (sqrt -1) 2))))) 2)))) x)) (/ (pow (exp (neg (+ (log -1) (* -1 (log (/ -1 x)))))) 2) (pow (- (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)) (cos (atan (* (sqrt x) (pow (sqrt -1) 2))))) 2)))
(-.f64 (/.f64 (fma.f64 (/.f64 (pow.f64 (exp.f64 (+.f64 (log.f64 (/.f64 #s(literal -1 binary64) x)) (neg.f64 (log.f64 #s(literal -1 binary64))))) #s(literal 2 binary64)) (pow.f64 (-.f64 (neg.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x))) (cos.f64 (atan.f64 (neg.f64 (sqrt.f64 x))))) #s(literal 2 binary64))) #s(literal -2 binary64) (/.f64 (-.f64 (/.f64 #s(literal 1 binary64) (pow.f64 (-.f64 (neg.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x))) (cos.f64 (atan.f64 (neg.f64 (sqrt.f64 x))))) #s(literal 2 binary64))) (*.f64 (/.f64 (pow.f64 (exp.f64 (+.f64 (log.f64 (/.f64 #s(literal -1 binary64) x)) (neg.f64 (log.f64 #s(literal -1 binary64))))) #s(literal 2 binary64)) (pow.f64 (-.f64 (neg.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x))) (cos.f64 (atan.f64 (neg.f64 (sqrt.f64 x))))) #s(literal 2 binary64))) #s(literal 3 binary64))) (neg.f64 x))) (neg.f64 x)) (/.f64 (pow.f64 (exp.f64 (+.f64 (log.f64 (/.f64 #s(literal -1 binary64) x)) (neg.f64 (log.f64 #s(literal -1 binary64))))) #s(literal 2 binary64)) (pow.f64 (-.f64 (neg.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x))) (cos.f64 (atan.f64 (neg.f64 (sqrt.f64 x))))) #s(literal 2 binary64))))
(- (* -1 (/ (- (* -1 (/ (- (+ (* 4 (/ (pow (exp (neg (+ (log -1) (* -1 (log (/ -1 x)))))) 2) (* x (pow (- (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)) (cos (atan (* (sqrt x) (pow (sqrt -1) 2))))) 2)))) (/ 1 (pow (- (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)) (cos (atan (* (sqrt x) (pow (sqrt -1) 2))))) 2))) (+ (* 2 (/ (pow (exp (neg (+ (log -1) (* -1 (log (/ -1 x)))))) 2) (pow (- (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)) (cos (atan (* (sqrt x) (pow (sqrt -1) 2))))) 2))) (/ (pow (exp (neg (+ (log -1) (* -1 (log (/ -1 x)))))) 2) (pow (- (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)) (cos (atan (* (sqrt x) (pow (sqrt -1) 2))))) 2)))) x)) (* 2 (/ (pow (exp (neg (+ (log -1) (* -1 (log (/ -1 x)))))) 2) (pow (- (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)) (cos (atan (* (sqrt x) (pow (sqrt -1) 2))))) 2)))) x)) (/ (pow (exp (neg (+ (log -1) (* -1 (log (/ -1 x)))))) 2) (pow (- (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)) (cos (atan (* (sqrt x) (pow (sqrt -1) 2))))) 2)))
(-.f64 (/.f64 (fma.f64 (/.f64 (pow.f64 (exp.f64 (+.f64 (log.f64 (/.f64 #s(literal -1 binary64) x)) (neg.f64 (log.f64 #s(literal -1 binary64))))) #s(literal 2 binary64)) (pow.f64 (-.f64 (neg.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x))) (cos.f64 (atan.f64 (neg.f64 (sqrt.f64 x))))) #s(literal 2 binary64))) #s(literal -2 binary64) (/.f64 (fma.f64 (/.f64 #s(literal 4 binary64) (pow.f64 (-.f64 (neg.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x))) (cos.f64 (atan.f64 (neg.f64 (sqrt.f64 x))))) #s(literal 2 binary64))) (/.f64 (pow.f64 (exp.f64 (+.f64 (log.f64 (/.f64 #s(literal -1 binary64) x)) (neg.f64 (log.f64 #s(literal -1 binary64))))) #s(literal 2 binary64)) x) (-.f64 (/.f64 #s(literal 1 binary64) (pow.f64 (-.f64 (neg.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x))) (cos.f64 (atan.f64 (neg.f64 (sqrt.f64 x))))) #s(literal 2 binary64))) (*.f64 (/.f64 (pow.f64 (exp.f64 (+.f64 (log.f64 (/.f64 #s(literal -1 binary64) x)) (neg.f64 (log.f64 #s(literal -1 binary64))))) #s(literal 2 binary64)) (pow.f64 (-.f64 (neg.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x))) (cos.f64 (atan.f64 (neg.f64 (sqrt.f64 x))))) #s(literal 2 binary64))) #s(literal 3 binary64)))) (neg.f64 x))) (neg.f64 x)) (/.f64 (pow.f64 (exp.f64 (+.f64 (log.f64 (/.f64 #s(literal -1 binary64) x)) (neg.f64 (log.f64 #s(literal -1 binary64))))) #s(literal 2 binary64)) (pow.f64 (-.f64 (neg.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x))) (cos.f64 (atan.f64 (neg.f64 (sqrt.f64 x))))) #s(literal 2 binary64))))
(/ 1 (* (pow x 2) (pow (- (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)) (cos (atan (* (sqrt x) (pow (sqrt -1) 2))))) 2)))
(/.f64 (/.f64 (/.f64 #s(literal 1 binary64) x) x) (pow.f64 (-.f64 (neg.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x))) (cos.f64 (atan.f64 (neg.f64 (sqrt.f64 x))))) #s(literal 2 binary64)))
(/ 1 (* x (- (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)) (cos (atan (* (sqrt x) (pow (sqrt -1) 2)))))))
(/.f64 (/.f64 #s(literal 1 binary64) x) (-.f64 (neg.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x))) (cos.f64 (atan.f64 (neg.f64 (sqrt.f64 x))))))
(cos (atan (* (sqrt x) (pow (sqrt -1) 2))))
(cos.f64 (atan.f64 (neg.f64 (sqrt.f64 x))))
(- (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)) (cos (atan (* (sqrt x) (pow (sqrt -1) 2)))))
(-.f64 (neg.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x))) (cos.f64 (atan.f64 (neg.f64 (sqrt.f64 x)))))

rewrite154.0ms (2.3%)

Memory
3.2MiB live, 143.0MiB allocated
Iterations

Useful iterations: 2 (0.0ms)

IterNodesCost
041241
072247
1284212
21968177
09349177
Stop Event
iter limit
node limit
iter limit
Counts
20 → 692
Calls
Call 1
Inputs
#s(approx (- (/ 1 (sqrt x)) (/ 1 (sqrt (+ x 1)))) (*.f64 (/.f64 (-.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) (sqrt.f64 x)) (*.f64 x x)) #s(literal -1/2 binary64)))
(*.f64 (/.f64 (-.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) (sqrt.f64 x)) (*.f64 x x)) #s(literal -1/2 binary64))
(/.f64 (-.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) (sqrt.f64 x)) (*.f64 x x))
(-.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) (sqrt.f64 x))
#s(approx (- (/ 1 (sqrt x)) (/ 1 (sqrt (+ x 1)))) (sqrt.f64 (/.f64 #s(literal 1 binary64) x)))
(sqrt.f64 (/.f64 #s(literal 1 binary64) x))
(/.f64 #s(literal 1 binary64) x)
(/.f64 (-.f64 (sqrt.f64 (+.f64 x #s(literal 1 binary64))) (sqrt.f64 x)) (sqrt.f64 (+.f64 x #s(literal 1 binary64))))
(/.f64 (/.f64 (-.f64 (sqrt.f64 (+.f64 x #s(literal 1 binary64))) (sqrt.f64 x)) (sqrt.f64 (+.f64 x #s(literal 1 binary64)))) (sqrt.f64 x))
(-.f64 (sqrt.f64 (+.f64 x #s(literal 1 binary64))) (sqrt.f64 x))
(sqrt.f64 (+.f64 x #s(literal 1 binary64)))
(/.f64 (-.f64 (sqrt.f64 (+.f64 x #s(literal 1 binary64))) (sqrt.f64 x)) (hypot.f64 (sqrt.f64 x) x))
(+.f64 x #s(literal 1 binary64))
(/.f64 (-.f64 (pow.f64 (/.f64 (pow.f64 x #s(literal -1 binary64)) (-.f64 (pow.f64 x #s(literal -1/2 binary64)) (cos.f64 (atan.f64 (sqrt.f64 x))))) #s(literal 2 binary64)) (pow.f64 (/.f64 (exp.f64 (neg.f64 (log1p.f64 x))) (-.f64 (pow.f64 x #s(literal -1/2 binary64)) (cos.f64 (atan.f64 (sqrt.f64 x))))) #s(literal 2 binary64))) (-.f64 (pow.f64 x #s(literal -1/2 binary64)) (cos.f64 (atan.f64 (sqrt.f64 x)))))
(-.f64 (pow.f64 (/.f64 (pow.f64 x #s(literal -1 binary64)) (-.f64 (pow.f64 x #s(literal -1/2 binary64)) (cos.f64 (atan.f64 (sqrt.f64 x))))) #s(literal 2 binary64)) (pow.f64 (/.f64 (exp.f64 (neg.f64 (log1p.f64 x))) (-.f64 (pow.f64 x #s(literal -1/2 binary64)) (cos.f64 (atan.f64 (sqrt.f64 x))))) #s(literal 2 binary64)))
(pow.f64 (/.f64 (pow.f64 x #s(literal -1 binary64)) (-.f64 (pow.f64 x #s(literal -1/2 binary64)) (cos.f64 (atan.f64 (sqrt.f64 x))))) #s(literal 2 binary64))
(/.f64 (pow.f64 x #s(literal -1 binary64)) (-.f64 (pow.f64 x #s(literal -1/2 binary64)) (cos.f64 (atan.f64 (sqrt.f64 x)))))
(sqrt.f64 x)
(cos.f64 (atan.f64 (sqrt.f64 x)))
(-.f64 (pow.f64 x #s(literal -1/2 binary64)) (cos.f64 (atan.f64 (sqrt.f64 x))))
Outputs
#s(approx (- (/ 1 (sqrt x)) (/ 1 (sqrt (+ x 1)))) (*.f64 #s(literal -1/2 binary64) (-.f64 (pow.f64 x #s(literal -5/2 binary64)) (pow.f64 x #s(literal -3/2 binary64)))))
(*.f64 (-.f64 (pow.f64 x #s(literal -3/2 binary64)) (pow.f64 x #s(literal -1/2 binary64))) (/.f64 #s(literal -1/2 binary64) x))
(*.f64 #s(literal -1/2 binary64) (-.f64 (pow.f64 x #s(literal -5/2 binary64)) (pow.f64 x #s(literal -3/2 binary64))))
(*.f64 (-.f64 (pow.f64 x #s(literal -5/2 binary64)) (pow.f64 x #s(literal -3/2 binary64))) #s(literal -1/2 binary64))
(*.f64 (-.f64 (pow.f64 x #s(literal -1/2 binary64)) (sqrt.f64 x)) (/.f64 #s(literal -1/2 binary64) (*.f64 x x)))
(/.f64 (/.f64 (*.f64 #s(literal -1/2 binary64) (-.f64 (pow.f64 x #s(literal -1/2 binary64)) (sqrt.f64 x))) x) x)
(/.f64 (*.f64 (-.f64 (pow.f64 x #s(literal -3/2 binary64)) (pow.f64 x #s(literal -1/2 binary64))) #s(literal -1/2 binary64)) x)
(/.f64 (*.f64 (neg.f64 (-.f64 (pow.f64 x #s(literal -1/2 binary64)) (sqrt.f64 x))) #s(literal -1/2 binary64)) (*.f64 x x))
(/.f64 (*.f64 #s(literal -1/2 binary64) (-.f64 (pow.f64 x #s(literal -3/2 binary64)) (pow.f64 x #s(literal -1/2 binary64)))) x)
(/.f64 (*.f64 #s(literal -1/2 binary64) (neg.f64 (-.f64 (pow.f64 x #s(literal -1/2 binary64)) (sqrt.f64 x)))) (*.f64 x x))
(/.f64 (neg.f64 (*.f64 #s(literal -1/2 binary64) (-.f64 (pow.f64 x #s(literal -1/2 binary64)) (sqrt.f64 x)))) (*.f64 x x))
(/.f64 (*.f64 #s(literal -1/2 binary64) (-.f64 (pow.f64 x #s(literal -1/2 binary64)) (sqrt.f64 x))) (*.f64 x x))
(/.f64 (-.f64 (*.f64 (pow.f64 x #s(literal -3/2 binary64)) x) (*.f64 x (pow.f64 x #s(literal -1/2 binary64)))) (*.f64 x x))
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(/.f64 (+.f64 (pow.f64 x #s(literal -3/2 binary64)) (pow.f64 (-.f64 x #s(literal 1 binary64)) #s(literal -3/2 binary64))) (+.f64 (-.f64 (exp.f64 (neg.f64 (log1p.f64 x))) (pow.f64 (fma.f64 x x x) #s(literal -1/2 binary64))) (pow.f64 x #s(literal -1 binary64))))
(/.f64 (neg.f64 (neg.f64 (-.f64 (sqrt.f64 (-.f64 x #s(literal 1 binary64))) (sqrt.f64 x)))) (neg.f64 (neg.f64 (hypot.f64 (sqrt.f64 x) x))))
(/.f64 (neg.f64 (-.f64 (pow.f64 x #s(literal -1 binary64)) (exp.f64 (neg.f64 (log1p.f64 x))))) (-.f64 (pow.f64 x #s(literal -1/2 binary64)) (cos.f64 (atan.f64 (sqrt.f64 x)))))
(/.f64 (neg.f64 (-.f64 (pow.f64 x #s(literal -3/2 binary64)) (pow.f64 (-.f64 x #s(literal 1 binary64)) #s(literal -3/2 binary64)))) (neg.f64 (+.f64 (-.f64 (exp.f64 (neg.f64 (log1p.f64 x))) (pow.f64 (fma.f64 x x x) #s(literal -1/2 binary64))) (pow.f64 x #s(literal -1 binary64)))))
(/.f64 (neg.f64 (-.f64 (pow.f64 x #s(literal -3/2 binary64)) (pow.f64 (-.f64 x #s(literal 1 binary64)) #s(literal -3/2 binary64)))) (+.f64 (-.f64 (exp.f64 (neg.f64 (log1p.f64 x))) (pow.f64 (fma.f64 x x x) #s(literal -1/2 binary64))) (pow.f64 x #s(literal -1 binary64))))
(/.f64 (-.f64 (*.f64 (sqrt.f64 (-.f64 x #s(literal 1 binary64))) (hypot.f64 (sqrt.f64 x) x)) (*.f64 (hypot.f64 (sqrt.f64 x) x) (sqrt.f64 x))) (fma.f64 x x x))
(/.f64 (-.f64 (*.f64 #s(literal -1 binary64) (neg.f64 (sqrt.f64 (-.f64 x #s(literal 1 binary64))))) (*.f64 (sqrt.f64 x) #s(literal -1 binary64))) (*.f64 (sqrt.f64 x) (neg.f64 (sqrt.f64 (-.f64 x #s(literal 1 binary64))))))
(/.f64 (-.f64 (*.f64 #s(literal -1 binary64) (sqrt.f64 (-.f64 x #s(literal 1 binary64)))) (sqrt.f64 x)) (hypot.f64 (sqrt.f64 x) x))
(/.f64 (-.f64 (*.f64 #s(literal 1 binary64) (neg.f64 (sqrt.f64 (-.f64 x #s(literal 1 binary64))))) (*.f64 (sqrt.f64 x) #s(literal -1 binary64))) (*.f64 (sqrt.f64 x) (neg.f64 (sqrt.f64 (-.f64 x #s(literal 1 binary64))))))
(/.f64 (-.f64 (pow.f64 x #s(literal -1 binary64)) (exp.f64 (neg.f64 (log1p.f64 x)))) (-.f64 (pow.f64 x #s(literal -1/2 binary64)) (cos.f64 (atan.f64 (sqrt.f64 x)))))
(/.f64 (fma.f64 #s(literal -1 binary64) (neg.f64 (sqrt.f64 (-.f64 x #s(literal 1 binary64)))) (*.f64 (sqrt.f64 x) #s(literal -1 binary64))) (*.f64 (sqrt.f64 x) (neg.f64 (sqrt.f64 (-.f64 x #s(literal 1 binary64))))))
(/.f64 (fma.f64 #s(literal -1 binary64) (sqrt.f64 (-.f64 x #s(literal 1 binary64))) (sqrt.f64 x)) (hypot.f64 (sqrt.f64 x) x))
(/.f64 (fma.f64 #s(literal 1 binary64) (neg.f64 (sqrt.f64 (-.f64 x #s(literal 1 binary64)))) (*.f64 (sqrt.f64 x) #s(literal -1 binary64))) (*.f64 (sqrt.f64 x) (neg.f64 (sqrt.f64 (-.f64 x #s(literal 1 binary64))))))
(/.f64 (-.f64 (sqrt.f64 (-.f64 x #s(literal 1 binary64))) (sqrt.f64 x)) (hypot.f64 (sqrt.f64 x) x))
(/.f64 (-.f64 (-.f64 x #s(literal 1 binary64)) x) (*.f64 (-.f64 (sqrt.f64 (-.f64 x #s(literal 1 binary64))) (sqrt.f64 x)) (hypot.f64 (sqrt.f64 x) x)))
(/.f64 (-.f64 (pow.f64 x #s(literal -3/2 binary64)) (pow.f64 (-.f64 x #s(literal 1 binary64)) #s(literal -3/2 binary64))) (neg.f64 (+.f64 (-.f64 (exp.f64 (neg.f64 (log1p.f64 x))) (pow.f64 (fma.f64 x x x) #s(literal -1/2 binary64))) (pow.f64 x #s(literal -1 binary64)))))
(/.f64 (-.f64 (pow.f64 x #s(literal -3/2 binary64)) (pow.f64 (-.f64 x #s(literal 1 binary64)) #s(literal -3/2 binary64))) (+.f64 (-.f64 (exp.f64 (neg.f64 (log1p.f64 x))) (pow.f64 (fma.f64 x x x) #s(literal -1/2 binary64))) (pow.f64 x #s(literal -1 binary64))))
(/.f64 (-.f64 (pow.f64 (-.f64 x #s(literal 1 binary64)) #s(literal 3/2 binary64)) (pow.f64 x #s(literal 3/2 binary64))) (*.f64 (+.f64 (-.f64 (-.f64 x #s(literal 1 binary64)) x) (hypot.f64 (sqrt.f64 x) x)) (hypot.f64 (sqrt.f64 x) x)))
(/.f64 (neg.f64 (-.f64 #s(literal 1 binary64) (tanh.f64 (asinh.f64 (sqrt.f64 x))))) (sqrt.f64 x))
(/.f64 (neg.f64 (-.f64 (sqrt.f64 (-.f64 x #s(literal 1 binary64))) (sqrt.f64 x))) (*.f64 (neg.f64 (sqrt.f64 (-.f64 x #s(literal 1 binary64)))) (sqrt.f64 x)))
(/.f64 (neg.f64 (-.f64 (sqrt.f64 (-.f64 x #s(literal 1 binary64))) (sqrt.f64 x))) (neg.f64 (hypot.f64 (sqrt.f64 x) x)))
(/.f64 (-.f64 #s(literal 1 binary64) (tanh.f64 (asinh.f64 (sqrt.f64 x)))) (sqrt.f64 x))
(neg.f64 (/.f64 (neg.f64 (-.f64 (sqrt.f64 (-.f64 x #s(literal 1 binary64))) (sqrt.f64 x))) (hypot.f64 (sqrt.f64 x) x)))
(neg.f64 (/.f64 (-.f64 (sqrt.f64 (-.f64 x #s(literal 1 binary64))) (sqrt.f64 x)) (neg.f64 (hypot.f64 (sqrt.f64 x) x))))
(neg.f64 (-.f64 (pow.f64 x #s(literal -1/2 binary64)) (cos.f64 (atan.f64 (sqrt.f64 x)))))
(fma.f64 (neg.f64 (pow.f64 (-.f64 x #s(literal 1 binary64)) #s(literal -1/4 binary64))) (neg.f64 (pow.f64 (-.f64 x #s(literal 1 binary64)) #s(literal -1/4 binary64))) (pow.f64 x #s(literal -1/2 binary64)))
(fma.f64 (neg.f64 (neg.f64 (pow.f64 x #s(literal -1/4 binary64)))) (neg.f64 (neg.f64 (pow.f64 x #s(literal -1/4 binary64)))) (cos.f64 (atan.f64 (sqrt.f64 x))))
(fma.f64 (fabs.f64 (pow.f64 (-.f64 x #s(literal 1 binary64)) #s(literal -1/4 binary64))) (fabs.f64 (pow.f64 (-.f64 x #s(literal 1 binary64)) #s(literal -1/4 binary64))) (pow.f64 x #s(literal -1/2 binary64)))
(fma.f64 (sqrt.f64 (pow.f64 x #s(literal -3/4 binary64))) (sqrt.f64 (pow.f64 x #s(literal -1/4 binary64))) (cos.f64 (atan.f64 (sqrt.f64 x))))
(fma.f64 (sqrt.f64 (pow.f64 x #s(literal -1/4 binary64))) (sqrt.f64 (pow.f64 x #s(literal -3/4 binary64))) (cos.f64 (atan.f64 (sqrt.f64 x))))
(fma.f64 (pow.f64 (pow.f64 x #s(literal 3/2 binary64)) #s(literal -1/4 binary64)) (pow.f64 x #s(literal -1/8 binary64)) (cos.f64 (atan.f64 (sqrt.f64 x))))
(fma.f64 (pow.f64 (pow.f64 x #s(literal 1/4 binary64)) #s(literal -1 binary64)) (pow.f64 (pow.f64 x #s(literal 1/4 binary64)) #s(literal -1 binary64)) (cos.f64 (atan.f64 (sqrt.f64 x))))
(fma.f64 (pow.f64 (pow.f64 x #s(literal -3/4 binary64)) #s(literal 1/2 binary64)) (pow.f64 (pow.f64 x #s(literal -1/4 binary64)) #s(literal 1/2 binary64)) (cos.f64 (atan.f64 (sqrt.f64 x))))
(fma.f64 (pow.f64 (pow.f64 x #s(literal -1/4 binary64)) #s(literal 1/2 binary64)) (pow.f64 (pow.f64 x #s(literal -3/4 binary64)) #s(literal 1/2 binary64)) (cos.f64 (atan.f64 (sqrt.f64 x))))
(fma.f64 (pow.f64 #s(literal 1 binary64) #s(literal -1/2 binary64)) (pow.f64 x #s(literal -1/2 binary64)) (cos.f64 (atan.f64 (sqrt.f64 x))))
(fma.f64 (pow.f64 (pow.f64 (-.f64 x #s(literal 1 binary64)) #s(literal 1/4 binary64)) #s(literal -1 binary64)) (pow.f64 (pow.f64 (-.f64 x #s(literal 1 binary64)) #s(literal 1/4 binary64)) #s(literal -1 binary64)) (pow.f64 x #s(literal -1/2 binary64)))
(fma.f64 (pow.f64 (neg.f64 (sqrt.f64 (-.f64 x #s(literal 1 binary64)))) #s(literal -1/2 binary64)) (pow.f64 (neg.f64 (sqrt.f64 (-.f64 x #s(literal 1 binary64)))) #s(literal -1/2 binary64)) (pow.f64 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 x #s(literal -1/2 binary64)))
(fma.f64 (neg.f64 (pow.f64 x #s(literal -1/4 binary64))) (neg.f64 (pow.f64 x #s(literal -1/4 binary64))) (cos.f64 (atan.f64 (sqrt.f64 x))))
(fma.f64 (pow.f64 x #s(literal -1/8 binary64)) (pow.f64 (pow.f64 x #s(literal 3/2 binary64)) #s(literal -1/4 binary64)) (cos.f64 (atan.f64 (sqrt.f64 x))))
(fma.f64 (pow.f64 x #s(literal -1/4 binary64)) (pow.f64 (+.f64 (sqrt.f64 x) (pow.f64 x #s(literal -1/2 binary64))) #s(literal -1/2 binary64)) (pow.f64 x #s(literal -1/2 binary64)))
(fma.f64 (pow.f64 x #s(literal -1/4 binary64)) (pow.f64 x #s(literal -1/4 binary64)) (cos.f64 (atan.f64 (sqrt.f64 x))))
(fma.f64 (pow.f64 x #s(literal -1/2 binary64)) (pow.f64 #s(literal 1 binary64) #s(literal -1/2 binary64)) (cos.f64 (atan.f64 (sqrt.f64 x))))
(fma.f64 (pow.f64 x #s(literal -1/2 binary64)) #s(literal 1 binary64) (cos.f64 (atan.f64 (sqrt.f64 x))))
(fma.f64 (cos.f64 (atan.f64 (sqrt.f64 x))) #s(literal 1 binary64) (pow.f64 x #s(literal -1/2 binary64)))
(fma.f64 #s(literal 1 binary64) (pow.f64 x #s(literal -1/2 binary64)) (cos.f64 (atan.f64 (sqrt.f64 x))))
(fma.f64 #s(literal 1 binary64) (cos.f64 (atan.f64 (sqrt.f64 x))) (pow.f64 x #s(literal -1/2 binary64)))
(-.f64 (/.f64 (pow.f64 x #s(literal -3/2 binary64)) (+.f64 (-.f64 (exp.f64 (neg.f64 (log1p.f64 x))) (pow.f64 (fma.f64 x x x) #s(literal -1/2 binary64))) (pow.f64 x #s(literal -1 binary64)))) (/.f64 (pow.f64 (-.f64 x #s(literal 1 binary64)) #s(literal -3/2 binary64)) (+.f64 (-.f64 (exp.f64 (neg.f64 (log1p.f64 x))) (pow.f64 (fma.f64 x x x) #s(literal -1/2 binary64))) (pow.f64 x #s(literal -1 binary64)))))
(-.f64 (/.f64 (sqrt.f64 (-.f64 x #s(literal 1 binary64))) (hypot.f64 (sqrt.f64 x) x)) (/.f64 (sqrt.f64 x) (hypot.f64 (sqrt.f64 x) x)))
(-.f64 (/.f64 (pow.f64 x #s(literal -1 binary64)) (-.f64 (pow.f64 x #s(literal -1/2 binary64)) (cos.f64 (atan.f64 (sqrt.f64 x))))) (/.f64 (exp.f64 (neg.f64 (log1p.f64 x))) (-.f64 (pow.f64 x #s(literal -1/2 binary64)) (cos.f64 (atan.f64 (sqrt.f64 x))))))
(-.f64 (pow.f64 x #s(literal -1/2 binary64)) (/.f64 (tanh.f64 (asinh.f64 (sqrt.f64 x))) (sqrt.f64 x)))
(-.f64 (pow.f64 x #s(literal -1/2 binary64)) (cos.f64 (atan.f64 (sqrt.f64 x))))
(+.f64 (pow.f64 x #s(literal -1/2 binary64)) (cos.f64 (atan.f64 (sqrt.f64 x))))
(+.f64 (cos.f64 (atan.f64 (sqrt.f64 x))) (pow.f64 x #s(literal -1/2 binary64)))

eval173.0ms (2.5%)

Memory
-14.0MiB live, 271.9MiB allocated
Compiler

Compiled 38 079 to 4 123 computations (89.2% saved)

prune32.0ms (0.5%)

Memory
22.8MiB live, 70.2MiB allocated
Pruning

19 alts after pruning (16 fresh and 3 done)

PrunedKeptTotal
New1 194131 207
Fresh033
Picked325
Done011
Total1 197191 216
Accuracy
100.0%
Counts
1 216 → 19
Alt Table
Click to see full alt table
StatusAccuracyProgram
37.4%
(/.f64 (/.f64 (-.f64 (sqrt.f64 (+.f64 x #s(literal 1 binary64))) (sqrt.f64 x)) (sqrt.f64 x)) (sqrt.f64 (+.f64 x #s(literal 1 binary64))))
98.8%
(/.f64 (/.f64 #s(approx (- (sqrt (+ x 1)) (sqrt x)) (/.f64 (fma.f64 #s(literal -1/8 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) (*.f64 #s(literal 1/2 binary64) (sqrt.f64 x))) x)) (sqrt.f64 (+.f64 x #s(literal 1 binary64)))) (sqrt.f64 x))
98.0%
(/.f64 (/.f64 #s(approx (- (sqrt (+ x 1)) (sqrt x)) (*.f64 #s(literal 1/2 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) x)))) (sqrt.f64 (+.f64 x #s(literal 1 binary64)))) (sqrt.f64 x))
38.3%
(/.f64 (-.f64 (+.f64 x #s(literal 1 binary64)) x) (*.f64 (+.f64 (sqrt.f64 (+.f64 x #s(literal 1 binary64))) (sqrt.f64 x)) (hypot.f64 (sqrt.f64 x) x)))
37.4%
(/.f64 (-.f64 (sqrt.f64 (+.f64 x #s(literal 1 binary64))) (sqrt.f64 x)) (hypot.f64 (sqrt.f64 x) x))
98.9%
(/.f64 #s(approx (/ (- (sqrt (+ x 1)) (sqrt x)) (sqrt (+ x 1))) (/.f64 (-.f64 (+.f64 (/.f64 #s(literal 1/4 binary64) (*.f64 x x)) #s(literal 1/2 binary64)) (/.f64 #s(literal 3/8 binary64) x)) x)) (sqrt.f64 x))
98.8%
(/.f64 #s(approx (/ (- (sqrt (+ x 1)) (sqrt x)) (sqrt (+ x 1))) (/.f64 (-.f64 #s(literal 1/2 binary64) (*.f64 #s(literal 1 binary64) (/.f64 #s(literal 3/8 binary64) x))) x)) (sqrt.f64 x))
98.1%
(/.f64 #s(approx (/ (- (sqrt (+ x 1)) (sqrt x)) (sqrt (+ x 1))) (/.f64 #s(literal 1/2 binary64) x)) (sqrt.f64 x))
98.3%
(/.f64 #s(approx (- (sqrt (+ x 1)) (sqrt x)) (*.f64 #s(literal 1/2 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) x)))) (hypot.f64 (sqrt.f64 x) x))
37.3%
(-.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 x)) (/.f64 #s(literal 1 binary64) (sqrt.f64 (+.f64 x #s(literal 1 binary64)))))
98.2%
#s(approx (- (/ 1 (sqrt x)) (/ 1 (sqrt (+ x 1)))) (/.f64 (/.f64 (*.f64 #s(literal -1/2 binary64) (-.f64 (pow.f64 x #s(literal -1/2 binary64)) (sqrt.f64 x))) x) x))
5.5%
#s(approx (- (/ 1 (sqrt x)) (/ 1 (sqrt (+ x 1)))) (/.f64 (sqrt.f64 x) x))
5.5%
#s(approx (- (/ 1 (sqrt x)) (/ 1 (sqrt (+ x 1)))) (/.f64 #s(literal 1 binary64) (sqrt.f64 x)))
82.0%
#s(approx (- (/ 1 (sqrt x)) (/ 1 (sqrt (+ x 1)))) (*.f64 (/.f64 #s(approx (- (sqrt (/ 1 x)) (sqrt x)) (neg.f64 (sqrt.f64 x))) (*.f64 x x)) #s(literal -1/2 binary64)))
82.1%
#s(approx (- (/ 1 (sqrt x)) (/ 1 (sqrt (+ x 1)))) (*.f64 (-.f64 (pow.f64 x #s(literal -1/2 binary64)) (sqrt.f64 x)) (/.f64 #s(literal -1/2 binary64) (*.f64 x x))))
98.6%
#s(approx (- (/ 1 (sqrt x)) (/ 1 (sqrt (+ x 1)))) (*.f64 (-.f64 (pow.f64 x #s(literal -5/2 binary64)) (pow.f64 x #s(literal -3/2 binary64))) #s(literal -1/2 binary64)))
65.2%
#s(approx (- (/ 1 (sqrt x)) (/ 1 (sqrt (+ x 1)))) (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 3 binary64)))) #s(literal 1/2 binary64)))
36.4%
#s(approx (- (/ 1 (sqrt x)) (/ 1 (sqrt (+ x 1)))) (sqrt.f64 (/.f64 x (*.f64 x x))))
5.5%
#s(approx (- (/ 1 (sqrt x)) (/ 1 (sqrt (+ x 1)))) (sqrt.f64 (/.f64 #s(literal 1 binary64) x)))
Compiler

Compiled 725 to 500 computations (31% saved)

simplify251.0ms (3.7%)

Memory
-20.0MiB live, 72.4MiB allocated
Algorithm
egg-herbie
Localize:

Found 19 expressions of interest:

NewMetricScoreProgram
cost-diff0
(sqrt.f64 (/.f64 #s(literal 1 binary64) x))
cost-diff0
(*.f64 #s(literal 1/2 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) x)))
cost-diff0
#s(approx (- (sqrt (+ x 1)) (sqrt x)) (*.f64 #s(literal 1/2 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) x))))
cost-diff0
(/.f64 #s(approx (- (sqrt (+ x 1)) (sqrt x)) (*.f64 #s(literal 1/2 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) x)))) (hypot.f64 (sqrt.f64 x) x))
cost-diff0
(/.f64 (fma.f64 #s(literal -1/8 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) (*.f64 #s(literal 1/2 binary64) (sqrt.f64 x))) x)
cost-diff0
#s(approx (- (sqrt (+ x 1)) (sqrt x)) (/.f64 (fma.f64 #s(literal -1/8 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) (*.f64 #s(literal 1/2 binary64) (sqrt.f64 x))) x))
cost-diff0
(/.f64 #s(approx (- (sqrt (+ x 1)) (sqrt x)) (/.f64 (fma.f64 #s(literal -1/8 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) (*.f64 #s(literal 1/2 binary64) (sqrt.f64 x))) x)) (sqrt.f64 (+.f64 x #s(literal 1 binary64))))
cost-diff0
(/.f64 (/.f64 #s(approx (- (sqrt (+ x 1)) (sqrt x)) (/.f64 (fma.f64 #s(literal -1/8 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) (*.f64 #s(literal 1/2 binary64) (sqrt.f64 x))) x)) (sqrt.f64 (+.f64 x #s(literal 1 binary64)))) (sqrt.f64 x))
cost-diff0
#s(approx (- (sqrt (/ 1 x)) (sqrt x)) (neg.f64 (sqrt.f64 x)))
cost-diff0
(/.f64 #s(approx (- (sqrt (/ 1 x)) (sqrt x)) (neg.f64 (sqrt.f64 x))) (*.f64 x x))
cost-diff0
(*.f64 (/.f64 #s(approx (- (sqrt (/ 1 x)) (sqrt x)) (neg.f64 (sqrt.f64 x))) (*.f64 x x)) #s(literal -1/2 binary64))
cost-diff0
#s(approx (- (/ 1 (sqrt x)) (/ 1 (sqrt (+ x 1)))) (*.f64 (/.f64 #s(approx (- (sqrt (/ 1 x)) (sqrt x)) (neg.f64 (sqrt.f64 x))) (*.f64 x x)) #s(literal -1/2 binary64)))
cost-diff0
(sqrt.f64 x)
cost-diff0
(/.f64 #s(literal 1 binary64) (sqrt.f64 x))
cost-diff0
#s(approx (- (/ 1 (sqrt x)) (/ 1 (sqrt (+ x 1)))) (/.f64 #s(literal 1 binary64) (sqrt.f64 x)))
cost-diff0
(-.f64 (+.f64 (/.f64 #s(literal 1/4 binary64) (*.f64 x x)) #s(literal 1/2 binary64)) (/.f64 #s(literal 3/8 binary64) x))
cost-diff0
(/.f64 (-.f64 (+.f64 (/.f64 #s(literal 1/4 binary64) (*.f64 x x)) #s(literal 1/2 binary64)) (/.f64 #s(literal 3/8 binary64) x)) x)
cost-diff0
#s(approx (/ (- (sqrt (+ x 1)) (sqrt x)) (sqrt (+ x 1))) (/.f64 (-.f64 (+.f64 (/.f64 #s(literal 1/4 binary64) (*.f64 x x)) #s(literal 1/2 binary64)) (/.f64 #s(literal 3/8 binary64) x)) x))
cost-diff0
(/.f64 #s(approx (/ (- (sqrt (+ x 1)) (sqrt x)) (sqrt (+ x 1))) (/.f64 (-.f64 (+.f64 (/.f64 #s(literal 1/4 binary64) (*.f64 x x)) #s(literal 1/2 binary64)) (/.f64 #s(literal 3/8 binary64) x)) x)) (sqrt.f64 x))
Iterations

Useful iterations: 1 (0.0ms)

IterNodesCost
048383
078383
1120377
2285377
3867377
41955377
54181377
65675377
76160377
86240377
96270377
106281377
116548377
126567377
136569377
146569377
156569377
166693377
176779377
186809377
196831377
206834377
216834377
226850377
236850377
08889377
Stop Event
iter limit
node limit
iter limit
Calls
Call 1
Inputs
(/.f64 #s(approx (/ (- (sqrt (+ x 1)) (sqrt x)) (sqrt (+ x 1))) (/.f64 (-.f64 (+.f64 (/.f64 #s(literal 1/4 binary64) (*.f64 x x)) #s(literal 1/2 binary64)) (/.f64 #s(literal 3/8 binary64) x)) x)) (sqrt.f64 x))
#s(approx (/ (- (sqrt (+ x 1)) (sqrt x)) (sqrt (+ x 1))) (/.f64 (-.f64 (+.f64 (/.f64 #s(literal 1/4 binary64) (*.f64 x x)) #s(literal 1/2 binary64)) (/.f64 #s(literal 3/8 binary64) x)) x))
(/.f64 (-.f64 (+.f64 (/.f64 #s(literal 1/4 binary64) (*.f64 x x)) #s(literal 1/2 binary64)) (/.f64 #s(literal 3/8 binary64) x)) x)
(-.f64 (+.f64 (/.f64 #s(literal 1/4 binary64) (*.f64 x x)) #s(literal 1/2 binary64)) (/.f64 #s(literal 3/8 binary64) x))
(+.f64 (/.f64 #s(literal 1/4 binary64) (*.f64 x x)) #s(literal 1/2 binary64))
(/.f64 #s(literal 1/4 binary64) (*.f64 x x))
#s(literal 1/4 binary64)
(*.f64 x x)
x
#s(literal 1/2 binary64)
(/.f64 #s(literal 3/8 binary64) x)
#s(literal 3/8 binary64)
(sqrt.f64 x)
#s(approx (- (/ 1 (sqrt x)) (/ 1 (sqrt (+ x 1)))) (/.f64 #s(literal 1 binary64) (sqrt.f64 x)))
(/.f64 #s(literal 1 binary64) (sqrt.f64 x))
#s(literal 1 binary64)
(sqrt.f64 x)
x
#s(approx (- (/ 1 (sqrt x)) (/ 1 (sqrt (+ x 1)))) (*.f64 (/.f64 #s(approx (- (sqrt (/ 1 x)) (sqrt x)) (neg.f64 (sqrt.f64 x))) (*.f64 x x)) #s(literal -1/2 binary64)))
(*.f64 (/.f64 #s(approx (- (sqrt (/ 1 x)) (sqrt x)) (neg.f64 (sqrt.f64 x))) (*.f64 x x)) #s(literal -1/2 binary64))
(/.f64 #s(approx (- (sqrt (/ 1 x)) (sqrt x)) (neg.f64 (sqrt.f64 x))) (*.f64 x x))
#s(approx (- (sqrt (/ 1 x)) (sqrt x)) (neg.f64 (sqrt.f64 x)))
(neg.f64 (sqrt.f64 x))
(sqrt.f64 x)
x
(*.f64 x x)
#s(literal -1/2 binary64)
(/.f64 (/.f64 #s(approx (- (sqrt (+ x 1)) (sqrt x)) (/.f64 (fma.f64 #s(literal -1/8 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) (*.f64 #s(literal 1/2 binary64) (sqrt.f64 x))) x)) (sqrt.f64 (+.f64 x #s(literal 1 binary64)))) (sqrt.f64 x))
(/.f64 #s(approx (- (sqrt (+ x 1)) (sqrt x)) (/.f64 (fma.f64 #s(literal -1/8 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) (*.f64 #s(literal 1/2 binary64) (sqrt.f64 x))) x)) (sqrt.f64 (+.f64 x #s(literal 1 binary64))))
#s(approx (- (sqrt (+ x 1)) (sqrt x)) (/.f64 (fma.f64 #s(literal -1/8 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) (*.f64 #s(literal 1/2 binary64) (sqrt.f64 x))) x))
(/.f64 (fma.f64 #s(literal -1/8 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) (*.f64 #s(literal 1/2 binary64) (sqrt.f64 x))) x)
(fma.f64 #s(literal -1/8 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) (*.f64 #s(literal 1/2 binary64) (sqrt.f64 x)))
#s(literal -1/8 binary64)
(sqrt.f64 (/.f64 #s(literal 1 binary64) x))
(/.f64 #s(literal 1 binary64) x)
#s(literal 1 binary64)
x
(*.f64 #s(literal 1/2 binary64) (sqrt.f64 x))
#s(literal 1/2 binary64)
(sqrt.f64 x)
(sqrt.f64 (+.f64 x #s(literal 1 binary64)))
(+.f64 x #s(literal 1 binary64))
(/.f64 #s(approx (- (sqrt (+ x 1)) (sqrt x)) (*.f64 #s(literal 1/2 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) x)))) (hypot.f64 (sqrt.f64 x) x))
#s(approx (- (sqrt (+ x 1)) (sqrt x)) (*.f64 #s(literal 1/2 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) x))))
(*.f64 #s(literal 1/2 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) x)))
#s(literal 1/2 binary64)
(sqrt.f64 (/.f64 #s(literal 1 binary64) x))
(/.f64 #s(literal 1 binary64) x)
#s(literal 1 binary64)
x
(hypot.f64 (sqrt.f64 x) x)
(sqrt.f64 x)
Outputs
(/.f64 #s(approx (/ (- (sqrt (+ x 1)) (sqrt x)) (sqrt (+ x 1))) (/.f64 (-.f64 (+.f64 (/.f64 #s(literal 1/4 binary64) (*.f64 x x)) #s(literal 1/2 binary64)) (/.f64 #s(literal 3/8 binary64) x)) x)) (sqrt.f64 x))
(/.f64 #s(approx (/ (- (sqrt (+ x 1)) (sqrt x)) (sqrt (+ x 1))) (/.f64 (-.f64 (-.f64 (/.f64 #s(literal 1/4 binary64) (*.f64 x x)) #s(literal -1/2 binary64)) (/.f64 #s(literal 3/8 binary64) x)) x)) (sqrt.f64 x))
#s(approx (/ (- (sqrt (+ x 1)) (sqrt x)) (sqrt (+ x 1))) (/.f64 (-.f64 (+.f64 (/.f64 #s(literal 1/4 binary64) (*.f64 x x)) #s(literal 1/2 binary64)) (/.f64 #s(literal 3/8 binary64) x)) x))
#s(approx (/ (- (sqrt (+ x 1)) (sqrt x)) (sqrt (+ x 1))) (/.f64 (-.f64 (-.f64 (/.f64 #s(literal 1/4 binary64) (*.f64 x x)) #s(literal -1/2 binary64)) (/.f64 #s(literal 3/8 binary64) x)) x))
(/.f64 (-.f64 (+.f64 (/.f64 #s(literal 1/4 binary64) (*.f64 x x)) #s(literal 1/2 binary64)) (/.f64 #s(literal 3/8 binary64) x)) x)
(/.f64 (-.f64 (-.f64 (/.f64 #s(literal 1/4 binary64) (*.f64 x x)) #s(literal -1/2 binary64)) (/.f64 #s(literal 3/8 binary64) x)) x)
(-.f64 (+.f64 (/.f64 #s(literal 1/4 binary64) (*.f64 x x)) #s(literal 1/2 binary64)) (/.f64 #s(literal 3/8 binary64) x))
(-.f64 (-.f64 (/.f64 #s(literal 1/4 binary64) (*.f64 x x)) #s(literal -1/2 binary64)) (/.f64 #s(literal 3/8 binary64) x))
(+.f64 (/.f64 #s(literal 1/4 binary64) (*.f64 x x)) #s(literal 1/2 binary64))
(-.f64 (/.f64 #s(literal 1/4 binary64) (*.f64 x x)) #s(literal -1/2 binary64))
(/.f64 #s(literal 1/4 binary64) (*.f64 x x))
#s(literal 1/4 binary64)
(*.f64 x x)
x
#s(literal 1/2 binary64)
(/.f64 #s(literal 3/8 binary64) x)
#s(literal 3/8 binary64)
(sqrt.f64 x)
#s(approx (- (/ 1 (sqrt x)) (/ 1 (sqrt (+ x 1)))) (/.f64 #s(literal 1 binary64) (sqrt.f64 x)))
#s(approx (- (/ 1 (sqrt x)) (/ 1 (sqrt (+ x 1)))) (/.f64 (sqrt.f64 x) x))
(/.f64 #s(literal 1 binary64) (sqrt.f64 x))
(/.f64 (sqrt.f64 x) x)
#s(literal 1 binary64)
(sqrt.f64 x)
x
#s(approx (- (/ 1 (sqrt x)) (/ 1 (sqrt (+ x 1)))) (*.f64 (/.f64 #s(approx (- (sqrt (/ 1 x)) (sqrt x)) (neg.f64 (sqrt.f64 x))) (*.f64 x x)) #s(literal -1/2 binary64)))
#s(approx (- (/ 1 (sqrt x)) (/ 1 (sqrt (+ x 1)))) (*.f64 (/.f64 (/.f64 #s(literal -1/2 binary64) x) x) #s(approx (- (sqrt (/ 1 x)) (sqrt x)) (neg.f64 (sqrt.f64 x)))))
(*.f64 (/.f64 #s(approx (- (sqrt (/ 1 x)) (sqrt x)) (neg.f64 (sqrt.f64 x))) (*.f64 x x)) #s(literal -1/2 binary64))
(*.f64 (/.f64 (/.f64 #s(literal -1/2 binary64) x) x) #s(approx (- (sqrt (/ 1 x)) (sqrt x)) (neg.f64 (sqrt.f64 x))))
(/.f64 #s(approx (- (sqrt (/ 1 x)) (sqrt x)) (neg.f64 (sqrt.f64 x))) (*.f64 x x))
#s(approx (- (sqrt (/ 1 x)) (sqrt x)) (neg.f64 (sqrt.f64 x)))
(neg.f64 (sqrt.f64 x))
(sqrt.f64 x)
x
(*.f64 x x)
#s(literal -1/2 binary64)
(/.f64 (/.f64 #s(approx (- (sqrt (+ x 1)) (sqrt x)) (/.f64 (fma.f64 #s(literal -1/8 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) (*.f64 #s(literal 1/2 binary64) (sqrt.f64 x))) x)) (sqrt.f64 (+.f64 x #s(literal 1 binary64)))) (sqrt.f64 x))
(/.f64 #s(approx (- (sqrt (+ x 1)) (sqrt x)) (fma.f64 (/.f64 #s(literal -1/8 binary64) x) (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) (/.f64 #s(literal 1/2 binary64) (sqrt.f64 x)))) (*.f64 (sqrt.f64 x) (sqrt.f64 (+.f64 #s(literal 1 binary64) x))))
(/.f64 #s(approx (- (sqrt (+ x 1)) (sqrt x)) (/.f64 (fma.f64 #s(literal -1/8 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) (*.f64 #s(literal 1/2 binary64) (sqrt.f64 x))) x)) (sqrt.f64 (+.f64 x #s(literal 1 binary64))))
(/.f64 #s(approx (- (sqrt (+ x 1)) (sqrt x)) (fma.f64 (/.f64 #s(literal -1/8 binary64) x) (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) (/.f64 #s(literal 1/2 binary64) (sqrt.f64 x)))) (sqrt.f64 (+.f64 #s(literal 1 binary64) x)))
#s(approx (- (sqrt (+ x 1)) (sqrt x)) (/.f64 (fma.f64 #s(literal -1/8 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) (*.f64 #s(literal 1/2 binary64) (sqrt.f64 x))) x))
#s(approx (- (sqrt (+ x 1)) (sqrt x)) (fma.f64 (/.f64 #s(literal -1/8 binary64) x) (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) (/.f64 #s(literal 1/2 binary64) (sqrt.f64 x))))
(/.f64 (fma.f64 #s(literal -1/8 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) (*.f64 #s(literal 1/2 binary64) (sqrt.f64 x))) x)
(fma.f64 (/.f64 #s(literal -1/8 binary64) x) (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) (/.f64 #s(literal 1/2 binary64) (sqrt.f64 x)))
(fma.f64 #s(literal -1/8 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) (*.f64 #s(literal 1/2 binary64) (sqrt.f64 x)))
(fma.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) #s(literal -1/8 binary64) (*.f64 (sqrt.f64 x) #s(literal 1/2 binary64)))
#s(literal -1/8 binary64)
(sqrt.f64 (/.f64 #s(literal 1 binary64) x))
(/.f64 #s(literal 1 binary64) x)
#s(literal 1 binary64)
x
(*.f64 #s(literal 1/2 binary64) (sqrt.f64 x))
(*.f64 (sqrt.f64 x) #s(literal 1/2 binary64))
#s(literal 1/2 binary64)
(sqrt.f64 x)
(sqrt.f64 (+.f64 x #s(literal 1 binary64)))
(sqrt.f64 (+.f64 #s(literal 1 binary64) x))
(+.f64 x #s(literal 1 binary64))
(+.f64 #s(literal 1 binary64) x)
(/.f64 #s(approx (- (sqrt (+ x 1)) (sqrt x)) (*.f64 #s(literal 1/2 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) x)))) (hypot.f64 (sqrt.f64 x) x))
(/.f64 #s(approx (- (sqrt (+ x 1)) (sqrt x)) (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) #s(literal 1/2 binary64))) (hypot.f64 (sqrt.f64 x) x))
#s(approx (- (sqrt (+ x 1)) (sqrt x)) (*.f64 #s(literal 1/2 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) x))))
#s(approx (- (sqrt (+ x 1)) (sqrt x)) (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) #s(literal 1/2 binary64)))
(*.f64 #s(literal 1/2 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) x)))
(*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) #s(literal 1/2 binary64))
#s(literal 1/2 binary64)
(sqrt.f64 (/.f64 #s(literal 1 binary64) x))
(/.f64 #s(literal 1 binary64) x)
#s(literal 1 binary64)
x
(hypot.f64 (sqrt.f64 x) x)
(sqrt.f64 x)

localize248.0ms (3.6%)

Memory
42.4MiB live, 184.4MiB allocated
Localize:

Found 19 expressions of interest:

NewMetricScoreProgram
accuracy0.0
(sqrt.f64 x)
accuracy0.15234375
(sqrt.f64 (/.f64 #s(literal 1 binary64) x))
accuracy0.1640625
(/.f64 #s(approx (- (sqrt (+ x 1)) (sqrt x)) (*.f64 #s(literal 1/2 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) x)))) (hypot.f64 (sqrt.f64 x) x))
accuracy0.9121702963124209
#s(approx (- (sqrt (+ x 1)) (sqrt x)) (*.f64 #s(literal 1/2 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) x))))
accuracy0.25390625
(/.f64 (fma.f64 #s(literal -1/8 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) (*.f64 #s(literal 1/2 binary64) (sqrt.f64 x))) x)
accuracy0.25390625
(/.f64 (/.f64 #s(approx (- (sqrt (+ x 1)) (sqrt x)) (/.f64 (fma.f64 #s(literal -1/8 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) (*.f64 #s(literal 1/2 binary64) (sqrt.f64 x))) x)) (sqrt.f64 (+.f64 x #s(literal 1 binary64)))) (sqrt.f64 x))
accuracy0.33822250976844204
(/.f64 #s(approx (- (sqrt (+ x 1)) (sqrt x)) (/.f64 (fma.f64 #s(literal -1/8 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) (*.f64 #s(literal 1/2 binary64) (sqrt.f64 x))) x)) (sqrt.f64 (+.f64 x #s(literal 1 binary64))))
accuracy0.4526051189963652
#s(approx (- (sqrt (+ x 1)) (sqrt x)) (/.f64 (fma.f64 #s(literal -1/8 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) (*.f64 #s(literal 1/2 binary64) (sqrt.f64 x))) x))
accuracy0.0
(neg.f64 (sqrt.f64 x))
accuracy0.9167017926041685
#s(approx (- (/ 1 (sqrt x)) (/ 1 (sqrt (+ x 1)))) (*.f64 (/.f64 #s(approx (- (sqrt (/ 1 x)) (sqrt x)) (neg.f64 (sqrt.f64 x))) (*.f64 x x)) #s(literal -1/2 binary64)))
accuracy0.9863772657980471
#s(approx (- (sqrt (/ 1 x)) (sqrt x)) (neg.f64 (sqrt.f64 x)))
accuracy10.569011443006001
(/.f64 #s(approx (- (sqrt (/ 1 x)) (sqrt x)) (neg.f64 (sqrt.f64 x))) (*.f64 x x))
accuracy0.0
(sqrt.f64 x)
accuracy0.25390625
(/.f64 #s(literal 1 binary64) (sqrt.f64 x))
accuracy60.464192040049284
#s(approx (- (/ 1 (sqrt x)) (/ 1 (sqrt (+ x 1)))) (/.f64 #s(literal 1 binary64) (sqrt.f64 x)))
accuracy0.015625
(-.f64 (+.f64 (/.f64 #s(literal 1/4 binary64) (*.f64 x x)) #s(literal 1/2 binary64)) (/.f64 #s(literal 3/8 binary64) x))
accuracy0.25390625
(/.f64 #s(approx (/ (- (sqrt (+ x 1)) (sqrt x)) (sqrt (+ x 1))) (/.f64 (-.f64 (+.f64 (/.f64 #s(literal 1/4 binary64) (*.f64 x x)) #s(literal 1/2 binary64)) (/.f64 #s(literal 3/8 binary64) x)) x)) (sqrt.f64 x))
accuracy0.45807543659067457
#s(approx (/ (- (sqrt (+ x 1)) (sqrt x)) (sqrt (+ x 1))) (/.f64 (-.f64 (+.f64 (/.f64 #s(literal 1/4 binary64) (*.f64 x x)) #s(literal 1/2 binary64)) (/.f64 #s(literal 3/8 binary64) x)) x))
accuracy0.93025542145477
(/.f64 #s(literal 1/4 binary64) (*.f64 x x))
Samples
189.0ms212×1valid
29.0ms41×2valid
1.0ms0valid
Compiler

Compiled 283 to 37 computations (86.9% saved)

Precisions
Click to see histograms. Total time spent on operations: 174.0ms
ival-sub: 78.0ms (44.9% of total)
ival-div: 28.0ms (16.1% of total)
adjust: 25.0ms (14.4% of total)
ival-sqrt: 12.0ms (6.9% of total)
ival-mult: 11.0ms (6.3% of total)
ival-hypot: 9.0ms (5.2% of total)
ival-add: 8.0ms (4.6% of total)
ival-neg: 2.0ms (1.2% of total)
exact: 1.0ms (0.6% of total)
ival-assert: 0.0ms (0% of total)
ival-true: 0.0ms (0% of total)

series33.0ms (0.5%)

Memory
-31.7MiB live, 14.1MiB allocated
Counts
21 → 87
Calls
Call 1
Inputs
(/.f64 #s(approx (/ (- (sqrt (+ x 1)) (sqrt x)) (sqrt (+ x 1))) (/.f64 (-.f64 (+.f64 (/.f64 #s(literal 1/4 binary64) (*.f64 x x)) #s(literal 1/2 binary64)) (/.f64 #s(literal 3/8 binary64) x)) x)) (sqrt.f64 x))
#s(approx (/ (- (sqrt (+ x 1)) (sqrt x)) (sqrt (+ x 1))) (/.f64 (-.f64 (+.f64 (/.f64 #s(literal 1/4 binary64) (*.f64 x x)) #s(literal 1/2 binary64)) (/.f64 #s(literal 3/8 binary64) x)) x))
(/.f64 (-.f64 (+.f64 (/.f64 #s(literal 1/4 binary64) (*.f64 x x)) #s(literal 1/2 binary64)) (/.f64 #s(literal 3/8 binary64) x)) x)
(-.f64 (+.f64 (/.f64 #s(literal 1/4 binary64) (*.f64 x x)) #s(literal 1/2 binary64)) (/.f64 #s(literal 3/8 binary64) x))
#s(approx (- (/ 1 (sqrt x)) (/ 1 (sqrt (+ x 1)))) (/.f64 #s(literal 1 binary64) (sqrt.f64 x)))
(/.f64 #s(literal 1 binary64) (sqrt.f64 x))
(sqrt.f64 x)
#s(approx (- (/ 1 (sqrt x)) (/ 1 (sqrt (+ x 1)))) (*.f64 (/.f64 #s(approx (- (sqrt (/ 1 x)) (sqrt x)) (neg.f64 (sqrt.f64 x))) (*.f64 x x)) #s(literal -1/2 binary64)))
(*.f64 (/.f64 #s(approx (- (sqrt (/ 1 x)) (sqrt x)) (neg.f64 (sqrt.f64 x))) (*.f64 x x)) #s(literal -1/2 binary64))
(/.f64 #s(approx (- (sqrt (/ 1 x)) (sqrt x)) (neg.f64 (sqrt.f64 x))) (*.f64 x x))
#s(approx (- (sqrt (/ 1 x)) (sqrt x)) (neg.f64 (sqrt.f64 x)))
(/.f64 (/.f64 #s(approx (- (sqrt (+ x 1)) (sqrt x)) (/.f64 (fma.f64 #s(literal -1/8 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) (*.f64 #s(literal 1/2 binary64) (sqrt.f64 x))) x)) (sqrt.f64 (+.f64 x #s(literal 1 binary64)))) (sqrt.f64 x))
(/.f64 #s(approx (- (sqrt (+ x 1)) (sqrt x)) (/.f64 (fma.f64 #s(literal -1/8 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) (*.f64 #s(literal 1/2 binary64) (sqrt.f64 x))) x)) (sqrt.f64 (+.f64 x #s(literal 1 binary64))))
#s(approx (- (sqrt (+ x 1)) (sqrt x)) (/.f64 (fma.f64 #s(literal -1/8 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) (*.f64 #s(literal 1/2 binary64) (sqrt.f64 x))) x))
(/.f64 (fma.f64 #s(literal -1/8 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) (*.f64 #s(literal 1/2 binary64) (sqrt.f64 x))) x)
(/.f64 #s(approx (- (sqrt (+ x 1)) (sqrt x)) (*.f64 #s(literal 1/2 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) x)))) (hypot.f64 (sqrt.f64 x) x))
#s(approx (- (sqrt (+ x 1)) (sqrt x)) (*.f64 #s(literal 1/2 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) x))))
(*.f64 #s(literal 1/2 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) x)))
(sqrt.f64 (/.f64 #s(literal 1 binary64) x))
(/.f64 #s(literal 1/4 binary64) (*.f64 x x))
(neg.f64 (sqrt.f64 x))
Outputs
(* (sqrt (/ 1 x)) (- 1 (sqrt x)))
(/ (+ (* 1/2 (sqrt (pow x 3))) (* (sqrt x) (- 1 (sqrt x)))) x)
(/ (+ (* x (+ (* 1/2 (sqrt x)) (* x (+ (* -1/2 (* (sqrt (/ 1 x)) (- 1 (sqrt x)))) (* -1/8 (sqrt x)))))) (* (sqrt x) (- 1 (sqrt x)))) x)
(/ (+ (* x (+ (* 1/2 (sqrt x)) (* x (+ (* -1/2 (* (sqrt (/ 1 x)) (- 1 (sqrt x)))) (+ (* -1/8 (sqrt x)) (* x (+ (* -1/4 (sqrt (/ 1 x))) (+ (* 1/16 (sqrt x)) (* 1/2 (* (sqrt (/ 1 x)) (- 1 (sqrt x)))))))))))) (* (sqrt x) (- 1 (sqrt x)))) x)
(- 1 (sqrt x))
(- (+ 1 (* x (+ 1/2 (* -1/2 (- 1 (sqrt x)))))) (sqrt x))
(- (+ 1 (* x (+ 1/2 (+ (* -1/2 (- 1 (sqrt x))) (* x (- (* 3/8 (- 1 (sqrt x))) 3/8)))))) (sqrt x))
(- (+ 1 (* x (+ 1/2 (+ (* -1/2 (- 1 (sqrt x))) (* x (- (+ (* 3/8 (- 1 (sqrt x))) (* x (+ 5/16 (* -5/16 (- 1 (sqrt x)))))) 3/8)))))) (sqrt x))
(/ 1/4 (pow x 3))
(/ (+ 1/4 (* -3/8 x)) (pow x 3))
(/ (+ 1/4 (* x (- (* 1/2 x) 3/8))) (pow x 3))
(/ 1/4 (pow x 2))
(/ (+ 1/4 (* -3/8 x)) (pow x 2))
(/ (+ 1/4 (* x (- (* 1/2 x) 3/8))) (pow x 2))
(sqrt (/ 1 x))
(/ (+ (sqrt x) (* -1 x)) x)
(/ (+ (sqrt x) (* x (- (* 1/2 x) 1))) x)
(/ (+ (sqrt x) (* x (- (* x (+ 1/2 (* -3/8 x))) 1))) x)
(sqrt x)
(* -1/2 (sqrt (/ 1 (pow x 5))))
(/ (+ (* -1/2 (sqrt x)) (* 1/2 (sqrt (pow x 3)))) (pow x 3))
(sqrt (/ 1 (pow x 5)))
(/ (+ (sqrt x) (* -1 (sqrt (pow x 3)))) (pow x 3))
(/ (+ (sqrt x) (* -1 (sqrt (pow x 3)))) x)
(- (+ 1 (* 1/2 x)) (sqrt x))
(- (+ 1 (* x (+ 1/2 (* -1/8 x)))) (sqrt x))
(- (+ 1 (* x (+ 1/2 (* x (- (* 1/16 x) 1/8))))) (sqrt x))
(* -1/8 (sqrt (/ 1 (pow x 3))))
(/ (+ (* -1/8 (sqrt x)) (* 1/2 (sqrt (pow x 3)))) (pow x 2))
(* 1/2 (sqrt (/ 1 x)))
(* -1 (sqrt x))
(* 1/2 (sqrt (/ 1 (pow x 3))))
(/ (+ (* -1/4 (sqrt (/ 1 x))) (* 1/2 (sqrt x))) (pow x 2))
(/ (+ (* -1/4 (sqrt (/ 1 x))) (+ (* -1/8 (sqrt (/ 1 x))) (+ (* 3/16 (sqrt (/ 1 (pow x 3)))) (* 1/2 (sqrt x))))) (pow x 2))
(/ (+ (* -1/4 (sqrt (/ 1 x))) (+ (* -5/32 (sqrt (/ 1 (pow x 5)))) (+ (* -1/8 (sqrt (/ 1 x))) (+ (* 1/16 (sqrt (/ 1 (pow x 3)))) (+ (* 3/16 (sqrt (/ 1 (pow x 3)))) (* 1/2 (sqrt x))))))) (pow x 2))
(/ 1/2 x)
(/ (+ 1/2 (* -1 (/ (+ (* 1/8 x) (* 1/4 x)) (pow x 2)))) x)
(/ (- (+ 1/2 (* 1/4 (/ 1 (pow x 2)))) (+ (/ 1/8 x) (/ 1/4 x))) x)
(/ (- (+ 1/2 (+ (* -1/4 (/ (+ 1 (* 1/4 x)) (pow x 3))) (* 3/8 (/ 1 (pow x 2))))) (+ (/ 1/8 x) (/ 1/4 x))) x)
(/ (- 1/2 (* 3/8 (/ 1 x))) x)
(/ (- (+ 1/2 (/ 1/4 (pow x 2))) (* 3/8 (/ 1 x))) x)
1/2
(- 1/2 (* 3/8 (/ 1 x)))
(- (+ 1/2 (/ 1/4 (pow x 2))) (* 3/8 (/ 1 x)))
(/ (- (* -1/2 (sqrt (/ 1 x))) (* -1/2 (sqrt x))) (pow x 2))
(/ (- (* 1/2 (* (sqrt (/ 1 (pow x 3))) (+ 1 (* 1/4 x)))) (+ (* -1/2 (sqrt x)) (* 1/2 (sqrt (/ 1 x))))) (pow x 2))
(/ (- (* -1/2 (* (sqrt (/ 1 (pow x 5))) (+ 1 (* 1/2 x)))) (+ (* -1/2 (sqrt x)) (+ (* -1/2 (* (sqrt (/ 1 (pow x 3))) (+ 1 (* 1/4 x)))) (* 1/2 (sqrt (/ 1 x)))))) (pow x 2))
(/ (+ (* -1/2 (sqrt (/ 1 (pow x 3)))) (* 1/2 (sqrt (/ 1 x)))) x)
(* -1 (sqrt (/ 1 (pow x 3))))
(/ (+ (sqrt (/ 1 (pow x 3))) (* -1 (sqrt (/ 1 x)))) x)
(* x (- (sqrt (/ 1 (pow x 3))) (sqrt (/ 1 x))))
(/ (+ (* -1/8 (sqrt (/ 1 x))) (* 1/2 (sqrt x))) x)
(/ (+ (* -1/8 (sqrt (/ 1 x))) (+ (* 1/16 (sqrt (/ 1 (pow x 3)))) (* 1/2 (sqrt x)))) x)
(/ (+ (* -1/8 (sqrt (/ 1 x))) (+ (* -5/128 (sqrt (/ 1 (pow x 5)))) (+ (* 1/16 (sqrt (/ 1 (pow x 3)))) (* 1/2 (sqrt x))))) x)
(+ (* -1/8 (sqrt (/ 1 (pow x 3)))) (* 1/2 (sqrt (/ 1 x))))
(/ (+ (* 1/4 (* (sqrt (/ 1 x)) (/ 1 (pow (sqrt -1) 2)))) (* 1/2 (sqrt x))) (pow x 2))
(/ (+ (* -1 (/ (+ (* -1 (/ (+ (* -1/4 (* (sqrt x) (/ (+ 1 (* 1/4 (/ 1 (pow (sqrt -1) 2)))) (pow (sqrt -1) 2)))) (* -1/8 (* (sqrt (pow x 3)) (/ 1 (pow (sqrt -1) 2))))) x)) (* -1/4 (* (sqrt x) (/ 1 (pow (sqrt -1) 2))))) x)) (* 1/2 (sqrt x))) (pow x 2))
(/ (+ (* -1 (/ (+ (* -1 (/ (+ (* -1 (/ (+ (* -1/4 (* (sqrt x) (/ (+ 1 (* 1/2 (/ (+ 1 (* 1/4 (/ 1 (pow (sqrt -1) 2)))) (pow (sqrt -1) 2)))) (pow (sqrt -1) 2)))) (* 1/16 (* (sqrt (pow x 3)) (/ 1 (pow (sqrt -1) 4))))) x)) (+ (* -1/4 (* (sqrt x) (/ (+ 1 (* 1/4 (/ 1 (pow (sqrt -1) 2)))) (pow (sqrt -1) 2)))) (* -1/8 (* (sqrt (pow x 3)) (/ 1 (pow (sqrt -1) 2)))))) x)) (* -1/4 (* (sqrt x) (/ 1 (pow (sqrt -1) 2))))) x)) (* 1/2 (sqrt x))) (pow x 2))
(/ -1/2 x)
(* -1 (/ (+ 1/2 (* -1 (/ (+ (* -1/4 (/ x (pow (sqrt -1) 2))) (* -1/8 (/ x (pow (sqrt -1) 2)))) (pow x 2)))) x))
(* -1 (/ (+ 1/2 (* -1 (/ (+ (* -1/4 (/ x (pow (sqrt -1) 2))) (+ (* -1/8 (/ x (pow (sqrt -1) 2))) (* 1/4 (/ 1 (pow (sqrt -1) 2))))) (pow x 2)))) x))
(* -1 (/ (- (+ 1/2 (* -1 (/ (- (* -1 (/ (+ (* 1/8 (/ (pow x 2) (pow (sqrt -1) 4))) (* 1/4 (/ (* x (+ 1 (* -1/4 (/ x (pow (sqrt -1) 2))))) (pow (sqrt -1) 2)))) x)) (* -1/4 (/ x (pow (sqrt -1) 2)))) (pow x 3)))) (+ (/ -1/4 (* x (pow (sqrt -1) 2))) (/ -1/8 (* x (pow (sqrt -1) 2))))) x))
(* -1 (/ (- (* 3/8 (/ 1 x)) 1/2) x))
(* -1 (/ (- (* -1 (/ (- (* 1/4 (/ 1 x)) 3/8) x)) 1/2) x))
(+ 1/2 (* -1 (/ (- 3/8 (* 1/4 (/ 1 x))) x)))
(- (sqrt (/ 1 x)) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)))
(- (+ (sqrt (/ 1 x)) (* 1/2 (sqrt (/ 1 (pow x 3))))) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)))
(- (+ (sqrt (/ 1 x)) (* -1/2 (sqrt (/ 1 (pow x 5))))) (+ (* -1/2 (sqrt (/ 1 (pow x 3)))) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))))
(- (+ (sqrt (/ 1 x)) (* -1 (/ (- (* -1/2 (* (sqrt (/ 1 x)) (+ 1 (* -1/4 (/ x (pow (sqrt -1) 2)))))) (* -1/2 (sqrt x))) (pow x 3)))) (+ (* -1/2 (sqrt (/ 1 (pow x 3)))) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))))
(* -1 (* (sqrt x) (pow (sqrt -1) 2)))
(* -1/2 (* (sqrt (/ 1 (pow x 3))) (pow (sqrt -1) 2)))
(* -1 (/ (+ (* 1/2 (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))) (* 1/2 (* (sqrt (/ 1 (pow x 3))) (pow (sqrt -1) 2)))) x))
(* (sqrt (/ 1 (pow x 3))) (pow (sqrt -1) 2))
(* -1 (/ (+ (* -1 (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))) (* -1 (* (sqrt (/ 1 (pow x 3))) (pow (sqrt -1) 2)))) x))
(* (sqrt x) (pow (sqrt -1) 2))
(* -1 (* x (- (* -1 (* (sqrt (/ 1 (pow x 3))) (pow (sqrt -1) 2))) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)))))
(* -1/2 (sqrt (/ 1 x)))
(* -1 (/ (+ (* -1/8 (* (sqrt (/ 1 x)) (/ 1 (pow (sqrt -1) 2)))) (* 1/2 (sqrt x))) x))
(* -1 (/ (+ (* -1/8 (* (sqrt (/ 1 x)) (/ 1 (pow (sqrt -1) 2)))) (+ (* 1/16 (* (sqrt (/ 1 (pow x 3))) (/ 1 (pow (sqrt -1) 4)))) (* 1/2 (sqrt x)))) x))
(* -1 (/ (+ (* -1/8 (* (sqrt (/ 1 x)) (/ 1 (pow (sqrt -1) 2)))) (+ (* -5/128 (* (sqrt (/ 1 (pow x 5))) (/ 1 (pow (sqrt -1) 6)))) (+ (* 1/16 (* (sqrt (/ 1 (pow x 3))) (/ 1 (pow (sqrt -1) 4)))) (* 1/2 (sqrt x))))) x))
(* -1/2 (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)))
(+ (* -1/2 (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))) (* -1/8 (* (sqrt (/ 1 (pow x 3))) (pow (sqrt -1) 2))))
(/ (+ (* 1/4 (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))) (* 1/2 (sqrt x))) (pow x 2))
(/ (+ (* -1 (/ (+ (* -1 (/ (+ (* -1/4 (* (sqrt x) (+ (* -1 (pow (sqrt -1) 4)) (* 1/4 (pow (sqrt -1) 4))))) (* -1/8 (* (sqrt (pow x 3)) (/ 1 (pow (sqrt -1) 2))))) x)) (* -1/4 (* (sqrt x) (pow (sqrt -1) 2)))) x)) (* 1/2 (sqrt x))) (pow x 2))
(/ (+ (* -1 (/ (+ (* -1 (/ (+ (* -1 (/ (+ (* -1/4 (* (sqrt x) (+ (* 1/2 (* (pow (sqrt -1) 2) (+ (* -1 (pow (sqrt -1) 4)) (* 1/4 (pow (sqrt -1) 4))))) (pow (sqrt -1) 6)))) (* 1/16 (sqrt (pow x 3)))) x)) (+ (* -1/4 (* (sqrt x) (+ (* -1 (pow (sqrt -1) 4)) (* 1/4 (pow (sqrt -1) 4))))) (* -1/8 (* (sqrt (pow x 3)) (/ 1 (pow (sqrt -1) 2)))))) x)) (* -1/4 (* (sqrt x) (pow (sqrt -1) 2)))) x)) (* 1/2 (sqrt x))) (pow x 2))
(* 1/2 (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)))
(* (sqrt (/ 1 x)) (pow (sqrt -1) 2))
Calls

3 calls:

TimeVariablePointExpression
26.0ms
x
@0
((/ (/ (- (sqrt (+ x 1)) (sqrt x)) (sqrt (+ x 1))) (sqrt x)) (/ (- (sqrt (+ x 1)) (sqrt x)) (sqrt (+ x 1))) (/ (- (+ (/ 1/4 (* x x)) 1/2) (/ 3/8 x)) x) (- (+ (/ 1/4 (* x x)) 1/2) (/ 3/8 x)) (- (/ 1 (sqrt x)) (/ 1 (sqrt (+ x 1)))) (/ 1 (sqrt x)) (sqrt x) (- (/ 1 (sqrt x)) (/ 1 (sqrt (+ x 1)))) (* (/ (- (sqrt (/ 1 x)) (sqrt x)) (* x x)) -1/2) (/ (- (sqrt (/ 1 x)) (sqrt x)) (* x x)) (- (sqrt (/ 1 x)) (sqrt x)) (/ (/ (- (sqrt (+ x 1)) (sqrt x)) (sqrt (+ x 1))) (sqrt x)) (/ (- (sqrt (+ x 1)) (sqrt x)) (sqrt (+ x 1))) (- (sqrt (+ x 1)) (sqrt x)) (/ (+ (* -1/8 (sqrt (/ 1 x))) (* 1/2 (sqrt x))) x) (/ (- (sqrt (+ x 1)) (sqrt x)) (sqrt (+ (* (sqrt x) (sqrt x)) (* x x)))) (- (sqrt (+ x 1)) (sqrt x)) (* 1/2 (sqrt (/ 1 x))) (sqrt (/ 1 x)) (/ 1/4 (* x x)) (neg (sqrt x)))
4.0ms
x
@-inf
((/ (/ (- (sqrt (+ x 1)) (sqrt x)) (sqrt (+ x 1))) (sqrt x)) (/ (- (sqrt (+ x 1)) (sqrt x)) (sqrt (+ x 1))) (/ (- (+ (/ 1/4 (* x x)) 1/2) (/ 3/8 x)) x) (- (+ (/ 1/4 (* x x)) 1/2) (/ 3/8 x)) (- (/ 1 (sqrt x)) (/ 1 (sqrt (+ x 1)))) (/ 1 (sqrt x)) (sqrt x) (- (/ 1 (sqrt x)) (/ 1 (sqrt (+ x 1)))) (* (/ (- (sqrt (/ 1 x)) (sqrt x)) (* x x)) -1/2) (/ (- (sqrt (/ 1 x)) (sqrt x)) (* x x)) (- (sqrt (/ 1 x)) (sqrt x)) (/ (/ (- (sqrt (+ x 1)) (sqrt x)) (sqrt (+ x 1))) (sqrt x)) (/ (- (sqrt (+ x 1)) (sqrt x)) (sqrt (+ x 1))) (- (sqrt (+ x 1)) (sqrt x)) (/ (+ (* -1/8 (sqrt (/ 1 x))) (* 1/2 (sqrt x))) x) (/ (- (sqrt (+ x 1)) (sqrt x)) (sqrt (+ (* (sqrt x) (sqrt x)) (* x x)))) (- (sqrt (+ x 1)) (sqrt x)) (* 1/2 (sqrt (/ 1 x))) (sqrt (/ 1 x)) (/ 1/4 (* x x)) (neg (sqrt x)))
2.0ms
x
@inf
((/ (/ (- (sqrt (+ x 1)) (sqrt x)) (sqrt (+ x 1))) (sqrt x)) (/ (- (sqrt (+ x 1)) (sqrt x)) (sqrt (+ x 1))) (/ (- (+ (/ 1/4 (* x x)) 1/2) (/ 3/8 x)) x) (- (+ (/ 1/4 (* x x)) 1/2) (/ 3/8 x)) (- (/ 1 (sqrt x)) (/ 1 (sqrt (+ x 1)))) (/ 1 (sqrt x)) (sqrt x) (- (/ 1 (sqrt x)) (/ 1 (sqrt (+ x 1)))) (* (/ (- (sqrt (/ 1 x)) (sqrt x)) (* x x)) -1/2) (/ (- (sqrt (/ 1 x)) (sqrt x)) (* x x)) (- (sqrt (/ 1 x)) (sqrt x)) (/ (/ (- (sqrt (+ x 1)) (sqrt x)) (sqrt (+ x 1))) (sqrt x)) (/ (- (sqrt (+ x 1)) (sqrt x)) (sqrt (+ x 1))) (- (sqrt (+ x 1)) (sqrt x)) (/ (+ (* -1/8 (sqrt (/ 1 x))) (* 1/2 (sqrt x))) x) (/ (- (sqrt (+ x 1)) (sqrt x)) (sqrt (+ (* (sqrt x) (sqrt x)) (* x x)))) (- (sqrt (+ x 1)) (sqrt x)) (* 1/2 (sqrt (/ 1 x))) (sqrt (/ 1 x)) (/ 1/4 (* x x)) (neg (sqrt x)))

simplify132.0ms (1.9%)

Memory
14.2MiB live, 115.5MiB allocated
Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
03981672
113291399
256041397
080931311
Stop Event
iter limit
node limit
Counts
87 → 87
Calls
Call 1
Inputs
(* (sqrt (/ 1 x)) (- 1 (sqrt x)))
(/ (+ (* 1/2 (sqrt (pow x 3))) (* (sqrt x) (- 1 (sqrt x)))) x)
(/ (+ (* x (+ (* 1/2 (sqrt x)) (* x (+ (* -1/2 (* (sqrt (/ 1 x)) (- 1 (sqrt x)))) (* -1/8 (sqrt x)))))) (* (sqrt x) (- 1 (sqrt x)))) x)
(/ (+ (* x (+ (* 1/2 (sqrt x)) (* x (+ (* -1/2 (* (sqrt (/ 1 x)) (- 1 (sqrt x)))) (+ (* -1/8 (sqrt x)) (* x (+ (* -1/4 (sqrt (/ 1 x))) (+ (* 1/16 (sqrt x)) (* 1/2 (* (sqrt (/ 1 x)) (- 1 (sqrt x)))))))))))) (* (sqrt x) (- 1 (sqrt x)))) x)
(- 1 (sqrt x))
(- (+ 1 (* x (+ 1/2 (* -1/2 (- 1 (sqrt x)))))) (sqrt x))
(- (+ 1 (* x (+ 1/2 (+ (* -1/2 (- 1 (sqrt x))) (* x (- (* 3/8 (- 1 (sqrt x))) 3/8)))))) (sqrt x))
(- (+ 1 (* x (+ 1/2 (+ (* -1/2 (- 1 (sqrt x))) (* x (- (+ (* 3/8 (- 1 (sqrt x))) (* x (+ 5/16 (* -5/16 (- 1 (sqrt x)))))) 3/8)))))) (sqrt x))
(/ 1/4 (pow x 3))
(/ (+ 1/4 (* -3/8 x)) (pow x 3))
(/ (+ 1/4 (* x (- (* 1/2 x) 3/8))) (pow x 3))
(/ 1/4 (pow x 2))
(/ (+ 1/4 (* -3/8 x)) (pow x 2))
(/ (+ 1/4 (* x (- (* 1/2 x) 3/8))) (pow x 2))
(sqrt (/ 1 x))
(/ (+ (sqrt x) (* -1 x)) x)
(/ (+ (sqrt x) (* x (- (* 1/2 x) 1))) x)
(/ (+ (sqrt x) (* x (- (* x (+ 1/2 (* -3/8 x))) 1))) x)
(sqrt x)
(* -1/2 (sqrt (/ 1 (pow x 5))))
(/ (+ (* -1/2 (sqrt x)) (* 1/2 (sqrt (pow x 3)))) (pow x 3))
(sqrt (/ 1 (pow x 5)))
(/ (+ (sqrt x) (* -1 (sqrt (pow x 3)))) (pow x 3))
(/ (+ (sqrt x) (* -1 (sqrt (pow x 3)))) x)
(- (+ 1 (* 1/2 x)) (sqrt x))
(- (+ 1 (* x (+ 1/2 (* -1/8 x)))) (sqrt x))
(- (+ 1 (* x (+ 1/2 (* x (- (* 1/16 x) 1/8))))) (sqrt x))
(* -1/8 (sqrt (/ 1 (pow x 3))))
(/ (+ (* -1/8 (sqrt x)) (* 1/2 (sqrt (pow x 3)))) (pow x 2))
(* 1/2 (sqrt (/ 1 x)))
(* -1 (sqrt x))
(* 1/2 (sqrt (/ 1 (pow x 3))))
(/ (+ (* -1/4 (sqrt (/ 1 x))) (* 1/2 (sqrt x))) (pow x 2))
(/ (+ (* -1/4 (sqrt (/ 1 x))) (+ (* -1/8 (sqrt (/ 1 x))) (+ (* 3/16 (sqrt (/ 1 (pow x 3)))) (* 1/2 (sqrt x))))) (pow x 2))
(/ (+ (* -1/4 (sqrt (/ 1 x))) (+ (* -5/32 (sqrt (/ 1 (pow x 5)))) (+ (* -1/8 (sqrt (/ 1 x))) (+ (* 1/16 (sqrt (/ 1 (pow x 3)))) (+ (* 3/16 (sqrt (/ 1 (pow x 3)))) (* 1/2 (sqrt x))))))) (pow x 2))
(/ 1/2 x)
(/ (+ 1/2 (* -1 (/ (+ (* 1/8 x) (* 1/4 x)) (pow x 2)))) x)
(/ (- (+ 1/2 (* 1/4 (/ 1 (pow x 2)))) (+ (/ 1/8 x) (/ 1/4 x))) x)
(/ (- (+ 1/2 (+ (* -1/4 (/ (+ 1 (* 1/4 x)) (pow x 3))) (* 3/8 (/ 1 (pow x 2))))) (+ (/ 1/8 x) (/ 1/4 x))) x)
(/ (- 1/2 (* 3/8 (/ 1 x))) x)
(/ (- (+ 1/2 (/ 1/4 (pow x 2))) (* 3/8 (/ 1 x))) x)
1/2
(- 1/2 (* 3/8 (/ 1 x)))
(- (+ 1/2 (/ 1/4 (pow x 2))) (* 3/8 (/ 1 x)))
(/ (- (* -1/2 (sqrt (/ 1 x))) (* -1/2 (sqrt x))) (pow x 2))
(/ (- (* 1/2 (* (sqrt (/ 1 (pow x 3))) (+ 1 (* 1/4 x)))) (+ (* -1/2 (sqrt x)) (* 1/2 (sqrt (/ 1 x))))) (pow x 2))
(/ (- (* -1/2 (* (sqrt (/ 1 (pow x 5))) (+ 1 (* 1/2 x)))) (+ (* -1/2 (sqrt x)) (+ (* -1/2 (* (sqrt (/ 1 (pow x 3))) (+ 1 (* 1/4 x)))) (* 1/2 (sqrt (/ 1 x)))))) (pow x 2))
(/ (+ (* -1/2 (sqrt (/ 1 (pow x 3)))) (* 1/2 (sqrt (/ 1 x)))) x)
(* -1 (sqrt (/ 1 (pow x 3))))
(/ (+ (sqrt (/ 1 (pow x 3))) (* -1 (sqrt (/ 1 x)))) x)
(* x (- (sqrt (/ 1 (pow x 3))) (sqrt (/ 1 x))))
(/ (+ (* -1/8 (sqrt (/ 1 x))) (* 1/2 (sqrt x))) x)
(/ (+ (* -1/8 (sqrt (/ 1 x))) (+ (* 1/16 (sqrt (/ 1 (pow x 3)))) (* 1/2 (sqrt x)))) x)
(/ (+ (* -1/8 (sqrt (/ 1 x))) (+ (* -5/128 (sqrt (/ 1 (pow x 5)))) (+ (* 1/16 (sqrt (/ 1 (pow x 3)))) (* 1/2 (sqrt x))))) x)
(+ (* -1/8 (sqrt (/ 1 (pow x 3)))) (* 1/2 (sqrt (/ 1 x))))
(/ (+ (* 1/4 (* (sqrt (/ 1 x)) (/ 1 (pow (sqrt -1) 2)))) (* 1/2 (sqrt x))) (pow x 2))
(/ (+ (* -1 (/ (+ (* -1 (/ (+ (* -1/4 (* (sqrt x) (/ (+ 1 (* 1/4 (/ 1 (pow (sqrt -1) 2)))) (pow (sqrt -1) 2)))) (* -1/8 (* (sqrt (pow x 3)) (/ 1 (pow (sqrt -1) 2))))) x)) (* -1/4 (* (sqrt x) (/ 1 (pow (sqrt -1) 2))))) x)) (* 1/2 (sqrt x))) (pow x 2))
(/ (+ (* -1 (/ (+ (* -1 (/ (+ (* -1 (/ (+ (* -1/4 (* (sqrt x) (/ (+ 1 (* 1/2 (/ (+ 1 (* 1/4 (/ 1 (pow (sqrt -1) 2)))) (pow (sqrt -1) 2)))) (pow (sqrt -1) 2)))) (* 1/16 (* (sqrt (pow x 3)) (/ 1 (pow (sqrt -1) 4))))) x)) (+ (* -1/4 (* (sqrt x) (/ (+ 1 (* 1/4 (/ 1 (pow (sqrt -1) 2)))) (pow (sqrt -1) 2)))) (* -1/8 (* (sqrt (pow x 3)) (/ 1 (pow (sqrt -1) 2)))))) x)) (* -1/4 (* (sqrt x) (/ 1 (pow (sqrt -1) 2))))) x)) (* 1/2 (sqrt x))) (pow x 2))
(/ -1/2 x)
(* -1 (/ (+ 1/2 (* -1 (/ (+ (* -1/4 (/ x (pow (sqrt -1) 2))) (* -1/8 (/ x (pow (sqrt -1) 2)))) (pow x 2)))) x))
(* -1 (/ (+ 1/2 (* -1 (/ (+ (* -1/4 (/ x (pow (sqrt -1) 2))) (+ (* -1/8 (/ x (pow (sqrt -1) 2))) (* 1/4 (/ 1 (pow (sqrt -1) 2))))) (pow x 2)))) x))
(* -1 (/ (- (+ 1/2 (* -1 (/ (- (* -1 (/ (+ (* 1/8 (/ (pow x 2) (pow (sqrt -1) 4))) (* 1/4 (/ (* x (+ 1 (* -1/4 (/ x (pow (sqrt -1) 2))))) (pow (sqrt -1) 2)))) x)) (* -1/4 (/ x (pow (sqrt -1) 2)))) (pow x 3)))) (+ (/ -1/4 (* x (pow (sqrt -1) 2))) (/ -1/8 (* x (pow (sqrt -1) 2))))) x))
(* -1 (/ (- (* 3/8 (/ 1 x)) 1/2) x))
(* -1 (/ (- (* -1 (/ (- (* 1/4 (/ 1 x)) 3/8) x)) 1/2) x))
(+ 1/2 (* -1 (/ (- 3/8 (* 1/4 (/ 1 x))) x)))
(- (sqrt (/ 1 x)) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)))
(- (+ (sqrt (/ 1 x)) (* 1/2 (sqrt (/ 1 (pow x 3))))) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)))
(- (+ (sqrt (/ 1 x)) (* -1/2 (sqrt (/ 1 (pow x 5))))) (+ (* -1/2 (sqrt (/ 1 (pow x 3)))) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))))
(- (+ (sqrt (/ 1 x)) (* -1 (/ (- (* -1/2 (* (sqrt (/ 1 x)) (+ 1 (* -1/4 (/ x (pow (sqrt -1) 2)))))) (* -1/2 (sqrt x))) (pow x 3)))) (+ (* -1/2 (sqrt (/ 1 (pow x 3)))) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))))
(* -1 (* (sqrt x) (pow (sqrt -1) 2)))
(* -1/2 (* (sqrt (/ 1 (pow x 3))) (pow (sqrt -1) 2)))
(* -1 (/ (+ (* 1/2 (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))) (* 1/2 (* (sqrt (/ 1 (pow x 3))) (pow (sqrt -1) 2)))) x))
(* (sqrt (/ 1 (pow x 3))) (pow (sqrt -1) 2))
(* -1 (/ (+ (* -1 (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))) (* -1 (* (sqrt (/ 1 (pow x 3))) (pow (sqrt -1) 2)))) x))
(* (sqrt x) (pow (sqrt -1) 2))
(* -1 (* x (- (* -1 (* (sqrt (/ 1 (pow x 3))) (pow (sqrt -1) 2))) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)))))
(* -1/2 (sqrt (/ 1 x)))
(* -1 (/ (+ (* -1/8 (* (sqrt (/ 1 x)) (/ 1 (pow (sqrt -1) 2)))) (* 1/2 (sqrt x))) x))
(* -1 (/ (+ (* -1/8 (* (sqrt (/ 1 x)) (/ 1 (pow (sqrt -1) 2)))) (+ (* 1/16 (* (sqrt (/ 1 (pow x 3))) (/ 1 (pow (sqrt -1) 4)))) (* 1/2 (sqrt x)))) x))
(* -1 (/ (+ (* -1/8 (* (sqrt (/ 1 x)) (/ 1 (pow (sqrt -1) 2)))) (+ (* -5/128 (* (sqrt (/ 1 (pow x 5))) (/ 1 (pow (sqrt -1) 6)))) (+ (* 1/16 (* (sqrt (/ 1 (pow x 3))) (/ 1 (pow (sqrt -1) 4)))) (* 1/2 (sqrt x))))) x))
(* -1/2 (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)))
(+ (* -1/2 (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))) (* -1/8 (* (sqrt (/ 1 (pow x 3))) (pow (sqrt -1) 2))))
(/ (+ (* 1/4 (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))) (* 1/2 (sqrt x))) (pow x 2))
(/ (+ (* -1 (/ (+ (* -1 (/ (+ (* -1/4 (* (sqrt x) (+ (* -1 (pow (sqrt -1) 4)) (* 1/4 (pow (sqrt -1) 4))))) (* -1/8 (* (sqrt (pow x 3)) (/ 1 (pow (sqrt -1) 2))))) x)) (* -1/4 (* (sqrt x) (pow (sqrt -1) 2)))) x)) (* 1/2 (sqrt x))) (pow x 2))
(/ (+ (* -1 (/ (+ (* -1 (/ (+ (* -1 (/ (+ (* -1/4 (* (sqrt x) (+ (* 1/2 (* (pow (sqrt -1) 2) (+ (* -1 (pow (sqrt -1) 4)) (* 1/4 (pow (sqrt -1) 4))))) (pow (sqrt -1) 6)))) (* 1/16 (sqrt (pow x 3)))) x)) (+ (* -1/4 (* (sqrt x) (+ (* -1 (pow (sqrt -1) 4)) (* 1/4 (pow (sqrt -1) 4))))) (* -1/8 (* (sqrt (pow x 3)) (/ 1 (pow (sqrt -1) 2)))))) x)) (* -1/4 (* (sqrt x) (pow (sqrt -1) 2)))) x)) (* 1/2 (sqrt x))) (pow x 2))
(* 1/2 (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)))
(* (sqrt (/ 1 x)) (pow (sqrt -1) 2))
Outputs
(* (sqrt (/ 1 x)) (- 1 (sqrt x)))
(*.f64 (-.f64 #s(literal 1 binary64) (sqrt.f64 x)) (sqrt.f64 (/.f64 #s(literal 1 binary64) x)))
(/ (+ (* 1/2 (sqrt (pow x 3))) (* (sqrt x) (- 1 (sqrt x)))) x)
(/.f64 (fma.f64 (sqrt.f64 (pow.f64 x #s(literal 3 binary64))) #s(literal 1/2 binary64) (*.f64 (-.f64 #s(literal 1 binary64) (sqrt.f64 x)) (sqrt.f64 x))) x)
(/ (+ (* x (+ (* 1/2 (sqrt x)) (* x (+ (* -1/2 (* (sqrt (/ 1 x)) (- 1 (sqrt x)))) (* -1/8 (sqrt x)))))) (* (sqrt x) (- 1 (sqrt x)))) x)
(/.f64 (fma.f64 (fma.f64 (fma.f64 (*.f64 #s(literal -1/2 binary64) (-.f64 #s(literal 1 binary64) (sqrt.f64 x))) (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) (*.f64 #s(literal -1/8 binary64) (sqrt.f64 x))) x (*.f64 #s(literal 1/2 binary64) (sqrt.f64 x))) x (*.f64 (-.f64 #s(literal 1 binary64) (sqrt.f64 x)) (sqrt.f64 x))) x)
(/ (+ (* x (+ (* 1/2 (sqrt x)) (* x (+ (* -1/2 (* (sqrt (/ 1 x)) (- 1 (sqrt x)))) (+ (* -1/8 (sqrt x)) (* x (+ (* -1/4 (sqrt (/ 1 x))) (+ (* 1/16 (sqrt x)) (* 1/2 (* (sqrt (/ 1 x)) (- 1 (sqrt x)))))))))))) (* (sqrt x) (- 1 (sqrt x)))) x)
(/.f64 (fma.f64 (fma.f64 (fma.f64 (fma.f64 (*.f64 #s(literal 1/2 binary64) (-.f64 #s(literal 1 binary64) (sqrt.f64 x))) (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) (fma.f64 #s(literal -1/4 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) (*.f64 #s(literal 1/16 binary64) (sqrt.f64 x)))) x (fma.f64 (*.f64 #s(literal -1/2 binary64) (-.f64 #s(literal 1 binary64) (sqrt.f64 x))) (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) (*.f64 #s(literal -1/8 binary64) (sqrt.f64 x)))) x (*.f64 #s(literal 1/2 binary64) (sqrt.f64 x))) x (*.f64 (-.f64 #s(literal 1 binary64) (sqrt.f64 x)) (sqrt.f64 x))) x)
(- 1 (sqrt x))
(-.f64 #s(literal 1 binary64) (sqrt.f64 x))
(- (+ 1 (* x (+ 1/2 (* -1/2 (- 1 (sqrt x)))))) (sqrt x))
(fma.f64 (fma.f64 #s(literal -1/2 binary64) (-.f64 #s(literal 1 binary64) (sqrt.f64 x)) #s(literal 1/2 binary64)) x (-.f64 #s(literal 1 binary64) (sqrt.f64 x)))
(- (+ 1 (* x (+ 1/2 (+ (* -1/2 (- 1 (sqrt x))) (* x (- (* 3/8 (- 1 (sqrt x))) 3/8)))))) (sqrt x))
(fma.f64 (fma.f64 (-.f64 (*.f64 #s(literal 3/8 binary64) (-.f64 #s(literal 1 binary64) (sqrt.f64 x))) #s(literal 3/8 binary64)) x (fma.f64 #s(literal -1/2 binary64) (-.f64 #s(literal 1 binary64) (sqrt.f64 x)) #s(literal 1/2 binary64))) x (-.f64 #s(literal 1 binary64) (sqrt.f64 x)))
(- (+ 1 (* x (+ 1/2 (+ (* -1/2 (- 1 (sqrt x))) (* x (- (+ (* 3/8 (- 1 (sqrt x))) (* x (+ 5/16 (* -5/16 (- 1 (sqrt x)))))) 3/8)))))) (sqrt x))
(fma.f64 (fma.f64 (fma.f64 (fma.f64 #s(literal -5/16 binary64) (-.f64 #s(literal 1 binary64) (sqrt.f64 x)) #s(literal 5/16 binary64)) x (-.f64 (*.f64 #s(literal 3/8 binary64) (-.f64 #s(literal 1 binary64) (sqrt.f64 x))) #s(literal 3/8 binary64))) x (fma.f64 #s(literal -1/2 binary64) (-.f64 #s(literal 1 binary64) (sqrt.f64 x)) #s(literal 1/2 binary64))) x (-.f64 #s(literal 1 binary64) (sqrt.f64 x)))
(/ 1/4 (pow x 3))
(/.f64 #s(literal 1/4 binary64) (pow.f64 x #s(literal 3 binary64)))
(/ (+ 1/4 (* -3/8 x)) (pow x 3))
(/.f64 (fma.f64 #s(literal -3/8 binary64) x #s(literal 1/4 binary64)) (pow.f64 x #s(literal 3 binary64)))
(/ (+ 1/4 (* x (- (* 1/2 x) 3/8))) (pow x 3))
(/.f64 (fma.f64 (-.f64 (*.f64 #s(literal 1/2 binary64) x) #s(literal 3/8 binary64)) x #s(literal 1/4 binary64)) (pow.f64 x #s(literal 3 binary64)))
(/ 1/4 (pow x 2))
(/.f64 #s(literal 1/4 binary64) (*.f64 x x))
(/ (+ 1/4 (* -3/8 x)) (pow x 2))
(/.f64 (/.f64 (fma.f64 #s(literal -3/8 binary64) x #s(literal 1/4 binary64)) x) x)
(/ (+ 1/4 (* x (- (* 1/2 x) 3/8))) (pow x 2))
(/.f64 (/.f64 (fma.f64 (-.f64 (*.f64 #s(literal 1/2 binary64) x) #s(literal 3/8 binary64)) x #s(literal 1/4 binary64)) x) x)
(sqrt (/ 1 x))
(sqrt.f64 (/.f64 #s(literal 1 binary64) x))
(/ (+ (sqrt x) (* -1 x)) x)
(/.f64 (-.f64 (sqrt.f64 x) x) x)
(/ (+ (sqrt x) (* x (- (* 1/2 x) 1))) x)
(/.f64 (fma.f64 (-.f64 (*.f64 #s(literal 1/2 binary64) x) #s(literal 1 binary64)) x (sqrt.f64 x)) x)
(/ (+ (sqrt x) (* x (- (* x (+ 1/2 (* -3/8 x))) 1))) x)
(/.f64 (fma.f64 (-.f64 (*.f64 (fma.f64 #s(literal -3/8 binary64) x #s(literal 1/2 binary64)) x) #s(literal 1 binary64)) x (sqrt.f64 x)) x)
(sqrt x)
(sqrt.f64 x)
(* -1/2 (sqrt (/ 1 (pow x 5))))
(*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 5 binary64)))) #s(literal -1/2 binary64))
(/ (+ (* -1/2 (sqrt x)) (* 1/2 (sqrt (pow x 3)))) (pow x 3))
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(/ (+ (* -1 (/ (+ (* -1 (/ (+ (* -1 (/ (+ (* -1/4 (* (sqrt x) (+ (* 1/2 (* (pow (sqrt -1) 2) (+ (* -1 (pow (sqrt -1) 4)) (* 1/4 (pow (sqrt -1) 4))))) (pow (sqrt -1) 6)))) (* 1/16 (sqrt (pow x 3)))) x)) (+ (* -1/4 (* (sqrt x) (+ (* -1 (pow (sqrt -1) 4)) (* 1/4 (pow (sqrt -1) 4))))) (* -1/8 (* (sqrt (pow x 3)) (/ 1 (pow (sqrt -1) 2)))))) x)) (* -1/4 (* (sqrt x) (pow (sqrt -1) 2)))) x)) (* 1/2 (sqrt x))) (pow x 2))
(/.f64 (fma.f64 #s(literal 1/2 binary64) (sqrt.f64 x) (/.f64 (fma.f64 #s(literal 1/4 binary64) (sqrt.f64 x) (/.f64 (fma.f64 (*.f64 (*.f64 #s(literal -1/4 binary64) (sqrt.f64 x)) (pow.f64 (sqrt.f64 #s(literal -1 binary64)) #s(literal 4 binary64))) #s(literal -3/4 binary64) (fma.f64 #s(literal 1/8 binary64) (sqrt.f64 (pow.f64 x #s(literal 3 binary64))) (/.f64 (fma.f64 (*.f64 (fma.f64 (*.f64 (pow.f64 (sqrt.f64 #s(literal -1 binary64)) #s(literal 4 binary64)) #s(literal 3/4 binary64)) #s(literal 1/2 binary64) (pow.f64 (sqrt.f64 #s(literal -1 binary64)) #s(literal 6 binary64))) (sqrt.f64 x)) #s(literal -1/4 binary64) (*.f64 #s(literal 1/16 binary64) (sqrt.f64 (pow.f64 x #s(literal 3 binary64))))) (neg.f64 x)))) (neg.f64 x))) (neg.f64 x))) (*.f64 x x))
(* 1/2 (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)))
(*.f64 #s(literal -1/2 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) x)))
(* (sqrt (/ 1 x)) (pow (sqrt -1) 2))
(neg.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)))

rewrite150.0ms (2.2%)

Memory
18.1MiB live, 199.0MiB allocated
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
048309
078308
1259270
21863254
09206250
Stop Event
iter limit
node limit
iter limit
Counts
21 → 310
Calls
Call 1
Inputs
(/.f64 #s(approx (/ (- (sqrt (+ x 1)) (sqrt x)) (sqrt (+ x 1))) (/.f64 (-.f64 (+.f64 (/.f64 #s(literal 1/4 binary64) (*.f64 x x)) #s(literal 1/2 binary64)) (/.f64 #s(literal 3/8 binary64) x)) x)) (sqrt.f64 x))
#s(approx (/ (- (sqrt (+ x 1)) (sqrt x)) (sqrt (+ x 1))) (/.f64 (-.f64 (+.f64 (/.f64 #s(literal 1/4 binary64) (*.f64 x x)) #s(literal 1/2 binary64)) (/.f64 #s(literal 3/8 binary64) x)) x))
(/.f64 (-.f64 (+.f64 (/.f64 #s(literal 1/4 binary64) (*.f64 x x)) #s(literal 1/2 binary64)) (/.f64 #s(literal 3/8 binary64) x)) x)
(-.f64 (+.f64 (/.f64 #s(literal 1/4 binary64) (*.f64 x x)) #s(literal 1/2 binary64)) (/.f64 #s(literal 3/8 binary64) x))
#s(approx (- (/ 1 (sqrt x)) (/ 1 (sqrt (+ x 1)))) (/.f64 #s(literal 1 binary64) (sqrt.f64 x)))
(/.f64 #s(literal 1 binary64) (sqrt.f64 x))
(sqrt.f64 x)
#s(approx (- (/ 1 (sqrt x)) (/ 1 (sqrt (+ x 1)))) (*.f64 (/.f64 #s(approx (- (sqrt (/ 1 x)) (sqrt x)) (neg.f64 (sqrt.f64 x))) (*.f64 x x)) #s(literal -1/2 binary64)))
(*.f64 (/.f64 #s(approx (- (sqrt (/ 1 x)) (sqrt x)) (neg.f64 (sqrt.f64 x))) (*.f64 x x)) #s(literal -1/2 binary64))
(/.f64 #s(approx (- (sqrt (/ 1 x)) (sqrt x)) (neg.f64 (sqrt.f64 x))) (*.f64 x x))
#s(approx (- (sqrt (/ 1 x)) (sqrt x)) (neg.f64 (sqrt.f64 x)))
(/.f64 (/.f64 #s(approx (- (sqrt (+ x 1)) (sqrt x)) (/.f64 (fma.f64 #s(literal -1/8 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) (*.f64 #s(literal 1/2 binary64) (sqrt.f64 x))) x)) (sqrt.f64 (+.f64 x #s(literal 1 binary64)))) (sqrt.f64 x))
(/.f64 #s(approx (- (sqrt (+ x 1)) (sqrt x)) (/.f64 (fma.f64 #s(literal -1/8 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) (*.f64 #s(literal 1/2 binary64) (sqrt.f64 x))) x)) (sqrt.f64 (+.f64 x #s(literal 1 binary64))))
#s(approx (- (sqrt (+ x 1)) (sqrt x)) (/.f64 (fma.f64 #s(literal -1/8 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) (*.f64 #s(literal 1/2 binary64) (sqrt.f64 x))) x))
(/.f64 (fma.f64 #s(literal -1/8 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) (*.f64 #s(literal 1/2 binary64) (sqrt.f64 x))) x)
(/.f64 #s(approx (- (sqrt (+ x 1)) (sqrt x)) (*.f64 #s(literal 1/2 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) x)))) (hypot.f64 (sqrt.f64 x) x))
#s(approx (- (sqrt (+ x 1)) (sqrt x)) (*.f64 #s(literal 1/2 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) x))))
(*.f64 #s(literal 1/2 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) x)))
(sqrt.f64 (/.f64 #s(literal 1 binary64) x))
(/.f64 #s(literal 1/4 binary64) (*.f64 x x))
(neg.f64 (sqrt.f64 x))
Outputs
(/.f64 (neg.f64 (neg.f64 #s(approx (/ (- (sqrt (+ x 1)) (sqrt x)) (sqrt (+ x 1))) (/.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 (-.f64 (/.f64 #s(literal -1/4 binary64) x) #s(literal -3/8 binary64)) x)) x)))) (sqrt.f64 x))
(/.f64 (neg.f64 #s(approx (/ (- (sqrt (+ x 1)) (sqrt x)) (sqrt (+ x 1))) (/.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 (-.f64 (/.f64 #s(literal -1/4 binary64) x) #s(literal -3/8 binary64)) x)) x))) (sqrt.f64 x))
(/.f64 #s(approx (/ (- (sqrt (+ x 1)) (sqrt x)) (sqrt (+ x 1))) (/.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 (-.f64 (/.f64 #s(literal -1/4 binary64) x) #s(literal -3/8 binary64)) x)) x)) (sqrt.f64 x))
(neg.f64 (/.f64 #s(approx (/ (- (sqrt (+ x 1)) (sqrt x)) (sqrt (+ x 1))) (/.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 (-.f64 (/.f64 #s(literal -1/4 binary64) x) #s(literal -3/8 binary64)) x)) x)) (sqrt.f64 x)))
#s(approx (/ (- (sqrt (+ x 1)) (sqrt x)) (sqrt (+ x 1))) (/.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 (-.f64 (/.f64 #s(literal -1/4 binary64) x) #s(literal -3/8 binary64)) x)) x))
(/.f64 (-.f64 (*.f64 (/.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/4 binary64) (*.f64 x x))) (sqrt.f64 x)) (sqrt.f64 x)) (*.f64 (sqrt.f64 x) (/.f64 (/.f64 #s(literal -3/8 binary64) x) (sqrt.f64 x)))) x)
(/.f64 (-.f64 (*.f64 (/.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/4 binary64) (*.f64 x x))) (sqrt.f64 x)) (*.f64 x x)) (*.f64 (sqrt.f64 x) #s(literal -3/8 binary64))) (pow.f64 x #s(literal 5/2 binary64)))
(/.f64 (-.f64 (*.f64 (/.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/4 binary64) (*.f64 x x))) (sqrt.f64 x)) x) (*.f64 (sqrt.f64 x) (/.f64 #s(literal -3/8 binary64) x))) (pow.f64 x #s(literal 3/2 binary64)))
(/.f64 (-.f64 (*.f64 (/.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/4 binary64) (*.f64 x x))) (sqrt.f64 x)) (*.f64 x x)) (*.f64 (sqrt.f64 x) #s(literal 3/8 binary64))) (pow.f64 x #s(literal 5/2 binary64)))
(/.f64 (-.f64 (*.f64 (neg.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/4 binary64) (*.f64 x x)))) (sqrt.f64 x)) (*.f64 x (/.f64 (/.f64 #s(literal -3/8 binary64) x) (sqrt.f64 x)))) (pow.f64 x #s(literal 3/2 binary64)))
(/.f64 (-.f64 (*.f64 (neg.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/4 binary64) (*.f64 x x)))) (*.f64 x x)) (*.f64 x #s(literal -3/8 binary64))) (pow.f64 x #s(literal 3 binary64)))
(/.f64 (-.f64 (*.f64 (neg.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/4 binary64) (*.f64 x x)))) x) (*.f64 x (/.f64 #s(literal -3/8 binary64) x))) (*.f64 x x))
(/.f64 (-.f64 (*.f64 (neg.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/4 binary64) (*.f64 x x)))) (*.f64 x x)) (*.f64 x #s(literal 3/8 binary64))) (pow.f64 x #s(literal 3 binary64)))
(/.f64 (-.f64 (*.f64 (-.f64 (/.f64 #s(literal -1/16 binary64) (pow.f64 x #s(literal 4 binary64))) #s(literal 1/4 binary64)) (sqrt.f64 x)) (*.f64 (*.f64 (-.f64 (/.f64 #s(literal -1/4 binary64) (*.f64 x x)) #s(literal 1/2 binary64)) x) (/.f64 (/.f64 #s(literal -3/8 binary64) x) (sqrt.f64 x)))) (*.f64 (*.f64 (-.f64 (/.f64 #s(literal -1/4 binary64) (*.f64 x x)) #s(literal 1/2 binary64)) x) (sqrt.f64 x)))
(/.f64 (-.f64 (*.f64 (-.f64 (/.f64 #s(literal -1/16 binary64) (pow.f64 x #s(literal 4 binary64))) #s(literal 1/4 binary64)) (*.f64 x x)) (*.f64 (*.f64 (-.f64 (/.f64 #s(literal -1/4 binary64) (*.f64 x x)) #s(literal 1/2 binary64)) x) #s(literal -3/8 binary64))) (*.f64 (*.f64 (-.f64 (/.f64 #s(literal -1/4 binary64) (*.f64 x x)) #s(literal 1/2 binary64)) x) (*.f64 x x)))
(/.f64 (-.f64 (*.f64 (-.f64 (/.f64 #s(literal -1/16 binary64) (pow.f64 x #s(literal 4 binary64))) #s(literal 1/4 binary64)) x) (*.f64 (*.f64 (-.f64 (/.f64 #s(literal -1/4 binary64) (*.f64 x x)) #s(literal 1/2 binary64)) x) (/.f64 #s(literal -3/8 binary64) x))) (*.f64 (*.f64 (-.f64 (/.f64 #s(literal -1/4 binary64) (*.f64 x x)) #s(literal 1/2 binary64)) x) x))
(/.f64 (-.f64 (*.f64 (-.f64 (/.f64 #s(literal -1/16 binary64) (pow.f64 x #s(literal 4 binary64))) #s(literal 1/4 binary64)) (*.f64 x x)) (*.f64 (*.f64 (-.f64 (/.f64 #s(literal -1/4 binary64) (*.f64 x x)) #s(literal 1/2 binary64)) x) #s(literal 3/8 binary64))) (*.f64 (*.f64 (-.f64 (/.f64 #s(literal -1/4 binary64) (*.f64 x x)) #s(literal 1/2 binary64)) x) (*.f64 x x)))
(/.f64 (-.f64 (*.f64 (+.f64 #s(literal 1/8 binary64) (/.f64 #s(literal -1/64 binary64) (pow.f64 x #s(literal 6 binary64)))) (sqrt.f64 x)) (*.f64 (*.f64 (-.f64 (+.f64 (/.f64 #s(literal -1/16 binary64) (pow.f64 x #s(literal 4 binary64))) #s(literal 1/4 binary64)) (/.f64 #s(literal 1/8 binary64) (*.f64 x x))) x) (/.f64 (/.f64 #s(literal -3/8 binary64) x) (sqrt.f64 x)))) (*.f64 (*.f64 (-.f64 (+.f64 (/.f64 #s(literal -1/16 binary64) (pow.f64 x #s(literal 4 binary64))) #s(literal 1/4 binary64)) (/.f64 #s(literal 1/8 binary64) (*.f64 x x))) x) (sqrt.f64 x)))
(/.f64 (-.f64 (*.f64 (+.f64 #s(literal 1/8 binary64) (/.f64 #s(literal -1/64 binary64) (pow.f64 x #s(literal 6 binary64)))) (*.f64 x x)) (*.f64 (*.f64 (-.f64 (+.f64 (/.f64 #s(literal -1/16 binary64) (pow.f64 x #s(literal 4 binary64))) #s(literal 1/4 binary64)) (/.f64 #s(literal 1/8 binary64) (*.f64 x x))) x) #s(literal -3/8 binary64))) (*.f64 (*.f64 (-.f64 (+.f64 (/.f64 #s(literal -1/16 binary64) (pow.f64 x #s(literal 4 binary64))) #s(literal 1/4 binary64)) (/.f64 #s(literal 1/8 binary64) (*.f64 x x))) x) (*.f64 x x)))
(/.f64 (-.f64 (*.f64 (+.f64 #s(literal 1/8 binary64) (/.f64 #s(literal -1/64 binary64) (pow.f64 x #s(literal 6 binary64)))) x) (*.f64 (*.f64 (-.f64 (+.f64 (/.f64 #s(literal -1/16 binary64) (pow.f64 x #s(literal 4 binary64))) #s(literal 1/4 binary64)) (/.f64 #s(literal 1/8 binary64) (*.f64 x x))) x) (/.f64 #s(literal -3/8 binary64) x))) (*.f64 (*.f64 (-.f64 (+.f64 (/.f64 #s(literal -1/16 binary64) (pow.f64 x #s(literal 4 binary64))) #s(literal 1/4 binary64)) (/.f64 #s(literal 1/8 binary64) (*.f64 x x))) x) x))
(/.f64 (-.f64 (*.f64 (+.f64 #s(literal 1/8 binary64) (/.f64 #s(literal -1/64 binary64) (pow.f64 x #s(literal 6 binary64)))) (*.f64 x x)) (*.f64 (*.f64 (-.f64 (+.f64 (/.f64 #s(literal -1/16 binary64) (pow.f64 x #s(literal 4 binary64))) #s(literal 1/4 binary64)) (/.f64 #s(literal 1/8 binary64) (*.f64 x x))) x) #s(literal 3/8 binary64))) (*.f64 (*.f64 (-.f64 (+.f64 (/.f64 #s(literal -1/16 binary64) (pow.f64 x #s(literal 4 binary64))) #s(literal 1/4 binary64)) (/.f64 #s(literal 1/8 binary64) (*.f64 x x))) x) (*.f64 x x)))
(/.f64 (-.f64 (*.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/4 binary64) (*.f64 x x))) (sqrt.f64 x)) (*.f64 x (/.f64 (/.f64 #s(literal -3/8 binary64) x) (sqrt.f64 x)))) (pow.f64 x #s(literal 3/2 binary64)))
(/.f64 (-.f64 (*.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/4 binary64) (*.f64 x x))) (*.f64 x x)) (*.f64 x #s(literal -3/8 binary64))) (pow.f64 x #s(literal 3 binary64)))
(/.f64 (-.f64 (*.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/4 binary64) (*.f64 x x))) (*.f64 x x)) (*.f64 x #s(literal 3/8 binary64))) (pow.f64 x #s(literal 3 binary64)))
(/.f64 (fma.f64 (/.f64 #s(literal -1/4 binary64) (*.f64 x x)) x (*.f64 x (-.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -3/8 binary64) x)))) (*.f64 x x))
(/.f64 (-.f64 (/.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/4 binary64) (*.f64 x x))) (sqrt.f64 x)) (/.f64 (/.f64 #s(literal -3/8 binary64) x) (sqrt.f64 x))) (sqrt.f64 x))
(/.f64 (-.f64 (neg.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/4 binary64) (*.f64 x x)))) (/.f64 #s(literal -3/8 binary64) x)) x)
(/.f64 (/.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 (-.f64 (/.f64 #s(literal -1/4 binary64) x) #s(literal -3/8 binary64)) x)) (sqrt.f64 x)) (sqrt.f64 x))
(/.f64 (-.f64 (pow.f64 (/.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/4 binary64) (*.f64 x x))) x) #s(literal 2 binary64)) (pow.f64 (/.f64 #s(literal -3/8 binary64) (*.f64 x x)) #s(literal 2 binary64))) (+.f64 (/.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/4 binary64) (*.f64 x x))) x) (/.f64 #s(literal -3/8 binary64) (*.f64 x x))))
(/.f64 (-.f64 (pow.f64 (/.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/4 binary64) (*.f64 x x))) x) #s(literal 3 binary64)) (/.f64 #s(literal -27/512 binary64) (pow.f64 x #s(literal 6 binary64)))) (+.f64 (pow.f64 (/.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/4 binary64) (*.f64 x x))) x) #s(literal 2 binary64)) (+.f64 (pow.f64 (/.f64 #s(literal -3/8 binary64) (*.f64 x x)) #s(literal 2 binary64)) (*.f64 (/.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/4 binary64) (*.f64 x x))) x) (/.f64 #s(literal -3/8 binary64) (*.f64 x x))))))
(/.f64 (neg.f64 (neg.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 (-.f64 (/.f64 #s(literal -1/4 binary64) x) #s(literal -3/8 binary64)) x)))) x)
(/.f64 (-.f64 (*.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/4 binary64) (*.f64 x x))) x) (*.f64 x (/.f64 #s(literal -3/8 binary64) x))) (*.f64 x x))
(/.f64 (-.f64 (pow.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/4 binary64) (*.f64 x x))) #s(literal 2 binary64)) (pow.f64 (/.f64 #s(literal -3/8 binary64) x) #s(literal 2 binary64))) (*.f64 (+.f64 (/.f64 #s(literal -3/8 binary64) x) (+.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/4 binary64) (*.f64 x x)))) x))
(/.f64 (-.f64 (pow.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/4 binary64) (*.f64 x x))) #s(literal 3 binary64)) (pow.f64 (/.f64 #s(literal -3/8 binary64) x) #s(literal 3 binary64))) (*.f64 (fma.f64 (/.f64 #s(literal -3/8 binary64) x) (+.f64 (/.f64 #s(literal -3/8 binary64) x) (+.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/4 binary64) (*.f64 x x)))) (pow.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/4 binary64) (*.f64 x x))) #s(literal 2 binary64))) x))
(/.f64 (neg.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 (-.f64 (/.f64 #s(literal -1/4 binary64) x) #s(literal -3/8 binary64)) x))) x)
(/.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 (-.f64 (/.f64 #s(literal -1/4 binary64) x) #s(literal -3/8 binary64)) x)) x)
(neg.f64 (/.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 (-.f64 (/.f64 #s(literal -1/4 binary64) x) #s(literal -3/8 binary64)) x)) x))
(-.f64 (/.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/4 binary64) (*.f64 x x))) x) (/.f64 #s(literal -3/8 binary64) (*.f64 x x)))
(+.f64 (/.f64 (/.f64 #s(literal -1/4 binary64) (*.f64 x x)) x) (/.f64 (-.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -3/8 binary64) x)) x))
(/.f64 (-.f64 (*.f64 (pow.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/4 binary64) (*.f64 x x))) #s(literal 2 binary64)) (+.f64 (/.f64 #s(literal -3/8 binary64) x) (+.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/4 binary64) (*.f64 x x))))) (*.f64 (+.f64 (/.f64 #s(literal -3/8 binary64) x) (+.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/4 binary64) (*.f64 x x)))) (pow.f64 (/.f64 #s(literal -3/8 binary64) x) #s(literal 2 binary64)))) (*.f64 (+.f64 (/.f64 #s(literal -3/8 binary64) x) (+.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/4 binary64) (*.f64 x x)))) (+.f64 (/.f64 #s(literal -3/8 binary64) x) (+.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/4 binary64) (*.f64 x x))))))
(/.f64 (-.f64 (*.f64 (pow.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/4 binary64) (*.f64 x x))) #s(literal 3 binary64)) (fma.f64 (/.f64 #s(literal -3/8 binary64) x) (+.f64 (/.f64 #s(literal -3/8 binary64) x) (+.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/4 binary64) (*.f64 x x)))) (pow.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/4 binary64) (*.f64 x x))) #s(literal 2 binary64)))) (*.f64 (fma.f64 (/.f64 #s(literal -3/8 binary64) x) (+.f64 (/.f64 #s(literal -3/8 binary64) x) (+.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/4 binary64) (*.f64 x x)))) (pow.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/4 binary64) (*.f64 x x))) #s(literal 2 binary64))) (pow.f64 (/.f64 #s(literal -3/8 binary64) x) #s(literal 3 binary64)))) (*.f64 (fma.f64 (/.f64 #s(literal -3/8 binary64) x) (+.f64 (/.f64 #s(literal -3/8 binary64) x) (+.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/4 binary64) (*.f64 x x)))) (pow.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/4 binary64) (*.f64 x x))) #s(literal 2 binary64))) (fma.f64 (/.f64 #s(literal -3/8 binary64) x) (+.f64 (/.f64 #s(literal -3/8 binary64) x) (+.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/4 binary64) (*.f64 x x)))) (pow.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/4 binary64) (*.f64 x x))) #s(literal 2 binary64)))))
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(/.f64 (fma.f64 (/.f64 #s(literal 1/8 binary64) (sqrt.f64 x)) (sqrt.f64 x) (*.f64 x (/.f64 (*.f64 (sqrt.f64 x) #s(literal 1/2 binary64)) (sqrt.f64 x)))) (pow.f64 x #s(literal 3/2 binary64)))
(/.f64 (fma.f64 (/.f64 #s(literal 1/8 binary64) (sqrt.f64 x)) x (*.f64 x (neg.f64 (*.f64 (sqrt.f64 x) #s(literal 1/2 binary64))))) (*.f64 x x))
(/.f64 (-.f64 (/.f64 (/.f64 #s(literal 1/8 binary64) (sqrt.f64 x)) (sqrt.f64 x)) (/.f64 (*.f64 (sqrt.f64 x) #s(literal 1/2 binary64)) (sqrt.f64 x))) (sqrt.f64 x))
(/.f64 (-.f64 (neg.f64 (/.f64 #s(literal 1/8 binary64) (sqrt.f64 x))) (neg.f64 (*.f64 (sqrt.f64 x) #s(literal 1/2 binary64)))) x)
(/.f64 (/.f64 (fma.f64 (sqrt.f64 x) #s(literal 1/2 binary64) (/.f64 #s(literal 1/8 binary64) (sqrt.f64 x))) (sqrt.f64 x)) (sqrt.f64 x))
(/.f64 (-.f64 (pow.f64 (*.f64 #s(literal -1/8 binary64) (pow.f64 x #s(literal -3/2 binary64))) #s(literal 2 binary64)) (pow.f64 (/.f64 #s(literal -1/2 binary64) (sqrt.f64 x)) #s(literal 2 binary64))) (fma.f64 #s(literal -1/8 binary64) (pow.f64 x #s(literal -3/2 binary64)) (/.f64 #s(literal -1/2 binary64) (sqrt.f64 x))))
(/.f64 (fma.f64 #s(literal -1/512 binary64) (pow.f64 (sqrt.f64 x) #s(literal -9 binary64)) (*.f64 #s(literal 1/8 binary64) (pow.f64 x #s(literal -3/2 binary64)))) (+.f64 (pow.f64 (*.f64 #s(literal -1/8 binary64) (pow.f64 x #s(literal -3/2 binary64))) #s(literal 2 binary64)) (-.f64 (pow.f64 (/.f64 #s(literal -1/2 binary64) (sqrt.f64 x)) #s(literal 2 binary64)) (*.f64 (*.f64 #s(literal -1/8 binary64) (pow.f64 x #s(literal -3/2 binary64))) (/.f64 #s(literal -1/2 binary64) (sqrt.f64 x))))))
(/.f64 (neg.f64 (neg.f64 (fma.f64 (sqrt.f64 x) #s(literal 1/2 binary64) (/.f64 #s(literal 1/8 binary64) (sqrt.f64 x))))) x)
(/.f64 (fma.f64 (/.f64 #s(literal 1/8 binary64) (sqrt.f64 x)) x (*.f64 x (*.f64 (sqrt.f64 x) #s(literal 1/2 binary64)))) (*.f64 x x))
(/.f64 (fma.f64 (sqrt.f64 x) #s(literal 1/2 binary64) (/.f64 #s(literal 1/8 binary64) (sqrt.f64 x))) x)
(/.f64 (-.f64 (*.f64 #s(literal 1/64 binary64) (pow.f64 x #s(literal -1 binary64))) (*.f64 #s(literal 1/4 binary64) x)) (*.f64 (fma.f64 (sqrt.f64 x) #s(literal 1/2 binary64) (/.f64 #s(literal 1/8 binary64) (sqrt.f64 x))) x))
(/.f64 (fma.f64 #s(literal -1/512 binary64) (pow.f64 x #s(literal -3/2 binary64)) (*.f64 (pow.f64 x #s(literal 3/2 binary64)) #s(literal 1/8 binary64))) (*.f64 (fma.f64 #s(literal 1/64 binary64) (pow.f64 x #s(literal -1 binary64)) (*.f64 (*.f64 (sqrt.f64 x) #s(literal 1/2 binary64)) (fma.f64 (sqrt.f64 x) #s(literal 1/2 binary64) (/.f64 #s(literal 1/8 binary64) (sqrt.f64 x))))) x))
(/.f64 (neg.f64 (fma.f64 (sqrt.f64 x) #s(literal 1/2 binary64) (/.f64 #s(literal 1/8 binary64) (sqrt.f64 x)))) x)
(neg.f64 (fma.f64 #s(literal -1/8 binary64) (pow.f64 x #s(literal -3/2 binary64)) (/.f64 #s(literal -1/2 binary64) (sqrt.f64 x))))
(fma.f64 (/.f64 #s(literal -1/2 binary64) (sqrt.f64 x)) #s(literal 1 binary64) (*.f64 #s(literal -1/8 binary64) (pow.f64 x #s(literal -3/2 binary64))))
(fma.f64 (/.f64 #s(literal 1/8 binary64) (sqrt.f64 x)) (pow.f64 x #s(literal -1 binary64)) (/.f64 #s(literal -1/2 binary64) (sqrt.f64 x)))
(fma.f64 (pow.f64 x #s(literal -1/2 binary64)) (/.f64 #s(literal -1/8 binary64) x) (/.f64 #s(literal -1/2 binary64) (sqrt.f64 x)))
(fma.f64 (pow.f64 x #s(literal -1/2 binary64)) #s(literal 1/2 binary64) (*.f64 #s(literal -1/8 binary64) (pow.f64 x #s(literal -3/2 binary64))))
(fma.f64 (pow.f64 x #s(literal -1 binary64)) (/.f64 #s(literal 1/8 binary64) (sqrt.f64 x)) (/.f64 #s(literal -1/2 binary64) (sqrt.f64 x)))
(fma.f64 #s(literal -1/8 binary64) (pow.f64 x #s(literal -3/2 binary64)) (/.f64 #s(literal -1/2 binary64) (sqrt.f64 x)))
(fma.f64 (sqrt.f64 x) (/.f64 #s(literal 1/2 binary64) x) (*.f64 #s(literal -1/8 binary64) (pow.f64 x #s(literal -3/2 binary64))))
(fma.f64 #s(literal 1/2 binary64) (pow.f64 x #s(literal -1/2 binary64)) (*.f64 #s(literal -1/8 binary64) (pow.f64 x #s(literal -3/2 binary64))))
(fma.f64 #s(literal 1 binary64) (/.f64 #s(literal -1/2 binary64) (sqrt.f64 x)) (*.f64 #s(literal -1/8 binary64) (pow.f64 x #s(literal -3/2 binary64))))
(-.f64 (*.f64 #s(literal -1/8 binary64) (pow.f64 x #s(literal -3/2 binary64))) (/.f64 (*.f64 #s(literal -1/2 binary64) (sqrt.f64 x)) x))
(-.f64 (*.f64 #s(literal -1/8 binary64) (pow.f64 x #s(literal -3/2 binary64))) (/.f64 #s(literal -1/2 binary64) (sqrt.f64 x)))
(+.f64 (/.f64 #s(literal -1/2 binary64) (sqrt.f64 x)) (*.f64 #s(literal -1/8 binary64) (pow.f64 x #s(literal -3/2 binary64))))
(+.f64 (*.f64 #s(literal -1/8 binary64) (pow.f64 x #s(literal -3/2 binary64))) (/.f64 #s(literal -1/2 binary64) (sqrt.f64 x)))
(/.f64 (neg.f64 (neg.f64 #s(approx (- (sqrt (+ x 1)) (sqrt x)) (/.f64 #s(literal -1/2 binary64) (sqrt.f64 x))))) (neg.f64 (neg.f64 (hypot.f64 (sqrt.f64 x) x))))
(/.f64 (neg.f64 #s(approx (- (sqrt (+ x 1)) (sqrt x)) (/.f64 #s(literal -1/2 binary64) (sqrt.f64 x)))) (neg.f64 (hypot.f64 (sqrt.f64 x) x)))
(/.f64 #s(approx (- (sqrt (+ x 1)) (sqrt x)) (/.f64 #s(literal -1/2 binary64) (sqrt.f64 x))) (hypot.f64 (sqrt.f64 x) x))
(neg.f64 (/.f64 (neg.f64 #s(approx (- (sqrt (+ x 1)) (sqrt x)) (/.f64 #s(literal -1/2 binary64) (sqrt.f64 x)))) (hypot.f64 (sqrt.f64 x) x)))
(neg.f64 (/.f64 #s(approx (- (sqrt (+ x 1)) (sqrt x)) (/.f64 #s(literal -1/2 binary64) (sqrt.f64 x))) (neg.f64 (hypot.f64 (sqrt.f64 x) x))))
#s(approx (- (sqrt (+ x 1)) (sqrt x)) (/.f64 #s(literal -1/2 binary64) (sqrt.f64 x)))
(*.f64 (/.f64 #s(literal -1/2 binary64) (sqrt.f64 x)) #s(literal 1 binary64))
(*.f64 (pow.f64 x #s(literal -1/2 binary64)) #s(literal 1/2 binary64))
(*.f64 (sqrt.f64 x) (/.f64 #s(literal 1/2 binary64) x))
(*.f64 #s(literal 1/2 binary64) (pow.f64 x #s(literal -1/2 binary64)))
(*.f64 #s(literal 1 binary64) (/.f64 #s(literal -1/2 binary64) (sqrt.f64 x)))
(/.f64 (/.f64 (*.f64 (sqrt.f64 x) #s(literal 1/2 binary64)) (sqrt.f64 x)) (sqrt.f64 x))
(/.f64 (neg.f64 (*.f64 (sqrt.f64 x) #s(literal 1/2 binary64))) x)
(/.f64 (*.f64 (sqrt.f64 x) #s(literal 1/2 binary64)) x)
(/.f64 #s(literal -1/2 binary64) (sqrt.f64 x))
(/.f64 #s(literal 1/2 binary64) (sqrt.f64 x))
(*.f64 (neg.f64 (pow.f64 x #s(literal -1/4 binary64))) (neg.f64 (pow.f64 x #s(literal -1/4 binary64))))
(*.f64 (fabs.f64 (pow.f64 x #s(literal -1/4 binary64))) (fabs.f64 (pow.f64 x #s(literal -1/4 binary64))))
(*.f64 (sqrt.f64 (pow.f64 x #s(literal -1/2 binary64))) (sqrt.f64 (pow.f64 x #s(literal -1/2 binary64))))
(*.f64 (pow.f64 (pow.f64 x #s(literal 1/4 binary64)) #s(literal -1 binary64)) (pow.f64 (pow.f64 x #s(literal 1/4 binary64)) #s(literal -1 binary64)))
(*.f64 (pow.f64 #s(literal 1 binary64) #s(literal -1/2 binary64)) (pow.f64 x #s(literal -1/2 binary64)))
(*.f64 (pow.f64 x #s(literal -1/4 binary64)) (pow.f64 x #s(literal -1/4 binary64)))
(*.f64 (pow.f64 x #s(literal -1/2 binary64)) (pow.f64 #s(literal 1 binary64) #s(literal -1/2 binary64)))
(*.f64 (pow.f64 x #s(literal -1/2 binary64)) #s(literal 1 binary64))
(*.f64 #s(literal 1 binary64) (pow.f64 x #s(literal -1/2 binary64)))
(pow.f64 (pow.f64 x #s(literal -1/4 binary64)) #s(literal 2 binary64))
(pow.f64 (pow.f64 x #s(literal -2 binary64)) #s(literal 1/4 binary64))
(pow.f64 (pow.f64 x #s(literal -1/2 binary64)) #s(literal 1 binary64))
(pow.f64 (pow.f64 x #s(literal -1 binary64)) #s(literal 1/2 binary64))
(pow.f64 (sqrt.f64 x) #s(literal -1 binary64))
(pow.f64 (*.f64 x x) #s(literal -1/4 binary64))
(pow.f64 x #s(literal -1/2 binary64))
(/.f64 (fabs.f64 (sqrt.f64 #s(literal -1 binary64))) (sqrt.f64 x))
(/.f64 (sqrt.f64 (*.f64 #s(literal -1 binary64) (pow.f64 x #s(literal -1/2 binary64)))) (pow.f64 x #s(literal 1/4 binary64)))
(/.f64 (sqrt.f64 (*.f64 (pow.f64 x #s(literal -1/2 binary64)) #s(literal -1 binary64))) (pow.f64 x #s(literal 1/4 binary64)))
(/.f64 (sqrt.f64 (pow.f64 x #s(literal -1/2 binary64))) (pow.f64 x #s(literal 1/4 binary64)))
(/.f64 (sqrt.f64 #s(literal -1 binary64)) (sqrt.f64 x))
(/.f64 #s(literal -1 binary64) (sqrt.f64 x))
(/.f64 (sqrt.f64 x) x)
(/.f64 #s(literal 1 binary64) (sqrt.f64 x))
(neg.f64 (pow.f64 x #s(literal -1/2 binary64)))
(sqrt.f64 (/.f64 x (*.f64 x x)))
(sqrt.f64 (pow.f64 x #s(literal -1 binary64)))
(fabs.f64 (pow.f64 x #s(literal -1/2 binary64)))
(+.f64 (cosh.f64 (*.f64 #s(literal -1/2 binary64) (log.f64 x))) (sinh.f64 (*.f64 #s(literal -1/2 binary64) (log.f64 x))))
(exp.f64 (-.f64 (log.f64 (sqrt.f64 x)) (log.f64 x)))
(exp.f64 (/.f64 (neg.f64 (log.f64 x)) #s(literal 2 binary64)))
(exp.f64 (*.f64 (log.f64 x) #s(literal -1/2 binary64)))
(exp.f64 (*.f64 #s(literal -1/2 binary64) (log.f64 x)))
(/.f64 (fabs.f64 (/.f64 (/.f64 #s(literal -1/4 binary64) x) (sqrt.f64 x))) (sqrt.f64 x))
(/.f64 (fabs.f64 (neg.f64 (/.f64 #s(literal -1/4 binary64) x))) x)
(/.f64 (fabs.f64 (/.f64 #s(literal -1/4 binary64) x)) x)
(/.f64 (/.f64 (/.f64 #s(literal -1/4 binary64) x) (sqrt.f64 x)) (sqrt.f64 x))
(/.f64 (neg.f64 (/.f64 #s(literal -1/4 binary64) x)) x)
(/.f64 (/.f64 #s(literal -1/4 binary64) x) x)
(/.f64 #s(literal -1/4 binary64) (*.f64 x x))
(/.f64 #s(literal 1/4 binary64) (*.f64 x x))
(neg.f64 (/.f64 #s(literal -1/4 binary64) (*.f64 x x)))
(sqrt.f64 (/.f64 #s(literal -1/16 binary64) (pow.f64 x #s(literal 4 binary64))))
(fabs.f64 (/.f64 #s(literal -1/4 binary64) (*.f64 x x)))
(*.f64 (neg.f64 (pow.f64 x #s(literal 1/4 binary64))) (neg.f64 (pow.f64 x #s(literal 1/4 binary64))))
(*.f64 (pow.f64 (pow.f64 x #s(literal 1/4 binary64)) #s(literal 1 binary64)) (pow.f64 (pow.f64 x #s(literal 1/4 binary64)) #s(literal 1 binary64)))
(*.f64 (pow.f64 (pow.f64 x #s(literal 3/2 binary64)) #s(literal 1/4 binary64)) (pow.f64 (sqrt.f64 x) #s(literal 1/4 binary64)))
(*.f64 (pow.f64 (sqrt.f64 x) #s(literal 1/4 binary64)) (pow.f64 (pow.f64 x #s(literal 3/2 binary64)) #s(literal 1/4 binary64)))
(*.f64 (pow.f64 x #s(literal 1/4 binary64)) (pow.f64 x #s(literal 1/4 binary64)))
(*.f64 (sqrt.f64 x) #s(literal 1 binary64))
(*.f64 #s(literal 1 binary64) (sqrt.f64 x))
(pow.f64 (pow.f64 x #s(literal 1/4 binary64)) #s(literal 2 binary64))
(pow.f64 (pow.f64 x #s(literal 4 binary64)) #s(literal 1/8 binary64))
(pow.f64 (sqrt.f64 x) #s(literal 1 binary64))
(pow.f64 (*.f64 x x) #s(literal 1/4 binary64))
(pow.f64 x #s(literal 1/2 binary64))
(neg.f64 (sqrt.f64 x))
(sqrt.f64 x)
(fabs.f64 (sqrt.f64 x))
(+.f64 (cosh.f64 (log.f64 (sqrt.f64 x))) (sinh.f64 (log.f64 (sqrt.f64 x))))
(exp.f64 (/.f64 (log.f64 x) #s(literal 2 binary64)))
(exp.f64 (*.f64 (*.f64 (log.f64 x) #s(literal 2 binary64)) #s(literal 1/4 binary64)))
(exp.f64 (*.f64 (log.f64 (sqrt.f64 x)) #s(literal 1 binary64)))
(exp.f64 (log.f64 (sqrt.f64 x)))

eval81.0ms (1.2%)

Memory
-15.2MiB live, 76.2MiB allocated
Compiler

Compiled 14 986 to 2 035 computations (86.4% saved)

prune24.0ms (0.4%)

Memory
-14.0MiB live, 42.8MiB allocated
Pruning

25 alts after pruning (17 fresh and 8 done)

PrunedKeptTotal
New43611447
Fresh5611
Picked055
Done033
Total44125466
Accuracy
100.0%
Counts
466 → 25
Alt Table
Click to see full alt table
StatusAccuracyProgram
37.4%
(/.f64 (/.f64 (-.f64 (sqrt.f64 (+.f64 x #s(literal 1 binary64))) (sqrt.f64 x)) (sqrt.f64 x)) (sqrt.f64 (+.f64 x #s(literal 1 binary64))))
98.8%
(/.f64 (/.f64 #s(approx (- (sqrt (+ x 1)) (sqrt x)) (/.f64 (fma.f64 #s(literal -1/8 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) (*.f64 #s(literal 1/2 binary64) (sqrt.f64 x))) x)) (sqrt.f64 (+.f64 x #s(literal 1 binary64)))) (sqrt.f64 x))
38.3%
(/.f64 (-.f64 (+.f64 x #s(literal 1 binary64)) x) (*.f64 (+.f64 (sqrt.f64 (+.f64 x #s(literal 1 binary64))) (sqrt.f64 x)) (hypot.f64 (sqrt.f64 x) x)))
37.4%
(/.f64 (-.f64 (sqrt.f64 (+.f64 x #s(literal 1 binary64))) (sqrt.f64 x)) (hypot.f64 (sqrt.f64 x) x))
81.9%
(/.f64 #s(approx (/ (- (sqrt (+ x 1)) (sqrt x)) (sqrt (+ x 1))) (/.f64 (fma.f64 (/.f64 #s(literal -1/4 binary64) (*.f64 x x)) x (*.f64 x (-.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -3/8 binary64) x)))) (*.f64 x x))) (sqrt.f64 x))
99.1%
(/.f64 #s(approx (/ (- (sqrt (+ x 1)) (sqrt x)) (sqrt (+ x 1))) (/.f64 (-.f64 (+.f64 (/.f64 (+.f64 #s(literal 3/8 binary64) (/.f64 (*.f64 (fma.f64 #s(literal 1/4 binary64) x #s(literal 1 binary64)) #s(literal -1/4 binary64)) x)) (*.f64 x x)) #s(literal 1/2 binary64)) (/.f64 #s(literal 3/8 binary64) x)) x)) (sqrt.f64 x))
98.9%
(/.f64 #s(approx (/ (- (sqrt (+ x 1)) (sqrt x)) (sqrt (+ x 1))) (/.f64 (-.f64 (+.f64 (/.f64 #s(literal 1/4 binary64) (*.f64 x x)) #s(literal 1/2 binary64)) (/.f64 #s(literal 3/8 binary64) x)) x)) (sqrt.f64 x))
97.4%
(/.f64 #s(approx (/ (- (sqrt (+ x 1)) (sqrt x)) (sqrt (+ x 1))) (/.f64 (-.f64 (*.f64 (/.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/4 binary64) (*.f64 x x))) (sqrt.f64 x)) x) (*.f64 (sqrt.f64 x) (/.f64 #s(literal -3/8 binary64) x))) (pow.f64 x #s(literal 3/2 binary64)))) (sqrt.f64 x))
98.9%
(/.f64 #s(approx (/ (- (sqrt (+ x 1)) (sqrt x)) (sqrt (+ x 1))) (/.f64 (+.f64 (/.f64 (-.f64 (/.f64 #s(literal 1/4 binary64) x) #s(literal 3/8 binary64)) x) #s(literal 1/2 binary64)) x)) (sqrt.f64 x))
98.8%
(/.f64 #s(approx (/ (- (sqrt (+ x 1)) (sqrt x)) (sqrt (+ x 1))) (/.f64 #s(approx (- (+ (/ 1/4 (* x x)) 1/2) (/ 3/8 x)) (-.f64 #s(literal 1/2 binary64) (/.f64 #s(literal 3/8 binary64) x))) x)) (sqrt.f64 x))
98.1%
(/.f64 #s(approx (/ (- (sqrt (+ x 1)) (sqrt x)) (sqrt (+ x 1))) (/.f64 #s(approx (- (+ (/ 1/4 (* x x)) 1/2) (/ 3/8 x)) #s(literal 1/2 binary64)) x)) (sqrt.f64 x))
98.2%
(/.f64 #s(approx (- (sqrt (+ x 1)) (sqrt x)) (/.f64 #s(literal 1/2 binary64) (sqrt.f64 x))) (hypot.f64 (sqrt.f64 x) x))
98.3%
(/.f64 #s(approx (- (sqrt (+ x 1)) (sqrt x)) (*.f64 #s(literal 1/2 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) x)))) (hypot.f64 (sqrt.f64 x) x))
37.3%
(-.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 x)) (/.f64 #s(literal 1 binary64) (sqrt.f64 (+.f64 x #s(literal 1 binary64)))))
65.2%
#s(approx (/ (/ (- (sqrt (+ x 1)) (sqrt x)) (sqrt (+ x 1))) (sqrt x)) (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 3 binary64)))) #s(literal 1/2 binary64)))
34.5%
#s(approx (- (/ 1 (sqrt x)) (/ 1 (sqrt (+ x 1)))) (/.f64 (*.f64 #s(literal -1/2 binary64) #s(approx (- (sqrt (/ 1 x)) (sqrt x)) (sqrt.f64 x))) (*.f64 x x)))
5.5%
#s(approx (- (/ 1 (sqrt x)) (/ 1 (sqrt (+ x 1)))) (/.f64 (sqrt.f64 x) x))
5.5%
#s(approx (- (/ 1 (sqrt x)) (/ 1 (sqrt (+ x 1)))) (/.f64 #s(literal 1 binary64) (sqrt.f64 x)))
98.1%
#s(approx (- (/ 1 (sqrt x)) (/ 1 (sqrt (+ x 1)))) (*.f64 (/.f64 (neg.f64 (/.f64 #s(approx (- (sqrt (/ 1 x)) (sqrt x)) (sqrt.f64 x)) x)) x) #s(literal -1/2 binary64)))
82.0%
#s(approx (- (/ 1 (sqrt x)) (/ 1 (sqrt (+ x 1)))) (*.f64 (/.f64 #s(approx (- (sqrt (/ 1 x)) (sqrt x)) (neg.f64 (sqrt.f64 x))) (*.f64 x x)) #s(literal -1/2 binary64)))
82.1%
#s(approx (- (/ 1 (sqrt x)) (/ 1 (sqrt (+ x 1)))) (*.f64 (-.f64 (pow.f64 x #s(literal -1/2 binary64)) (sqrt.f64 x)) (/.f64 #s(literal -1/2 binary64) (*.f64 x x))))
98.6%
#s(approx (- (/ 1 (sqrt x)) (/ 1 (sqrt (+ x 1)))) (*.f64 (-.f64 (pow.f64 x #s(literal -5/2 binary64)) (pow.f64 x #s(literal -3/2 binary64))) #s(literal -1/2 binary64)))
34.5%
#s(approx (- (/ 1 (sqrt x)) (/ 1 (sqrt (+ x 1)))) (*.f64 #s(approx (- (sqrt (/ 1 x)) (sqrt x)) (sqrt.f64 x)) (/.f64 #s(literal -1/2 binary64) (*.f64 x x))))
36.4%
#s(approx (- (/ 1 (sqrt x)) (/ 1 (sqrt (+ x 1)))) (sqrt.f64 (/.f64 x (*.f64 x x))))
5.5%
#s(approx (- (/ 1 (sqrt x)) (/ 1 (sqrt (+ x 1)))) (sqrt.f64 (/.f64 #s(literal 1 binary64) x)))
Compiler

Compiled 1 044 to 689 computations (34% saved)

simplify106.0ms (1.6%)

Memory
1.7MiB live, 92.8MiB allocated
Algorithm
egg-herbie
Localize:

Found 19 expressions of interest:

NewMetricScoreProgram
cost-diff0
(sqrt.f64 x)
cost-diff0
(/.f64 #s(literal 1/2 binary64) (sqrt.f64 x))
cost-diff0
#s(approx (- (sqrt (+ x 1)) (sqrt x)) (/.f64 #s(literal 1/2 binary64) (sqrt.f64 x)))
cost-diff0
(/.f64 #s(approx (- (sqrt (+ x 1)) (sqrt x)) (/.f64 #s(literal 1/2 binary64) (sqrt.f64 x))) (hypot.f64 (sqrt.f64 x) x))
cost-diff0
(sqrt.f64 (+.f64 x #s(literal 1 binary64)))
cost-diff0
(-.f64 (sqrt.f64 (+.f64 x #s(literal 1 binary64))) (sqrt.f64 x))
cost-diff1
(/.f64 (-.f64 (sqrt.f64 (+.f64 x #s(literal 1 binary64))) (sqrt.f64 x)) (sqrt.f64 x))
cost-diff3
(/.f64 (/.f64 (-.f64 (sqrt.f64 (+.f64 x #s(literal 1 binary64))) (sqrt.f64 x)) (sqrt.f64 x)) (sqrt.f64 (+.f64 x #s(literal 1 binary64))))
cost-diff0
#s(approx (- (+ (/ 1/4 (* x x)) 1/2) (/ 3/8 x)) #s(literal 1/2 binary64))
cost-diff0
(/.f64 #s(approx (- (+ (/ 1/4 (* x x)) 1/2) (/ 3/8 x)) #s(literal 1/2 binary64)) x)
cost-diff0
#s(approx (/ (- (sqrt (+ x 1)) (sqrt x)) (sqrt (+ x 1))) (/.f64 #s(approx (- (+ (/ 1/4 (* x x)) 1/2) (/ 3/8 x)) #s(literal 1/2 binary64)) x))
cost-diff0
(/.f64 #s(approx (/ (- (sqrt (+ x 1)) (sqrt x)) (sqrt (+ x 1))) (/.f64 #s(approx (- (+ (/ 1/4 (* x x)) 1/2) (/ 3/8 x)) #s(literal 1/2 binary64)) x)) (sqrt.f64 x))
cost-diff0
(sqrt.f64 x)
cost-diff0
(/.f64 (sqrt.f64 x) x)
cost-diff0
#s(approx (- (/ 1 (sqrt x)) (/ 1 (sqrt (+ x 1)))) (/.f64 (sqrt.f64 x) x))
cost-diff0
(/.f64 (-.f64 (+.f64 (/.f64 (+.f64 #s(literal 3/8 binary64) (/.f64 (*.f64 (fma.f64 #s(literal 1/4 binary64) x #s(literal 1 binary64)) #s(literal -1/4 binary64)) x)) (*.f64 x x)) #s(literal 1/2 binary64)) (/.f64 #s(literal 3/8 binary64) x)) x)
cost-diff0
#s(approx (/ (- (sqrt (+ x 1)) (sqrt x)) (sqrt (+ x 1))) (/.f64 (-.f64 (+.f64 (/.f64 (+.f64 #s(literal 3/8 binary64) (/.f64 (*.f64 (fma.f64 #s(literal 1/4 binary64) x #s(literal 1 binary64)) #s(literal -1/4 binary64)) x)) (*.f64 x x)) #s(literal 1/2 binary64)) (/.f64 #s(literal 3/8 binary64) x)) x))
cost-diff0
(/.f64 #s(approx (/ (- (sqrt (+ x 1)) (sqrt x)) (sqrt (+ x 1))) (/.f64 (-.f64 (+.f64 (/.f64 (+.f64 #s(literal 3/8 binary64) (/.f64 (*.f64 (fma.f64 #s(literal 1/4 binary64) x #s(literal 1 binary64)) #s(literal -1/4 binary64)) x)) (*.f64 x x)) #s(literal 1/2 binary64)) (/.f64 #s(literal 3/8 binary64) x)) x)) (sqrt.f64 x))
cost-diff2
(*.f64 (fma.f64 #s(literal 1/4 binary64) x #s(literal 1 binary64)) #s(literal -1/4 binary64))
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
047385
077385
1121371
2301359
31130359
45023359
09004350
Stop Event
iter limit
node limit
iter limit
Calls
Call 1
Inputs
(/.f64 #s(approx (/ (- (sqrt (+ x 1)) (sqrt x)) (sqrt (+ x 1))) (/.f64 (-.f64 (+.f64 (/.f64 (+.f64 #s(literal 3/8 binary64) (/.f64 (*.f64 (fma.f64 #s(literal 1/4 binary64) x #s(literal 1 binary64)) #s(literal -1/4 binary64)) x)) (*.f64 x x)) #s(literal 1/2 binary64)) (/.f64 #s(literal 3/8 binary64) x)) x)) (sqrt.f64 x))
#s(approx (/ (- (sqrt (+ x 1)) (sqrt x)) (sqrt (+ x 1))) (/.f64 (-.f64 (+.f64 (/.f64 (+.f64 #s(literal 3/8 binary64) (/.f64 (*.f64 (fma.f64 #s(literal 1/4 binary64) x #s(literal 1 binary64)) #s(literal -1/4 binary64)) x)) (*.f64 x x)) #s(literal 1/2 binary64)) (/.f64 #s(literal 3/8 binary64) x)) x))
(/.f64 (-.f64 (+.f64 (/.f64 (+.f64 #s(literal 3/8 binary64) (/.f64 (*.f64 (fma.f64 #s(literal 1/4 binary64) x #s(literal 1 binary64)) #s(literal -1/4 binary64)) x)) (*.f64 x x)) #s(literal 1/2 binary64)) (/.f64 #s(literal 3/8 binary64) x)) x)
(-.f64 (+.f64 (/.f64 (+.f64 #s(literal 3/8 binary64) (/.f64 (*.f64 (fma.f64 #s(literal 1/4 binary64) x #s(literal 1 binary64)) #s(literal -1/4 binary64)) x)) (*.f64 x x)) #s(literal 1/2 binary64)) (/.f64 #s(literal 3/8 binary64) x))
(+.f64 (/.f64 (+.f64 #s(literal 3/8 binary64) (/.f64 (*.f64 (fma.f64 #s(literal 1/4 binary64) x #s(literal 1 binary64)) #s(literal -1/4 binary64)) x)) (*.f64 x x)) #s(literal 1/2 binary64))
(/.f64 (+.f64 #s(literal 3/8 binary64) (/.f64 (*.f64 (fma.f64 #s(literal 1/4 binary64) x #s(literal 1 binary64)) #s(literal -1/4 binary64)) x)) (*.f64 x x))
(+.f64 #s(literal 3/8 binary64) (/.f64 (*.f64 (fma.f64 #s(literal 1/4 binary64) x #s(literal 1 binary64)) #s(literal -1/4 binary64)) x))
#s(literal 3/8 binary64)
(/.f64 (*.f64 (fma.f64 #s(literal 1/4 binary64) x #s(literal 1 binary64)) #s(literal -1/4 binary64)) x)
(*.f64 (fma.f64 #s(literal 1/4 binary64) x #s(literal 1 binary64)) #s(literal -1/4 binary64))
(fma.f64 #s(literal 1/4 binary64) x #s(literal 1 binary64))
#s(literal 1/4 binary64)
x
#s(literal 1 binary64)
#s(literal -1/4 binary64)
(*.f64 x x)
#s(literal 1/2 binary64)
(/.f64 #s(literal 3/8 binary64) x)
(sqrt.f64 x)
#s(approx (- (/ 1 (sqrt x)) (/ 1 (sqrt (+ x 1)))) (/.f64 (sqrt.f64 x) x))
(/.f64 (sqrt.f64 x) x)
(sqrt.f64 x)
x
(/.f64 #s(approx (/ (- (sqrt (+ x 1)) (sqrt x)) (sqrt (+ x 1))) (/.f64 #s(approx (- (+ (/ 1/4 (* x x)) 1/2) (/ 3/8 x)) #s(literal 1/2 binary64)) x)) (sqrt.f64 x))
#s(approx (/ (- (sqrt (+ x 1)) (sqrt x)) (sqrt (+ x 1))) (/.f64 #s(approx (- (+ (/ 1/4 (* x x)) 1/2) (/ 3/8 x)) #s(literal 1/2 binary64)) x))
(/.f64 #s(approx (- (+ (/ 1/4 (* x x)) 1/2) (/ 3/8 x)) #s(literal 1/2 binary64)) x)
#s(approx (- (+ (/ 1/4 (* x x)) 1/2) (/ 3/8 x)) #s(literal 1/2 binary64))
#s(literal 1/2 binary64)
x
(sqrt.f64 x)
(/.f64 (/.f64 (-.f64 (sqrt.f64 (+.f64 x #s(literal 1 binary64))) (sqrt.f64 x)) (sqrt.f64 x)) (sqrt.f64 (+.f64 x #s(literal 1 binary64))))
(/.f64 (-.f64 (sqrt.f64 (+.f64 x #s(literal 1 binary64))) (sqrt.f64 x)) (sqrt.f64 x))
(-.f64 (sqrt.f64 (+.f64 x #s(literal 1 binary64))) (sqrt.f64 x))
(sqrt.f64 (+.f64 x #s(literal 1 binary64)))
(+.f64 x #s(literal 1 binary64))
x
#s(literal 1 binary64)
(sqrt.f64 x)
(/.f64 #s(approx (- (sqrt (+ x 1)) (sqrt x)) (/.f64 #s(literal 1/2 binary64) (sqrt.f64 x))) (hypot.f64 (sqrt.f64 x) x))
#s(approx (- (sqrt (+ x 1)) (sqrt x)) (/.f64 #s(literal 1/2 binary64) (sqrt.f64 x)))
(/.f64 #s(literal 1/2 binary64) (sqrt.f64 x))
#s(literal 1/2 binary64)
(sqrt.f64 x)
x
(hypot.f64 (sqrt.f64 x) x)
Outputs
(/.f64 #s(approx (/ (- (sqrt (+ x 1)) (sqrt x)) (sqrt (+ x 1))) (/.f64 (-.f64 (+.f64 (/.f64 (+.f64 #s(literal 3/8 binary64) (/.f64 (*.f64 (fma.f64 #s(literal 1/4 binary64) x #s(literal 1 binary64)) #s(literal -1/4 binary64)) x)) (*.f64 x x)) #s(literal 1/2 binary64)) (/.f64 #s(literal 3/8 binary64) x)) x)) (sqrt.f64 x))
(/.f64 #s(approx (/ (- (sqrt (+ x 1)) (sqrt x)) (sqrt (+ x 1))) (/.f64 (-.f64 (/.f64 (/.f64 (+.f64 (/.f64 (fma.f64 #s(literal -1/16 binary64) x #s(literal -1/4 binary64)) x) #s(literal 3/8 binary64)) x) x) (-.f64 (/.f64 #s(literal 3/8 binary64) x) #s(literal 1/2 binary64))) x)) (sqrt.f64 x))
#s(approx (/ (- (sqrt (+ x 1)) (sqrt x)) (sqrt (+ x 1))) (/.f64 (-.f64 (+.f64 (/.f64 (+.f64 #s(literal 3/8 binary64) (/.f64 (*.f64 (fma.f64 #s(literal 1/4 binary64) x #s(literal 1 binary64)) #s(literal -1/4 binary64)) x)) (*.f64 x x)) #s(literal 1/2 binary64)) (/.f64 #s(literal 3/8 binary64) x)) x))
#s(approx (/ (- (sqrt (+ x 1)) (sqrt x)) (sqrt (+ x 1))) (/.f64 (-.f64 (/.f64 (/.f64 (+.f64 (/.f64 (fma.f64 #s(literal -1/16 binary64) x #s(literal -1/4 binary64)) x) #s(literal 3/8 binary64)) x) x) (-.f64 (/.f64 #s(literal 3/8 binary64) x) #s(literal 1/2 binary64))) x))
(/.f64 (-.f64 (+.f64 (/.f64 (+.f64 #s(literal 3/8 binary64) (/.f64 (*.f64 (fma.f64 #s(literal 1/4 binary64) x #s(literal 1 binary64)) #s(literal -1/4 binary64)) x)) (*.f64 x x)) #s(literal 1/2 binary64)) (/.f64 #s(literal 3/8 binary64) x)) x)
(/.f64 (-.f64 (/.f64 (/.f64 (+.f64 (/.f64 (fma.f64 #s(literal -1/16 binary64) x #s(literal -1/4 binary64)) x) #s(literal 3/8 binary64)) x) x) (-.f64 (/.f64 #s(literal 3/8 binary64) x) #s(literal 1/2 binary64))) x)
(-.f64 (+.f64 (/.f64 (+.f64 #s(literal 3/8 binary64) (/.f64 (*.f64 (fma.f64 #s(literal 1/4 binary64) x #s(literal 1 binary64)) #s(literal -1/4 binary64)) x)) (*.f64 x x)) #s(literal 1/2 binary64)) (/.f64 #s(literal 3/8 binary64) x))
(-.f64 (/.f64 (/.f64 (+.f64 (/.f64 (fma.f64 #s(literal -1/16 binary64) x #s(literal -1/4 binary64)) x) #s(literal 3/8 binary64)) x) x) (-.f64 (/.f64 #s(literal 3/8 binary64) x) #s(literal 1/2 binary64)))
(+.f64 (/.f64 (+.f64 #s(literal 3/8 binary64) (/.f64 (*.f64 (fma.f64 #s(literal 1/4 binary64) x #s(literal 1 binary64)) #s(literal -1/4 binary64)) x)) (*.f64 x x)) #s(literal 1/2 binary64))
(+.f64 #s(literal 1/2 binary64) (/.f64 (/.f64 (+.f64 (/.f64 (fma.f64 #s(literal -1/16 binary64) x #s(literal -1/4 binary64)) x) #s(literal 3/8 binary64)) x) x))
(/.f64 (+.f64 #s(literal 3/8 binary64) (/.f64 (*.f64 (fma.f64 #s(literal 1/4 binary64) x #s(literal 1 binary64)) #s(literal -1/4 binary64)) x)) (*.f64 x x))
(/.f64 (/.f64 (+.f64 (/.f64 (fma.f64 #s(literal -1/16 binary64) x #s(literal -1/4 binary64)) x) #s(literal 3/8 binary64)) x) x)
(+.f64 #s(literal 3/8 binary64) (/.f64 (*.f64 (fma.f64 #s(literal 1/4 binary64) x #s(literal 1 binary64)) #s(literal -1/4 binary64)) x))
(+.f64 (/.f64 (fma.f64 #s(literal -1/16 binary64) x #s(literal -1/4 binary64)) x) #s(literal 3/8 binary64))
#s(literal 3/8 binary64)
(/.f64 (*.f64 (fma.f64 #s(literal 1/4 binary64) x #s(literal 1 binary64)) #s(literal -1/4 binary64)) x)
(/.f64 (fma.f64 #s(literal -1/16 binary64) x #s(literal -1/4 binary64)) x)
(*.f64 (fma.f64 #s(literal 1/4 binary64) x #s(literal 1 binary64)) #s(literal -1/4 binary64))
(fma.f64 #s(literal -1/16 binary64) x #s(literal -1/4 binary64))
(fma.f64 #s(literal 1/4 binary64) x #s(literal 1 binary64))
#s(literal 1/4 binary64)
x
#s(literal 1 binary64)
#s(literal -1/4 binary64)
(*.f64 x x)
#s(literal 1/2 binary64)
(/.f64 #s(literal 3/8 binary64) x)
(sqrt.f64 x)
#s(approx (- (/ 1 (sqrt x)) (/ 1 (sqrt (+ x 1)))) (/.f64 (sqrt.f64 x) x))
(/.f64 (sqrt.f64 x) x)
(sqrt.f64 x)
x
(/.f64 #s(approx (/ (- (sqrt (+ x 1)) (sqrt x)) (sqrt (+ x 1))) (/.f64 #s(approx (- (+ (/ 1/4 (* x x)) 1/2) (/ 3/8 x)) #s(literal 1/2 binary64)) x)) (sqrt.f64 x))
#s(approx (/ (- (sqrt (+ x 1)) (sqrt x)) (sqrt (+ x 1))) (/.f64 #s(approx (- (+ (/ 1/4 (* x x)) 1/2) (/ 3/8 x)) #s(literal 1/2 binary64)) x))
(/.f64 #s(approx (- (+ (/ 1/4 (* x x)) 1/2) (/ 3/8 x)) #s(literal 1/2 binary64)) x)
#s(approx (- (+ (/ 1/4 (* x x)) 1/2) (/ 3/8 x)) #s(literal 1/2 binary64))
#s(literal 1/2 binary64)
x
(sqrt.f64 x)
(/.f64 (/.f64 (-.f64 (sqrt.f64 (+.f64 x #s(literal 1 binary64))) (sqrt.f64 x)) (sqrt.f64 x)) (sqrt.f64 (+.f64 x #s(literal 1 binary64))))
(-.f64 (/.f64 (sqrt.f64 x) x) (/.f64 #s(literal 1 binary64) (sqrt.f64 (+.f64 #s(literal 1 binary64) x))))
(/.f64 (-.f64 (sqrt.f64 (+.f64 x #s(literal 1 binary64))) (sqrt.f64 x)) (sqrt.f64 x))
(-.f64 (/.f64 (sqrt.f64 (+.f64 #s(literal 1 binary64) x)) (sqrt.f64 x)) #s(literal 1 binary64))
(-.f64 (sqrt.f64 (+.f64 x #s(literal 1 binary64))) (sqrt.f64 x))
(-.f64 (sqrt.f64 (+.f64 #s(literal 1 binary64) x)) (sqrt.f64 x))
(sqrt.f64 (+.f64 x #s(literal 1 binary64)))
(sqrt.f64 (+.f64 #s(literal 1 binary64) x))
(+.f64 x #s(literal 1 binary64))
(+.f64 #s(literal 1 binary64) x)
x
#s(literal 1 binary64)
(sqrt.f64 x)
(/.f64 #s(approx (- (sqrt (+ x 1)) (sqrt x)) (/.f64 #s(literal 1/2 binary64) (sqrt.f64 x))) (hypot.f64 (sqrt.f64 x) x))
#s(approx (- (sqrt (+ x 1)) (sqrt x)) (/.f64 #s(literal 1/2 binary64) (sqrt.f64 x)))
(/.f64 #s(literal 1/2 binary64) (sqrt.f64 x))
#s(literal 1/2 binary64)
(sqrt.f64 x)
x
(hypot.f64 (sqrt.f64 x) x)

localize223.0ms (3.3%)

Memory
2.2MiB live, 187.9MiB allocated
Localize:

Found 19 expressions of interest:

NewMetricScoreProgram
accuracy0.0
(sqrt.f64 x)
accuracy0.1640625
(/.f64 #s(approx (- (sqrt (+ x 1)) (sqrt x)) (/.f64 #s(literal 1/2 binary64) (sqrt.f64 x))) (hypot.f64 (sqrt.f64 x) x))
accuracy0.25390625
(/.f64 #s(literal 1/2 binary64) (sqrt.f64 x))
accuracy0.9121702963124209
#s(approx (- (sqrt (+ x 1)) (sqrt x)) (/.f64 #s(literal 1/2 binary64) (sqrt.f64 x)))
accuracy0.0
(sqrt.f64 x)
accuracy0.24609375
(/.f64 (/.f64 (-.f64 (sqrt.f64 (+.f64 x #s(literal 1 binary64))) (sqrt.f64 x)) (sqrt.f64 x)) (sqrt.f64 (+.f64 x #s(literal 1 binary64))))
accuracy0.33822250976844204
(/.f64 (-.f64 (sqrt.f64 (+.f64 x #s(literal 1 binary64))) (sqrt.f64 x)) (sqrt.f64 x))
accuracy60.18462999946927
(-.f64 (sqrt.f64 (+.f64 x #s(literal 1 binary64))) (sqrt.f64 x))
accuracy0.01171875
(/.f64 #s(approx (- (+ (/ 1/4 (* x x)) 1/2) (/ 3/8 x)) #s(literal 1/2 binary64)) x)
accuracy0.25390625
(/.f64 #s(approx (/ (- (sqrt (+ x 1)) (sqrt x)) (sqrt (+ x 1))) (/.f64 #s(approx (- (+ (/ 1/4 (* x x)) 1/2) (/ 3/8 x)) #s(literal 1/2 binary64)) x)) (sqrt.f64 x))
accuracy0.45807543659067457
#s(approx (/ (- (sqrt (+ x 1)) (sqrt x)) (sqrt (+ x 1))) (/.f64 #s(approx (- (+ (/ 1/4 (* x x)) 1/2) (/ 3/8 x)) #s(literal 1/2 binary64)) x))
accuracy0.9831007575677138
#s(approx (- (+ (/ 1/4 (* x x)) 1/2) (/ 3/8 x)) #s(literal 1/2 binary64))
accuracy0.0
(sqrt.f64 x)
accuracy0.2578125
(/.f64 (sqrt.f64 x) x)
accuracy60.464192040049284
#s(approx (- (/ 1 (sqrt x)) (/ 1 (sqrt (+ x 1)))) (/.f64 (sqrt.f64 x) x))
accuracy0.0078125
(-.f64 (+.f64 (/.f64 (+.f64 #s(literal 3/8 binary64) (/.f64 (*.f64 (fma.f64 #s(literal 1/4 binary64) x #s(literal 1 binary64)) #s(literal -1/4 binary64)) x)) (*.f64 x x)) #s(literal 1/2 binary64)) (/.f64 #s(literal 3/8 binary64) x))
accuracy0.25390625
(/.f64 #s(approx (/ (- (sqrt (+ x 1)) (sqrt x)) (sqrt (+ x 1))) (/.f64 (-.f64 (+.f64 (/.f64 (+.f64 #s(literal 3/8 binary64) (/.f64 (*.f64 (fma.f64 #s(literal 1/4 binary64) x #s(literal 1 binary64)) #s(literal -1/4 binary64)) x)) (*.f64 x x)) #s(literal 1/2 binary64)) (/.f64 #s(literal 3/8 binary64) x)) x)) (sqrt.f64 x))
accuracy0.3215595824926397
#s(approx (/ (- (sqrt (+ x 1)) (sqrt x)) (sqrt (+ x 1))) (/.f64 (-.f64 (+.f64 (/.f64 (+.f64 #s(literal 3/8 binary64) (/.f64 (*.f64 (fma.f64 #s(literal 1/4 binary64) x #s(literal 1 binary64)) #s(literal -1/4 binary64)) x)) (*.f64 x x)) #s(literal 1/2 binary64)) (/.f64 #s(literal 3/8 binary64) x)) x))
accuracy0.9117143927864858
(/.f64 (+.f64 #s(literal 3/8 binary64) (/.f64 (*.f64 (fma.f64 #s(literal 1/4 binary64) x #s(literal 1 binary64)) #s(literal -1/4 binary64)) x)) (*.f64 x x))
Samples
153.0ms212×1valid
29.0ms41×2valid
1.0ms0valid
Compiler

Compiled 310 to 38 computations (87.7% saved)

Precisions
Click to see histograms. Total time spent on operations: 130.0ms
ival-div: 54.0ms (41.6% of total)
adjust: 30.0ms (23.1% of total)
ival-sqrt: 14.0ms (10.8% of total)
ival-add: 10.0ms (7.7% of total)
ival-hypot: 9.0ms (6.9% of total)
ival-sub: 8.0ms (6.2% of total)
ival-mult: 4.0ms (3.1% of total)
exact: 1.0ms (0.8% of total)
ival-assert: 0.0ms (0% of total)
ival-true: 0.0ms (0% of total)

series11.0ms (0.2%)

Memory
11.5MiB live, 11.5MiB allocated
Counts
20 → 106
Calls
Call 1
Inputs
(*.f64 (fma.f64 #s(literal 1/4 binary64) x #s(literal 1 binary64)) #s(literal -1/4 binary64))
(/.f64 #s(approx (/ (- (sqrt (+ x 1)) (sqrt x)) (sqrt (+ x 1))) (/.f64 (-.f64 (+.f64 (/.f64 (+.f64 #s(literal 3/8 binary64) (/.f64 (*.f64 (fma.f64 #s(literal 1/4 binary64) x #s(literal 1 binary64)) #s(literal -1/4 binary64)) x)) (*.f64 x x)) #s(literal 1/2 binary64)) (/.f64 #s(literal 3/8 binary64) x)) x)) (sqrt.f64 x))
#s(approx (/ (- (sqrt (+ x 1)) (sqrt x)) (sqrt (+ x 1))) (/.f64 (-.f64 (+.f64 (/.f64 (+.f64 #s(literal 3/8 binary64) (/.f64 (*.f64 (fma.f64 #s(literal 1/4 binary64) x #s(literal 1 binary64)) #s(literal -1/4 binary64)) x)) (*.f64 x x)) #s(literal 1/2 binary64)) (/.f64 #s(literal 3/8 binary64) x)) x))
(/.f64 (-.f64 (+.f64 (/.f64 (+.f64 #s(literal 3/8 binary64) (/.f64 (*.f64 (fma.f64 #s(literal 1/4 binary64) x #s(literal 1 binary64)) #s(literal -1/4 binary64)) x)) (*.f64 x x)) #s(literal 1/2 binary64)) (/.f64 #s(literal 3/8 binary64) x)) x)
#s(approx (- (/ 1 (sqrt x)) (/ 1 (sqrt (+ x 1)))) (/.f64 (sqrt.f64 x) x))
(/.f64 (sqrt.f64 x) x)
(sqrt.f64 x)
(/.f64 #s(approx (/ (- (sqrt (+ x 1)) (sqrt x)) (sqrt (+ x 1))) (/.f64 #s(approx (- (+ (/ 1/4 (* x x)) 1/2) (/ 3/8 x)) #s(literal 1/2 binary64)) x)) (sqrt.f64 x))
#s(approx (/ (- (sqrt (+ x 1)) (sqrt x)) (sqrt (+ x 1))) (/.f64 #s(approx (- (+ (/ 1/4 (* x x)) 1/2) (/ 3/8 x)) #s(literal 1/2 binary64)) x))
(/.f64 #s(approx (- (+ (/ 1/4 (* x x)) 1/2) (/ 3/8 x)) #s(literal 1/2 binary64)) x)
#s(approx (- (+ (/ 1/4 (* x x)) 1/2) (/ 3/8 x)) #s(literal 1/2 binary64))
(/.f64 (/.f64 (-.f64 (sqrt.f64 (+.f64 x #s(literal 1 binary64))) (sqrt.f64 x)) (sqrt.f64 x)) (sqrt.f64 (+.f64 x #s(literal 1 binary64))))
(/.f64 (-.f64 (sqrt.f64 (+.f64 x #s(literal 1 binary64))) (sqrt.f64 x)) (sqrt.f64 x))
(-.f64 (sqrt.f64 (+.f64 x #s(literal 1 binary64))) (sqrt.f64 x))
(sqrt.f64 (+.f64 x #s(literal 1 binary64)))
(/.f64 #s(approx (- (sqrt (+ x 1)) (sqrt x)) (/.f64 #s(literal 1/2 binary64) (sqrt.f64 x))) (hypot.f64 (sqrt.f64 x) x))
#s(approx (- (sqrt (+ x 1)) (sqrt x)) (/.f64 #s(literal 1/2 binary64) (sqrt.f64 x)))
(/.f64 #s(literal 1/2 binary64) (sqrt.f64 x))
(/.f64 (+.f64 #s(literal 3/8 binary64) (/.f64 (*.f64 (fma.f64 #s(literal 1/4 binary64) x #s(literal 1 binary64)) #s(literal -1/4 binary64)) x)) (*.f64 x x))
(-.f64 (+.f64 (/.f64 (+.f64 #s(literal 3/8 binary64) (/.f64 (*.f64 (fma.f64 #s(literal 1/4 binary64) x #s(literal 1 binary64)) #s(literal -1/4 binary64)) x)) (*.f64 x x)) #s(literal 1/2 binary64)) (/.f64 #s(literal 3/8 binary64) x))
Outputs
-1/4
(- (* -1/16 x) 1/4)
(* (sqrt (/ 1 x)) (- 1 (sqrt x)))
(/ (+ (* 1/2 (sqrt (pow x 3))) (* (sqrt x) (- 1 (sqrt x)))) x)
(/ (+ (* x (+ (* 1/2 (sqrt x)) (* x (+ (* -1/2 (* (sqrt (/ 1 x)) (- 1 (sqrt x)))) (* -1/8 (sqrt x)))))) (* (sqrt x) (- 1 (sqrt x)))) x)
(/ (+ (* x (+ (* 1/2 (sqrt x)) (* x (+ (* -1/2 (* (sqrt (/ 1 x)) (- 1 (sqrt x)))) (+ (* -1/8 (sqrt x)) (* x (+ (* -1/4 (sqrt (/ 1 x))) (+ (* 1/16 (sqrt x)) (* 1/2 (* (sqrt (/ 1 x)) (- 1 (sqrt x)))))))))))) (* (sqrt x) (- 1 (sqrt x)))) x)
(- 1 (sqrt x))
(- (+ 1 (* x (+ 1/2 (* -1/2 (- 1 (sqrt x)))))) (sqrt x))
(- (+ 1 (* x (+ 1/2 (+ (* -1/2 (- 1 (sqrt x))) (* x (- (* 3/8 (- 1 (sqrt x))) 3/8)))))) (sqrt x))
(- (+ 1 (* x (+ 1/2 (+ (* -1/2 (- 1 (sqrt x))) (* x (- (+ (* 3/8 (- 1 (sqrt x))) (* x (+ 5/16 (* -5/16 (- 1 (sqrt x)))))) 3/8)))))) (sqrt x))
(/ -1/4 (pow x 4))
(/ (- (* 5/16 x) 1/4) (pow x 4))
(/ (- (* x (+ 5/16 (* -3/8 x))) 1/4) (pow x 4))
(/ (- (* x (+ 5/16 (* x (- (* 1/2 x) 3/8)))) 1/4) (pow x 4))
(sqrt (/ 1 x))
(/ (+ (sqrt x) (* -1 x)) x)
(/ (+ (sqrt x) (* x (- (* 1/2 x) 1))) x)
(/ (+ (sqrt x) (* x (- (* x (+ 1/2 (* -3/8 x))) 1))) x)
(sqrt x)
(/ 1/4 (pow x 3))
(/ (+ 1/4 (* -3/8 x)) (pow x 3))
(/ (+ 1/4 (* x (- (* 1/2 x) 3/8))) (pow x 3))
(/ 1/4 (pow x 2))
(/ (+ 1/4 (* -3/8 x)) (pow x 2))
(/ (+ 1/4 (* x (- (* 1/2 x) 3/8))) (pow x 2))
(/ (+ (* x (+ (* -1/8 (sqrt (pow x 3))) (* 1/2 (sqrt x)))) (* (sqrt x) (- 1 (sqrt x)))) x)
(/ (+ (* x (+ (* 1/2 (sqrt x)) (* x (+ (* -1/8 (sqrt x)) (* 1/16 (sqrt (pow x 3))))))) (* (sqrt x) (- 1 (sqrt x)))) x)
(- (+ 1 (* 1/2 x)) (sqrt x))
(- (+ 1 (* x (+ 1/2 (* -1/8 x)))) (sqrt x))
(- (+ 1 (* x (+ 1/2 (* x (- (* 1/16 x) 1/8))))) (sqrt x))
1
(+ 1 (* 1/2 x))
(+ 1 (* x (+ 1/2 (* -1/8 x))))
(+ 1 (* x (+ 1/2 (* x (- (* 1/16 x) 1/8)))))
(* 1/2 (sqrt (/ 1 x)))
(/ -1/4 (pow x 3))
(/ (- (* 5/16 x) 1/4) (pow x 3))
(/ (- (* x (+ 5/16 (* -3/8 x))) 1/4) (pow x 3))
(/ (- (* x (+ 5/16 (* x (- (* 1/2 x) 3/8)))) 1/4) (pow x 3))
(* -1/16 x)
(* -1 (* x (+ 1/16 (* 1/4 (/ 1 x)))))
(* 1/2 (sqrt (/ 1 (pow x 3))))
(/ (+ (* -1/4 (sqrt (/ 1 x))) (* 1/2 (sqrt x))) (pow x 2))
(/ (+ (* -1/4 (sqrt (/ 1 x))) (+ (* -1/8 (sqrt (/ 1 x))) (+ (* 3/16 (sqrt (/ 1 (pow x 3)))) (* 1/2 (sqrt x))))) (pow x 2))
(/ (+ (* -1/4 (sqrt (/ 1 x))) (+ (* -5/32 (sqrt (/ 1 (pow x 5)))) (+ (* -1/8 (sqrt (/ 1 x))) (+ (* 1/16 (sqrt (/ 1 (pow x 3)))) (+ (* 3/16 (sqrt (/ 1 (pow x 3)))) (* 1/2 (sqrt x))))))) (pow x 2))
(/ 1/2 x)
(/ (+ 1/2 (* -1 (/ (+ (* 1/8 x) (* 1/4 x)) (pow x 2)))) x)
(/ (- (+ 1/2 (* 1/4 (/ 1 (pow x 2)))) (+ (/ 1/8 x) (/ 1/4 x))) x)
(/ (- (+ 1/2 (+ (* -1/4 (/ (+ 1 (* 1/4 x)) (pow x 3))) (* 3/8 (/ 1 (pow x 2))))) (+ (/ 1/8 x) (/ 1/4 x))) x)
(/ (- 1/2 (* 3/8 (/ 1 x))) x)
(/ (- (+ 1/2 (/ 5/16 (pow x 2))) (* 3/8 (/ 1 x))) x)
(/ (- (+ 1/2 (/ 5/16 (pow x 2))) (+ (* 3/8 (/ 1 x)) (* 1/4 (/ 1 (pow x 3))))) x)
(/ (- (* -1/2 (sqrt (/ 1 x))) (* -1/2 (sqrt x))) (pow x 2))
(/ (- (* 1/2 (* (sqrt (/ 1 (pow x 3))) (+ 1 (* 1/4 x)))) (+ (* -1/2 (sqrt x)) (* 1/2 (sqrt (/ 1 x))))) (pow x 2))
(/ (- (* -1/2 (* (sqrt (/ 1 (pow x 5))) (+ 1 (* 1/2 x)))) (+ (* -1/2 (sqrt x)) (+ (* -1/2 (* (sqrt (/ 1 (pow x 3))) (+ 1 (* 1/4 x)))) (* 1/2 (sqrt (/ 1 x)))))) (pow x 2))
(/ (- (+ 1/2 (/ 1/4 (pow x 2))) (* 3/8 (/ 1 x))) x)
1/2
(- 1/2 (* 3/8 (/ 1 x)))
(- (+ 1/2 (/ 1/4 (pow x 2))) (* 3/8 (/ 1 x)))
(/ (- 1/2 (* 1/8 (/ 1 x))) x)
(/ (- (+ 1/2 (* 1/16 (/ 1 (pow x 2)))) (/ 1/8 x)) x)
(/ (- (+ 1/2 (* 1/16 (/ 1 (pow x 2)))) (+ (/ 1/8 x) (* 5/128 (/ 1 (pow x 3))))) x)
(/ (+ (* -1/8 (sqrt (/ 1 x))) (* 1/2 (sqrt x))) x)
(/ (+ (* -1/8 (sqrt (/ 1 x))) (+ (* 1/16 (sqrt (/ 1 (pow x 3)))) (* 1/2 (sqrt x)))) x)
(/ (+ (* -1/8 (sqrt (/ 1 x))) (+ (* -5/128 (sqrt (/ 1 (pow x 5)))) (+ (* 1/16 (sqrt (/ 1 (pow x 3)))) (* 1/2 (sqrt x))))) 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))))))))
(/ 5/16 (pow x 2))
(/ (- 5/16 (* 1/4 (/ 1 x))) (pow x 2))
(- (+ 1/2 (/ 5/16 (pow x 2))) (* 3/8 (/ 1 x)))
(- (+ 1/2 (/ 5/16 (pow x 2))) (+ (* 3/8 (/ 1 x)) (* 1/4 (/ 1 (pow x 3)))))
(/ (+ (* 1/4 (* (sqrt (/ 1 x)) (/ 1 (pow (sqrt -1) 2)))) (* 1/2 (sqrt x))) (pow x 2))
(/ (+ (* -1 (/ (+ (* -1 (/ (+ (* -1/4 (* (sqrt x) (/ (+ 1 (* 1/4 (/ 1 (pow (sqrt -1) 2)))) (pow (sqrt -1) 2)))) (* -1/8 (* (sqrt (pow x 3)) (/ 1 (pow (sqrt -1) 2))))) x)) (* -1/4 (* (sqrt x) (/ 1 (pow (sqrt -1) 2))))) x)) (* 1/2 (sqrt x))) (pow x 2))
(/ (+ (* -1 (/ (+ (* -1 (/ (+ (* -1 (/ (+ (* -1/4 (* (sqrt x) (/ (+ 1 (* 1/2 (/ (+ 1 (* 1/4 (/ 1 (pow (sqrt -1) 2)))) (pow (sqrt -1) 2)))) (pow (sqrt -1) 2)))) (* 1/16 (* (sqrt (pow x 3)) (/ 1 (pow (sqrt -1) 4))))) x)) (+ (* -1/4 (* (sqrt x) (/ (+ 1 (* 1/4 (/ 1 (pow (sqrt -1) 2)))) (pow (sqrt -1) 2)))) (* -1/8 (* (sqrt (pow x 3)) (/ 1 (pow (sqrt -1) 2)))))) x)) (* -1/4 (* (sqrt x) (/ 1 (pow (sqrt -1) 2))))) x)) (* 1/2 (sqrt x))) (pow x 2))
(/ -1/2 x)
(* -1 (/ (+ 1/2 (* -1 (/ (+ (* -1/4 (/ x (pow (sqrt -1) 2))) (* -1/8 (/ x (pow (sqrt -1) 2)))) (pow x 2)))) x))
(* -1 (/ (+ 1/2 (* -1 (/ (+ (* -1/4 (/ x (pow (sqrt -1) 2))) (+ (* -1/8 (/ x (pow (sqrt -1) 2))) (* 1/4 (/ 1 (pow (sqrt -1) 2))))) (pow x 2)))) x))
(* -1 (/ (- (+ 1/2 (* -1 (/ (- (* -1 (/ (+ (* 1/8 (/ (pow x 2) (pow (sqrt -1) 4))) (* 1/4 (/ (* x (+ 1 (* -1/4 (/ x (pow (sqrt -1) 2))))) (pow (sqrt -1) 2)))) x)) (* -1/4 (/ x (pow (sqrt -1) 2)))) (pow x 3)))) (+ (/ -1/4 (* x (pow (sqrt -1) 2))) (/ -1/8 (* x (pow (sqrt -1) 2))))) x))
(* -1 (/ (- (* 3/8 (/ 1 x)) 1/2) x))
(* -1 (/ (- (* -1 (/ (- (* 5/16 (/ 1 x)) 3/8) x)) 1/2) x))
(* -1 (/ (- (* -1 (/ (- (* -1 (/ (- (* 1/4 (/ 1 x)) 5/16) x)) 3/8) x)) 1/2) x))
(- (sqrt (/ 1 x)) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)))
(- (+ (sqrt (/ 1 x)) (* 1/2 (sqrt (/ 1 (pow x 3))))) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)))
(- (+ (sqrt (/ 1 x)) (* -1/2 (sqrt (/ 1 (pow x 5))))) (+ (* -1/2 (sqrt (/ 1 (pow x 3)))) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))))
(- (+ (sqrt (/ 1 x)) (* -1 (/ (- (* -1/2 (* (sqrt (/ 1 x)) (+ 1 (* -1/4 (/ x (pow (sqrt -1) 2)))))) (* -1/2 (sqrt x))) (pow x 3)))) (+ (* -1/2 (sqrt (/ 1 (pow x 3)))) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))))
(* -1 (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)))
(* -1 (* (sqrt x) (pow (sqrt -1) 2)))
(* -1 (/ (- (* -1 (/ (- (* 1/4 (/ 1 x)) 3/8) x)) 1/2) x))
(+ 1/2 (* -1 (/ (- 3/8 (* 1/4 (/ 1 x))) x)))
(/ -1/2 (* x (pow (sqrt -1) 2)))
(* -1 (/ (+ (* 1/8 (/ 1 (* x (pow (sqrt -1) 4)))) (* 1/2 (/ 1 (pow (sqrt -1) 2)))) x))
(* -1 (/ (- (+ (/ 1/16 (* (pow x 2) (pow (sqrt -1) 6))) (* 1/2 (/ 1 (pow (sqrt -1) 2)))) (/ -1/8 (* x (pow (sqrt -1) 4)))) x))
(* -1 (/ (- (+ (* 1/16 (/ 1 (* (pow x 2) (pow (sqrt -1) 6)))) (+ (* 5/128 (/ 1 (* (pow x 3) (pow (sqrt -1) 8)))) (* 1/2 (/ 1 (pow (sqrt -1) 2))))) (/ -1/8 (* x (pow (sqrt -1) 4)))) x))
(* -1/2 (sqrt (/ 1 x)))
(* -1 (/ (+ (* -1/8 (* (sqrt (/ 1 x)) (/ 1 (pow (sqrt -1) 2)))) (* 1/2 (sqrt x))) x))
(* -1 (/ (+ (* -1/8 (* (sqrt (/ 1 x)) (/ 1 (pow (sqrt -1) 2)))) (+ (* 1/16 (* (sqrt (/ 1 (pow x 3))) (/ 1 (pow (sqrt -1) 4)))) (* 1/2 (sqrt x)))) x))
(* -1 (/ (+ (* -1/8 (* (sqrt (/ 1 x)) (/ 1 (pow (sqrt -1) 2)))) (+ (* -5/128 (* (sqrt (/ 1 (pow x 5))) (/ 1 (pow (sqrt -1) 6)))) (+ (* 1/16 (* (sqrt (/ 1 (pow x 3))) (/ 1 (pow (sqrt -1) 4)))) (* 1/2 (sqrt x))))) x))
(* -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)))))))
(/ (+ (* 1/4 (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))) (* 1/2 (sqrt x))) (pow x 2))
(/ (+ (* -1 (/ (+ (* -1 (/ (+ (* -1/4 (* (sqrt x) (+ (* -1 (pow (sqrt -1) 4)) (* 1/4 (pow (sqrt -1) 4))))) (* -1/8 (* (sqrt (pow x 3)) (/ 1 (pow (sqrt -1) 2))))) x)) (* -1/4 (* (sqrt x) (pow (sqrt -1) 2)))) x)) (* 1/2 (sqrt x))) (pow x 2))
(/ (+ (* -1 (/ (+ (* -1 (/ (+ (* -1 (/ (+ (* -1/4 (* (sqrt x) (+ (* 1/2 (* (pow (sqrt -1) 2) (+ (* -1 (pow (sqrt -1) 4)) (* 1/4 (pow (sqrt -1) 4))))) (pow (sqrt -1) 6)))) (* 1/16 (sqrt (pow x 3)))) x)) (+ (* -1/4 (* (sqrt x) (+ (* -1 (pow (sqrt -1) 4)) (* 1/4 (pow (sqrt -1) 4))))) (* -1/8 (* (sqrt (pow x 3)) (/ 1 (pow (sqrt -1) 2)))))) x)) (* -1/4 (* (sqrt x) (pow (sqrt -1) 2)))) x)) (* 1/2 (sqrt x))) (pow x 2))
(+ 1/2 (* -1 (/ (- 3/8 (* 5/16 (/ 1 x))) x)))
(+ 1/2 (* -1 (/ (+ 3/8 (* -1 (/ (- 5/16 (* 1/4 (/ 1 x))) x))) x)))
Calls

3 calls:

TimeVariablePointExpression
4.0ms
x
@-inf
((* (+ (* 1/4 x) 1) -1/4) (/ (/ (- (sqrt (+ x 1)) (sqrt x)) (sqrt (+ x 1))) (sqrt x)) (/ (- (sqrt (+ x 1)) (sqrt x)) (sqrt (+ x 1))) (/ (- (+ (/ (+ 3/8 (/ (* (+ (* 1/4 x) 1) -1/4) x)) (* x x)) 1/2) (/ 3/8 x)) x) (- (/ 1 (sqrt x)) (/ 1 (sqrt (+ x 1)))) (/ (sqrt x) x) (sqrt x) (/ (/ (- (sqrt (+ x 1)) (sqrt x)) (sqrt (+ x 1))) (sqrt x)) (/ (- (sqrt (+ x 1)) (sqrt x)) (sqrt (+ x 1))) (/ (- (+ (/ 1/4 (* x x)) 1/2) (/ 3/8 x)) x) (- (+ (/ 1/4 (* x x)) 1/2) (/ 3/8 x)) (/ (/ (- (sqrt (+ x 1)) (sqrt x)) (sqrt x)) (sqrt (+ x 1))) (/ (- (sqrt (+ x 1)) (sqrt x)) (sqrt x)) (- (sqrt (+ x 1)) (sqrt x)) (sqrt (+ x 1)) (/ (- (sqrt (+ x 1)) (sqrt x)) (sqrt (+ (* (sqrt x) (sqrt x)) (* x x)))) (- (sqrt (+ x 1)) (sqrt x)) (/ 1/2 (sqrt x)) (/ (+ 3/8 (/ (* (+ (* 1/4 x) 1) -1/4) x)) (* x x)) (- (+ (/ (+ 3/8 (/ (* (+ (* 1/4 x) 1) -1/4) x)) (* x x)) 1/2) (/ 3/8 x)))
3.0ms
x
@inf
((* (+ (* 1/4 x) 1) -1/4) (/ (/ (- (sqrt (+ x 1)) (sqrt x)) (sqrt (+ x 1))) (sqrt x)) (/ (- (sqrt (+ x 1)) (sqrt x)) (sqrt (+ x 1))) (/ (- (+ (/ (+ 3/8 (/ (* (+ (* 1/4 x) 1) -1/4) x)) (* x x)) 1/2) (/ 3/8 x)) x) (- (/ 1 (sqrt x)) (/ 1 (sqrt (+ x 1)))) (/ (sqrt x) x) (sqrt x) (/ (/ (- (sqrt (+ x 1)) (sqrt x)) (sqrt (+ x 1))) (sqrt x)) (/ (- (sqrt (+ x 1)) (sqrt x)) (sqrt (+ x 1))) (/ (- (+ (/ 1/4 (* x x)) 1/2) (/ 3/8 x)) x) (- (+ (/ 1/4 (* x x)) 1/2) (/ 3/8 x)) (/ (/ (- (sqrt (+ x 1)) (sqrt x)) (sqrt x)) (sqrt (+ x 1))) (/ (- (sqrt (+ x 1)) (sqrt x)) (sqrt x)) (- (sqrt (+ x 1)) (sqrt x)) (sqrt (+ x 1)) (/ (- (sqrt (+ x 1)) (sqrt x)) (sqrt (+ (* (sqrt x) (sqrt x)) (* x x)))) (- (sqrt (+ x 1)) (sqrt x)) (/ 1/2 (sqrt x)) (/ (+ 3/8 (/ (* (+ (* 1/4 x) 1) -1/4) x)) (* x x)) (- (+ (/ (+ 3/8 (/ (* (+ (* 1/4 x) 1) -1/4) x)) (* x x)) 1/2) (/ 3/8 x)))
2.0ms
x
@0
((* (+ (* 1/4 x) 1) -1/4) (/ (/ (- (sqrt (+ x 1)) (sqrt x)) (sqrt (+ x 1))) (sqrt x)) (/ (- (sqrt (+ x 1)) (sqrt x)) (sqrt (+ x 1))) (/ (- (+ (/ (+ 3/8 (/ (* (+ (* 1/4 x) 1) -1/4) x)) (* x x)) 1/2) (/ 3/8 x)) x) (- (/ 1 (sqrt x)) (/ 1 (sqrt (+ x 1)))) (/ (sqrt x) x) (sqrt x) (/ (/ (- (sqrt (+ x 1)) (sqrt x)) (sqrt (+ x 1))) (sqrt x)) (/ (- (sqrt (+ x 1)) (sqrt x)) (sqrt (+ x 1))) (/ (- (+ (/ 1/4 (* x x)) 1/2) (/ 3/8 x)) x) (- (+ (/ 1/4 (* x x)) 1/2) (/ 3/8 x)) (/ (/ (- (sqrt (+ x 1)) (sqrt x)) (sqrt x)) (sqrt (+ x 1))) (/ (- (sqrt (+ x 1)) (sqrt x)) (sqrt x)) (- (sqrt (+ x 1)) (sqrt x)) (sqrt (+ x 1)) (/ (- (sqrt (+ x 1)) (sqrt x)) (sqrt (+ (* (sqrt x) (sqrt x)) (* x x)))) (- (sqrt (+ x 1)) (sqrt x)) (/ 1/2 (sqrt x)) (/ (+ 3/8 (/ (* (+ (* 1/4 x) 1) -1/4) x)) (* x x)) (- (+ (/ (+ 3/8 (/ (* (+ (* 1/4 x) 1) -1/4) x)) (* x x)) 1/2) (/ 3/8 x)))

simplify139.0ms (2%)

Memory
9.3MiB live, 109.1MiB allocated
Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
04992021
116601744
267551738
080351630
Stop Event
iter limit
node limit
Counts
106 → 106
Calls
Call 1
Inputs
-1/4
(- (* -1/16 x) 1/4)
(* (sqrt (/ 1 x)) (- 1 (sqrt x)))
(/ (+ (* 1/2 (sqrt (pow x 3))) (* (sqrt x) (- 1 (sqrt x)))) x)
(/ (+ (* x (+ (* 1/2 (sqrt x)) (* x (+ (* -1/2 (* (sqrt (/ 1 x)) (- 1 (sqrt x)))) (* -1/8 (sqrt x)))))) (* (sqrt x) (- 1 (sqrt x)))) x)
(/ (+ (* x (+ (* 1/2 (sqrt x)) (* x (+ (* -1/2 (* (sqrt (/ 1 x)) (- 1 (sqrt x)))) (+ (* -1/8 (sqrt x)) (* x (+ (* -1/4 (sqrt (/ 1 x))) (+ (* 1/16 (sqrt x)) (* 1/2 (* (sqrt (/ 1 x)) (- 1 (sqrt x)))))))))))) (* (sqrt x) (- 1 (sqrt x)))) x)
(- 1 (sqrt x))
(- (+ 1 (* x (+ 1/2 (* -1/2 (- 1 (sqrt x)))))) (sqrt x))
(- (+ 1 (* x (+ 1/2 (+ (* -1/2 (- 1 (sqrt x))) (* x (- (* 3/8 (- 1 (sqrt x))) 3/8)))))) (sqrt x))
(- (+ 1 (* x (+ 1/2 (+ (* -1/2 (- 1 (sqrt x))) (* x (- (+ (* 3/8 (- 1 (sqrt x))) (* x (+ 5/16 (* -5/16 (- 1 (sqrt x)))))) 3/8)))))) (sqrt x))
(/ -1/4 (pow x 4))
(/ (- (* 5/16 x) 1/4) (pow x 4))
(/ (- (* x (+ 5/16 (* -3/8 x))) 1/4) (pow x 4))
(/ (- (* x (+ 5/16 (* x (- (* 1/2 x) 3/8)))) 1/4) (pow x 4))
(sqrt (/ 1 x))
(/ (+ (sqrt x) (* -1 x)) x)
(/ (+ (sqrt x) (* x (- (* 1/2 x) 1))) x)
(/ (+ (sqrt x) (* x (- (* x (+ 1/2 (* -3/8 x))) 1))) x)
(sqrt x)
(/ 1/4 (pow x 3))
(/ (+ 1/4 (* -3/8 x)) (pow x 3))
(/ (+ 1/4 (* x (- (* 1/2 x) 3/8))) (pow x 3))
(/ 1/4 (pow x 2))
(/ (+ 1/4 (* -3/8 x)) (pow x 2))
(/ (+ 1/4 (* x (- (* 1/2 x) 3/8))) (pow x 2))
(/ (+ (* x (+ (* -1/8 (sqrt (pow x 3))) (* 1/2 (sqrt x)))) (* (sqrt x) (- 1 (sqrt x)))) x)
(/ (+ (* x (+ (* 1/2 (sqrt x)) (* x (+ (* -1/8 (sqrt x)) (* 1/16 (sqrt (pow x 3))))))) (* (sqrt x) (- 1 (sqrt x)))) x)
(- (+ 1 (* 1/2 x)) (sqrt x))
(- (+ 1 (* x (+ 1/2 (* -1/8 x)))) (sqrt x))
(- (+ 1 (* x (+ 1/2 (* x (- (* 1/16 x) 1/8))))) (sqrt x))
1
(+ 1 (* 1/2 x))
(+ 1 (* x (+ 1/2 (* -1/8 x))))
(+ 1 (* x (+ 1/2 (* x (- (* 1/16 x) 1/8)))))
(* 1/2 (sqrt (/ 1 x)))
(/ -1/4 (pow x 3))
(/ (- (* 5/16 x) 1/4) (pow x 3))
(/ (- (* x (+ 5/16 (* -3/8 x))) 1/4) (pow x 3))
(/ (- (* x (+ 5/16 (* x (- (* 1/2 x) 3/8)))) 1/4) (pow x 3))
(* -1/16 x)
(* -1 (* x (+ 1/16 (* 1/4 (/ 1 x)))))
(* 1/2 (sqrt (/ 1 (pow x 3))))
(/ (+ (* -1/4 (sqrt (/ 1 x))) (* 1/2 (sqrt x))) (pow x 2))
(/ (+ (* -1/4 (sqrt (/ 1 x))) (+ (* -1/8 (sqrt (/ 1 x))) (+ (* 3/16 (sqrt (/ 1 (pow x 3)))) (* 1/2 (sqrt x))))) (pow x 2))
(/ (+ (* -1/4 (sqrt (/ 1 x))) (+ (* -5/32 (sqrt (/ 1 (pow x 5)))) (+ (* -1/8 (sqrt (/ 1 x))) (+ (* 1/16 (sqrt (/ 1 (pow x 3)))) (+ (* 3/16 (sqrt (/ 1 (pow x 3)))) (* 1/2 (sqrt x))))))) (pow x 2))
(/ 1/2 x)
(/ (+ 1/2 (* -1 (/ (+ (* 1/8 x) (* 1/4 x)) (pow x 2)))) x)
(/ (- (+ 1/2 (* 1/4 (/ 1 (pow x 2)))) (+ (/ 1/8 x) (/ 1/4 x))) x)
(/ (- (+ 1/2 (+ (* -1/4 (/ (+ 1 (* 1/4 x)) (pow x 3))) (* 3/8 (/ 1 (pow x 2))))) (+ (/ 1/8 x) (/ 1/4 x))) x)
(/ (- 1/2 (* 3/8 (/ 1 x))) x)
(/ (- (+ 1/2 (/ 5/16 (pow x 2))) (* 3/8 (/ 1 x))) x)
(/ (- (+ 1/2 (/ 5/16 (pow x 2))) (+ (* 3/8 (/ 1 x)) (* 1/4 (/ 1 (pow x 3))))) x)
(/ (- (* -1/2 (sqrt (/ 1 x))) (* -1/2 (sqrt x))) (pow x 2))
(/ (- (* 1/2 (* (sqrt (/ 1 (pow x 3))) (+ 1 (* 1/4 x)))) (+ (* -1/2 (sqrt x)) (* 1/2 (sqrt (/ 1 x))))) (pow x 2))
(/ (- (* -1/2 (* (sqrt (/ 1 (pow x 5))) (+ 1 (* 1/2 x)))) (+ (* -1/2 (sqrt x)) (+ (* -1/2 (* (sqrt (/ 1 (pow x 3))) (+ 1 (* 1/4 x)))) (* 1/2 (sqrt (/ 1 x)))))) (pow x 2))
(/ (- (+ 1/2 (/ 1/4 (pow x 2))) (* 3/8 (/ 1 x))) x)
1/2
(- 1/2 (* 3/8 (/ 1 x)))
(- (+ 1/2 (/ 1/4 (pow x 2))) (* 3/8 (/ 1 x)))
(/ (- 1/2 (* 1/8 (/ 1 x))) x)
(/ (- (+ 1/2 (* 1/16 (/ 1 (pow x 2)))) (/ 1/8 x)) x)
(/ (- (+ 1/2 (* 1/16 (/ 1 (pow x 2)))) (+ (/ 1/8 x) (* 5/128 (/ 1 (pow x 3))))) x)
(/ (+ (* -1/8 (sqrt (/ 1 x))) (* 1/2 (sqrt x))) x)
(/ (+ (* -1/8 (sqrt (/ 1 x))) (+ (* 1/16 (sqrt (/ 1 (pow x 3)))) (* 1/2 (sqrt x)))) x)
(/ (+ (* -1/8 (sqrt (/ 1 x))) (+ (* -5/128 (sqrt (/ 1 (pow x 5)))) (+ (* 1/16 (sqrt (/ 1 (pow x 3)))) (* 1/2 (sqrt x))))) 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))))))))
(/ 5/16 (pow x 2))
(/ (- 5/16 (* 1/4 (/ 1 x))) (pow x 2))
(- (+ 1/2 (/ 5/16 (pow x 2))) (* 3/8 (/ 1 x)))
(- (+ 1/2 (/ 5/16 (pow x 2))) (+ (* 3/8 (/ 1 x)) (* 1/4 (/ 1 (pow x 3)))))
(/ (+ (* 1/4 (* (sqrt (/ 1 x)) (/ 1 (pow (sqrt -1) 2)))) (* 1/2 (sqrt x))) (pow x 2))
(/ (+ (* -1 (/ (+ (* -1 (/ (+ (* -1/4 (* (sqrt x) (/ (+ 1 (* 1/4 (/ 1 (pow (sqrt -1) 2)))) (pow (sqrt -1) 2)))) (* -1/8 (* (sqrt (pow x 3)) (/ 1 (pow (sqrt -1) 2))))) x)) (* -1/4 (* (sqrt x) (/ 1 (pow (sqrt -1) 2))))) x)) (* 1/2 (sqrt x))) (pow x 2))
(/ (+ (* -1 (/ (+ (* -1 (/ (+ (* -1 (/ (+ (* -1/4 (* (sqrt x) (/ (+ 1 (* 1/2 (/ (+ 1 (* 1/4 (/ 1 (pow (sqrt -1) 2)))) (pow (sqrt -1) 2)))) (pow (sqrt -1) 2)))) (* 1/16 (* (sqrt (pow x 3)) (/ 1 (pow (sqrt -1) 4))))) x)) (+ (* -1/4 (* (sqrt x) (/ (+ 1 (* 1/4 (/ 1 (pow (sqrt -1) 2)))) (pow (sqrt -1) 2)))) (* -1/8 (* (sqrt (pow x 3)) (/ 1 (pow (sqrt -1) 2)))))) x)) (* -1/4 (* (sqrt x) (/ 1 (pow (sqrt -1) 2))))) x)) (* 1/2 (sqrt x))) (pow x 2))
(/ -1/2 x)
(* -1 (/ (+ 1/2 (* -1 (/ (+ (* -1/4 (/ x (pow (sqrt -1) 2))) (* -1/8 (/ x (pow (sqrt -1) 2)))) (pow x 2)))) x))
(* -1 (/ (+ 1/2 (* -1 (/ (+ (* -1/4 (/ x (pow (sqrt -1) 2))) (+ (* -1/8 (/ x (pow (sqrt -1) 2))) (* 1/4 (/ 1 (pow (sqrt -1) 2))))) (pow x 2)))) x))
(* -1 (/ (- (+ 1/2 (* -1 (/ (- (* -1 (/ (+ (* 1/8 (/ (pow x 2) (pow (sqrt -1) 4))) (* 1/4 (/ (* x (+ 1 (* -1/4 (/ x (pow (sqrt -1) 2))))) (pow (sqrt -1) 2)))) x)) (* -1/4 (/ x (pow (sqrt -1) 2)))) (pow x 3)))) (+ (/ -1/4 (* x (pow (sqrt -1) 2))) (/ -1/8 (* x (pow (sqrt -1) 2))))) x))
(* -1 (/ (- (* 3/8 (/ 1 x)) 1/2) x))
(* -1 (/ (- (* -1 (/ (- (* 5/16 (/ 1 x)) 3/8) x)) 1/2) x))
(* -1 (/ (- (* -1 (/ (- (* -1 (/ (- (* 1/4 (/ 1 x)) 5/16) x)) 3/8) x)) 1/2) x))
(- (sqrt (/ 1 x)) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)))
(- (+ (sqrt (/ 1 x)) (* 1/2 (sqrt (/ 1 (pow x 3))))) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)))
(- (+ (sqrt (/ 1 x)) (* -1/2 (sqrt (/ 1 (pow x 5))))) (+ (* -1/2 (sqrt (/ 1 (pow x 3)))) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))))
(- (+ (sqrt (/ 1 x)) (* -1 (/ (- (* -1/2 (* (sqrt (/ 1 x)) (+ 1 (* -1/4 (/ x (pow (sqrt -1) 2)))))) (* -1/2 (sqrt x))) (pow x 3)))) (+ (* -1/2 (sqrt (/ 1 (pow x 3)))) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))))
(* -1 (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)))
(* -1 (* (sqrt x) (pow (sqrt -1) 2)))
(* -1 (/ (- (* -1 (/ (- (* 1/4 (/ 1 x)) 3/8) x)) 1/2) x))
(+ 1/2 (* -1 (/ (- 3/8 (* 1/4 (/ 1 x))) x)))
(/ -1/2 (* x (pow (sqrt -1) 2)))
(* -1 (/ (+ (* 1/8 (/ 1 (* x (pow (sqrt -1) 4)))) (* 1/2 (/ 1 (pow (sqrt -1) 2)))) x))
(* -1 (/ (- (+ (/ 1/16 (* (pow x 2) (pow (sqrt -1) 6))) (* 1/2 (/ 1 (pow (sqrt -1) 2)))) (/ -1/8 (* x (pow (sqrt -1) 4)))) x))
(* -1 (/ (- (+ (* 1/16 (/ 1 (* (pow x 2) (pow (sqrt -1) 6)))) (+ (* 5/128 (/ 1 (* (pow x 3) (pow (sqrt -1) 8)))) (* 1/2 (/ 1 (pow (sqrt -1) 2))))) (/ -1/8 (* x (pow (sqrt -1) 4)))) x))
(* -1/2 (sqrt (/ 1 x)))
(* -1 (/ (+ (* -1/8 (* (sqrt (/ 1 x)) (/ 1 (pow (sqrt -1) 2)))) (* 1/2 (sqrt x))) x))
(* -1 (/ (+ (* -1/8 (* (sqrt (/ 1 x)) (/ 1 (pow (sqrt -1) 2)))) (+ (* 1/16 (* (sqrt (/ 1 (pow x 3))) (/ 1 (pow (sqrt -1) 4)))) (* 1/2 (sqrt x)))) x))
(* -1 (/ (+ (* -1/8 (* (sqrt (/ 1 x)) (/ 1 (pow (sqrt -1) 2)))) (+ (* -5/128 (* (sqrt (/ 1 (pow x 5))) (/ 1 (pow (sqrt -1) 6)))) (+ (* 1/16 (* (sqrt (/ 1 (pow x 3))) (/ 1 (pow (sqrt -1) 4)))) (* 1/2 (sqrt x))))) x))
(* -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)))))))
(/ (+ (* 1/4 (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))) (* 1/2 (sqrt x))) (pow x 2))
(/ (+ (* -1 (/ (+ (* -1 (/ (+ (* -1/4 (* (sqrt x) (+ (* -1 (pow (sqrt -1) 4)) (* 1/4 (pow (sqrt -1) 4))))) (* -1/8 (* (sqrt (pow x 3)) (/ 1 (pow (sqrt -1) 2))))) x)) (* -1/4 (* (sqrt x) (pow (sqrt -1) 2)))) x)) (* 1/2 (sqrt x))) (pow x 2))
(/ (+ (* -1 (/ (+ (* -1 (/ (+ (* -1 (/ (+ (* -1/4 (* (sqrt x) (+ (* 1/2 (* (pow (sqrt -1) 2) (+ (* -1 (pow (sqrt -1) 4)) (* 1/4 (pow (sqrt -1) 4))))) (pow (sqrt -1) 6)))) (* 1/16 (sqrt (pow x 3)))) x)) (+ (* -1/4 (* (sqrt x) (+ (* -1 (pow (sqrt -1) 4)) (* 1/4 (pow (sqrt -1) 4))))) (* -1/8 (* (sqrt (pow x 3)) (/ 1 (pow (sqrt -1) 2)))))) x)) (* -1/4 (* (sqrt x) (pow (sqrt -1) 2)))) x)) (* 1/2 (sqrt x))) (pow x 2))
(+ 1/2 (* -1 (/ (- 3/8 (* 5/16 (/ 1 x))) x)))
(+ 1/2 (* -1 (/ (+ 3/8 (* -1 (/ (- 5/16 (* 1/4 (/ 1 x))) x))) x)))
Outputs
-1/4
#s(literal -1/4 binary64)
(- (* -1/16 x) 1/4)
(-.f64 (*.f64 #s(literal -1/16 binary64) x) #s(literal 1/4 binary64))
(* (sqrt (/ 1 x)) (- 1 (sqrt x)))
(*.f64 (-.f64 #s(literal 1 binary64) (sqrt.f64 x)) (sqrt.f64 (/.f64 #s(literal 1 binary64) x)))
(/ (+ (* 1/2 (sqrt (pow x 3))) (* (sqrt x) (- 1 (sqrt x)))) x)
(/.f64 (fma.f64 (sqrt.f64 (pow.f64 x #s(literal 3 binary64))) #s(literal 1/2 binary64) (*.f64 (-.f64 #s(literal 1 binary64) (sqrt.f64 x)) (sqrt.f64 x))) x)
(/ (+ (* x (+ (* 1/2 (sqrt x)) (* x (+ (* -1/2 (* (sqrt (/ 1 x)) (- 1 (sqrt x)))) (* -1/8 (sqrt x)))))) (* (sqrt x) (- 1 (sqrt x)))) x)
(/.f64 (fma.f64 (fma.f64 (fma.f64 (*.f64 #s(literal -1/2 binary64) (-.f64 #s(literal 1 binary64) (sqrt.f64 x))) (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) (*.f64 #s(literal -1/8 binary64) (sqrt.f64 x))) x (*.f64 #s(literal 1/2 binary64) (sqrt.f64 x))) x (*.f64 (-.f64 #s(literal 1 binary64) (sqrt.f64 x)) (sqrt.f64 x))) x)
(/ (+ (* x (+ (* 1/2 (sqrt x)) (* x (+ (* -1/2 (* (sqrt (/ 1 x)) (- 1 (sqrt x)))) (+ (* -1/8 (sqrt x)) (* x (+ (* -1/4 (sqrt (/ 1 x))) (+ (* 1/16 (sqrt x)) (* 1/2 (* (sqrt (/ 1 x)) (- 1 (sqrt x)))))))))))) (* (sqrt x) (- 1 (sqrt x)))) x)
(/.f64 (fma.f64 (fma.f64 (fma.f64 (fma.f64 (*.f64 (-.f64 #s(literal 1 binary64) (sqrt.f64 x)) #s(literal 1/2 binary64)) (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) (fma.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) #s(literal -1/4 binary64) (*.f64 #s(literal 1/16 binary64) (sqrt.f64 x)))) x (fma.f64 (*.f64 #s(literal -1/2 binary64) (-.f64 #s(literal 1 binary64) (sqrt.f64 x))) (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) (*.f64 #s(literal -1/8 binary64) (sqrt.f64 x)))) x (*.f64 #s(literal 1/2 binary64) (sqrt.f64 x))) x (*.f64 (-.f64 #s(literal 1 binary64) (sqrt.f64 x)) (sqrt.f64 x))) x)
(- 1 (sqrt x))
(-.f64 #s(literal 1 binary64) (sqrt.f64 x))
(- (+ 1 (* x (+ 1/2 (* -1/2 (- 1 (sqrt x)))))) (sqrt x))
(fma.f64 (fma.f64 #s(literal -1/2 binary64) (-.f64 #s(literal 1 binary64) (sqrt.f64 x)) #s(literal 1/2 binary64)) x (-.f64 #s(literal 1 binary64) (sqrt.f64 x)))
(- (+ 1 (* x (+ 1/2 (+ (* -1/2 (- 1 (sqrt x))) (* x (- (* 3/8 (- 1 (sqrt x))) 3/8)))))) (sqrt x))
(fma.f64 (fma.f64 (-.f64 (*.f64 (-.f64 #s(literal 1 binary64) (sqrt.f64 x)) #s(literal 3/8 binary64)) #s(literal 3/8 binary64)) x (fma.f64 #s(literal -1/2 binary64) (-.f64 #s(literal 1 binary64) (sqrt.f64 x)) #s(literal 1/2 binary64))) x (-.f64 #s(literal 1 binary64) (sqrt.f64 x)))
(- (+ 1 (* x (+ 1/2 (+ (* -1/2 (- 1 (sqrt x))) (* x (- (+ (* 3/8 (- 1 (sqrt x))) (* x (+ 5/16 (* -5/16 (- 1 (sqrt x)))))) 3/8)))))) (sqrt x))
(fma.f64 (fma.f64 (fma.f64 (fma.f64 #s(literal -5/16 binary64) (-.f64 #s(literal 1 binary64) (sqrt.f64 x)) #s(literal 5/16 binary64)) x (-.f64 (*.f64 (-.f64 #s(literal 1 binary64) (sqrt.f64 x)) #s(literal 3/8 binary64)) #s(literal 3/8 binary64))) x (fma.f64 #s(literal -1/2 binary64) (-.f64 #s(literal 1 binary64) (sqrt.f64 x)) #s(literal 1/2 binary64))) x (-.f64 #s(literal 1 binary64) (sqrt.f64 x)))
(/ -1/4 (pow x 4))
(/.f64 #s(literal -1/4 binary64) (pow.f64 x #s(literal 4 binary64)))
(/ (- (* 5/16 x) 1/4) (pow x 4))
(/.f64 (-.f64 (*.f64 #s(literal 5/16 binary64) x) #s(literal 1/4 binary64)) (pow.f64 x #s(literal 4 binary64)))
(/ (- (* x (+ 5/16 (* -3/8 x))) 1/4) (pow x 4))
(/.f64 (-.f64 (*.f64 (fma.f64 #s(literal -3/8 binary64) x #s(literal 5/16 binary64)) x) #s(literal 1/4 binary64)) (pow.f64 x #s(literal 4 binary64)))
(/ (- (* x (+ 5/16 (* x (- (* 1/2 x) 3/8)))) 1/4) (pow x 4))
(/.f64 (-.f64 (*.f64 (fma.f64 (-.f64 (*.f64 #s(literal 1/2 binary64) x) #s(literal 3/8 binary64)) x #s(literal 5/16 binary64)) x) #s(literal 1/4 binary64)) (pow.f64 x #s(literal 4 binary64)))
(sqrt (/ 1 x))
(sqrt.f64 (/.f64 #s(literal 1 binary64) x))
(/ (+ (sqrt x) (* -1 x)) x)
(/.f64 (-.f64 (sqrt.f64 x) x) x)
(/ (+ (sqrt x) (* x (- (* 1/2 x) 1))) x)
(/.f64 (fma.f64 (-.f64 (*.f64 #s(literal 1/2 binary64) x) #s(literal 1 binary64)) x (sqrt.f64 x)) x)
(/ (+ (sqrt x) (* x (- (* x (+ 1/2 (* -3/8 x))) 1))) x)
(/.f64 (fma.f64 (-.f64 (*.f64 (fma.f64 #s(literal -3/8 binary64) x #s(literal 1/2 binary64)) x) #s(literal 1 binary64)) x (sqrt.f64 x)) x)
(sqrt x)
(sqrt.f64 x)
(/ 1/4 (pow x 3))
(/.f64 #s(literal 1/4 binary64) (pow.f64 x #s(literal 3 binary64)))
(/ (+ 1/4 (* -3/8 x)) (pow x 3))
(/.f64 (fma.f64 #s(literal -3/8 binary64) x #s(literal 1/4 binary64)) (pow.f64 x #s(literal 3 binary64)))
(/ (+ 1/4 (* x (- (* 1/2 x) 3/8))) (pow x 3))
(/.f64 (fma.f64 (-.f64 (*.f64 #s(literal 1/2 binary64) x) #s(literal 3/8 binary64)) x #s(literal 1/4 binary64)) (pow.f64 x #s(literal 3 binary64)))
(/ 1/4 (pow x 2))
(/.f64 #s(literal 1/4 binary64) (*.f64 x x))
(/ (+ 1/4 (* -3/8 x)) (pow x 2))
(/.f64 (/.f64 (fma.f64 #s(literal -3/8 binary64) x #s(literal 1/4 binary64)) x) x)
(/ (+ 1/4 (* x (- (* 1/2 x) 3/8))) (pow x 2))
(/.f64 (/.f64 (fma.f64 (-.f64 (*.f64 #s(literal 1/2 binary64) x) #s(literal 3/8 binary64)) x #s(literal 1/4 binary64)) x) x)
(/ (+ (* x (+ (* -1/8 (sqrt (pow x 3))) (* 1/2 (sqrt x)))) (* (sqrt x) (- 1 (sqrt x)))) x)
(/.f64 (fma.f64 (fma.f64 #s(literal -1/8 binary64) (sqrt.f64 (pow.f64 x #s(literal 3 binary64))) (*.f64 #s(literal 1/2 binary64) (sqrt.f64 x))) x (*.f64 (-.f64 #s(literal 1 binary64) (sqrt.f64 x)) (sqrt.f64 x))) x)
(/ (+ (* x (+ (* 1/2 (sqrt x)) (* x (+ (* -1/8 (sqrt x)) (* 1/16 (sqrt (pow x 3))))))) (* (sqrt x) (- 1 (sqrt x)))) x)
(/.f64 (fma.f64 (fma.f64 (fma.f64 #s(literal 1/16 binary64) (sqrt.f64 (pow.f64 x #s(literal 3 binary64))) (*.f64 #s(literal -1/8 binary64) (sqrt.f64 x))) x (*.f64 #s(literal 1/2 binary64) (sqrt.f64 x))) x (*.f64 (-.f64 #s(literal 1 binary64) (sqrt.f64 x)) (sqrt.f64 x))) x)
(- (+ 1 (* 1/2 x)) (sqrt x))
(fma.f64 #s(literal 1/2 binary64) x (-.f64 #s(literal 1 binary64) (sqrt.f64 x)))
(- (+ 1 (* x (+ 1/2 (* -1/8 x)))) (sqrt x))
(fma.f64 (fma.f64 #s(literal -1/8 binary64) x #s(literal 1/2 binary64)) x (-.f64 #s(literal 1 binary64) (sqrt.f64 x)))
(- (+ 1 (* x (+ 1/2 (* x (- (* 1/16 x) 1/8))))) (sqrt x))
(fma.f64 (fma.f64 (-.f64 (*.f64 #s(literal 1/16 binary64) x) #s(literal 1/8 binary64)) x #s(literal 1/2 binary64)) x (-.f64 #s(literal 1 binary64) (sqrt.f64 x)))
1
#s(literal 1 binary64)
(+ 1 (* 1/2 x))
(fma.f64 #s(literal 1/2 binary64) x #s(literal 1 binary64))
(+ 1 (* x (+ 1/2 (* -1/8 x))))
(fma.f64 (fma.f64 #s(literal -1/8 binary64) x #s(literal 1/2 binary64)) x #s(literal 1 binary64))
(+ 1 (* x (+ 1/2 (* x (- (* 1/16 x) 1/8)))))
(fma.f64 (fma.f64 (-.f64 (*.f64 #s(literal 1/16 binary64) x) #s(literal 1/8 binary64)) x #s(literal 1/2 binary64)) x #s(literal 1 binary64))
(* 1/2 (sqrt (/ 1 x)))
(*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) #s(literal 1/2 binary64))
(/ -1/4 (pow x 3))
(/.f64 #s(literal -1/4 binary64) (pow.f64 x #s(literal 3 binary64)))
(/ (- (* 5/16 x) 1/4) (pow x 3))
(/.f64 (fma.f64 #s(literal 5/16 binary64) x #s(literal -1/4 binary64)) (pow.f64 x #s(literal 3 binary64)))
(/ (- (* x (+ 5/16 (* -3/8 x))) 1/4) (pow x 3))
(/.f64 (fma.f64 (fma.f64 #s(literal -3/8 binary64) x #s(literal 5/16 binary64)) x #s(literal -1/4 binary64)) (pow.f64 x #s(literal 3 binary64)))
(/ (- (* x (+ 5/16 (* x (- (* 1/2 x) 3/8)))) 1/4) (pow x 3))
(/.f64 (fma.f64 (fma.f64 (-.f64 (*.f64 #s(literal 1/2 binary64) x) #s(literal 3/8 binary64)) x #s(literal 5/16 binary64)) x #s(literal -1/4 binary64)) (pow.f64 x #s(literal 3 binary64)))
(* -1/16 x)
(*.f64 #s(literal -1/16 binary64) x)
(* -1 (* x (+ 1/16 (* 1/4 (/ 1 x)))))
(*.f64 (neg.f64 x) (+.f64 (/.f64 #s(literal 1/4 binary64) x) #s(literal 1/16 binary64)))
(* 1/2 (sqrt (/ 1 (pow x 3))))
(*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 3 binary64)))) #s(literal 1/2 binary64))
(/ (+ (* -1/4 (sqrt (/ 1 x))) (* 1/2 (sqrt x))) (pow x 2))
(/.f64 (fma.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) #s(literal -1/4 binary64) (*.f64 #s(literal 1/2 binary64) (sqrt.f64 x))) (*.f64 x x))
(/ (+ (* -1/4 (sqrt (/ 1 x))) (+ (* -1/8 (sqrt (/ 1 x))) (+ (* 3/16 (sqrt (/ 1 (pow x 3)))) (* 1/2 (sqrt x))))) (pow x 2))
(/.f64 (fma.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) #s(literal -3/8 binary64) (fma.f64 #s(literal 3/16 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 3 binary64)))) (*.f64 #s(literal 1/2 binary64) (sqrt.f64 x)))) (*.f64 x x))
(/ (+ (* -1/4 (sqrt (/ 1 x))) (+ (* -5/32 (sqrt (/ 1 (pow x 5)))) (+ (* -1/8 (sqrt (/ 1 x))) (+ (* 1/16 (sqrt (/ 1 (pow x 3)))) (+ (* 3/16 (sqrt (/ 1 (pow x 3)))) (* 1/2 (sqrt x))))))) (pow x 2))
(/.f64 (fma.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) #s(literal -1/4 binary64) (fma.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 5 binary64)))) #s(literal -5/32 binary64) (fma.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 3 binary64)))) #s(literal 1/4 binary64) (fma.f64 #s(literal -1/8 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) (*.f64 #s(literal 1/2 binary64) (sqrt.f64 x)))))) (*.f64 x x))
(/ 1/2 x)
(/.f64 #s(literal 1/2 binary64) x)
(/ (+ 1/2 (* -1 (/ (+ (* 1/8 x) (* 1/4 x)) (pow x 2)))) x)
(/.f64 (-.f64 #s(literal 1/2 binary64) (*.f64 (/.f64 x x) (/.f64 #s(literal 3/8 binary64) x))) x)
(/ (- (+ 1/2 (* 1/4 (/ 1 (pow x 2)))) (+ (/ 1/8 x) (/ 1/4 x))) x)
(/.f64 (+.f64 (/.f64 (-.f64 (/.f64 #s(literal 1/4 binary64) x) #s(literal 3/8 binary64)) x) #s(literal 1/2 binary64)) x)
(/ (- (+ 1/2 (+ (* -1/4 (/ (+ 1 (* 1/4 x)) (pow x 3))) (* 3/8 (/ 1 (pow x 2))))) (+ (/ 1/8 x) (/ 1/4 x))) x)
(/.f64 (-.f64 (+.f64 (/.f64 (+.f64 #s(literal 3/8 binary64) (/.f64 (*.f64 (fma.f64 #s(literal 1/4 binary64) x #s(literal 1 binary64)) #s(literal -1/4 binary64)) x)) (*.f64 x x)) #s(literal 1/2 binary64)) (/.f64 #s(literal 3/8 binary64) x)) x)
(/ (- 1/2 (* 3/8 (/ 1 x))) x)
(/.f64 (-.f64 #s(literal 1/2 binary64) (/.f64 #s(literal 3/8 binary64) x)) x)
(/ (- (+ 1/2 (/ 5/16 (pow x 2))) (* 3/8 (/ 1 x))) x)
(/.f64 (+.f64 (/.f64 (-.f64 (/.f64 #s(literal 5/16 binary64) x) #s(literal 3/8 binary64)) x) #s(literal 1/2 binary64)) x)
(/ (- (+ 1/2 (/ 5/16 (pow x 2))) (+ (* 3/8 (/ 1 x)) (* 1/4 (/ 1 (pow x 3))))) x)
(/.f64 (-.f64 (+.f64 (/.f64 (-.f64 (/.f64 #s(literal 5/16 binary64) x) #s(literal 3/8 binary64)) x) #s(literal 1/2 binary64)) (/.f64 #s(literal 1/4 binary64) (pow.f64 x #s(literal 3 binary64)))) x)
(/ (- (* -1/2 (sqrt (/ 1 x))) (* -1/2 (sqrt x))) (pow x 2))
(*.f64 #s(literal -1/2 binary64) (/.f64 (-.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) (sqrt.f64 x)) (*.f64 x x)))
(/ (- (* 1/2 (* (sqrt (/ 1 (pow x 3))) (+ 1 (* 1/4 x)))) (+ (* -1/2 (sqrt x)) (* 1/2 (sqrt (/ 1 x))))) (pow x 2))
(/.f64 (-.f64 (*.f64 (*.f64 #s(literal 1/2 binary64) (fma.f64 #s(literal 1/4 binary64) x #s(literal 1 binary64))) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 3 binary64))))) (*.f64 #s(literal -1/2 binary64) (-.f64 (sqrt.f64 x) (sqrt.f64 (/.f64 #s(literal 1 binary64) x))))) (*.f64 x x))
(/ (- (* -1/2 (* (sqrt (/ 1 (pow x 5))) (+ 1 (* 1/2 x)))) (+ (* -1/2 (sqrt x)) (+ (* -1/2 (* (sqrt (/ 1 (pow x 3))) (+ 1 (* 1/4 x)))) (* 1/2 (sqrt (/ 1 x)))))) (pow x 2))
(/.f64 (-.f64 (*.f64 #s(literal -1/2 binary64) (-.f64 (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 5 binary64)))) (fma.f64 #s(literal 1/2 binary64) x #s(literal 1 binary64))) (sqrt.f64 x))) (*.f64 #s(literal -1/2 binary64) (-.f64 (*.f64 (fma.f64 #s(literal 1/4 binary64) x #s(literal 1 binary64)) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 3 binary64))))) (sqrt.f64 (/.f64 #s(literal 1 binary64) x))))) (*.f64 x x))
(/ (- (+ 1/2 (/ 1/4 (pow x 2))) (* 3/8 (/ 1 x))) x)
(/.f64 (+.f64 (/.f64 (-.f64 (/.f64 #s(literal 1/4 binary64) x) #s(literal 3/8 binary64)) x) #s(literal 1/2 binary64)) x)
1/2
#s(literal 1/2 binary64)
(- 1/2 (* 3/8 (/ 1 x)))
(-.f64 #s(literal 1/2 binary64) (/.f64 #s(literal 3/8 binary64) x))
(- (+ 1/2 (/ 1/4 (pow x 2))) (* 3/8 (/ 1 x)))
(+.f64 (/.f64 (-.f64 (/.f64 #s(literal 1/4 binary64) x) #s(literal 3/8 binary64)) x) #s(literal 1/2 binary64))
(/ (- 1/2 (* 1/8 (/ 1 x))) x)
(/.f64 (-.f64 #s(literal 1/2 binary64) (/.f64 #s(literal 1/8 binary64) x)) x)
(/ (- (+ 1/2 (* 1/16 (/ 1 (pow x 2)))) (/ 1/8 x)) x)
(/.f64 (+.f64 (/.f64 (+.f64 (/.f64 #s(literal 1/16 binary64) x) #s(literal -1/8 binary64)) x) #s(literal 1/2 binary64)) x)
(/ (- (+ 1/2 (* 1/16 (/ 1 (pow x 2)))) (+ (/ 1/8 x) (* 5/128 (/ 1 (pow x 3))))) x)
(/.f64 (-.f64 (+.f64 (/.f64 (+.f64 (/.f64 #s(literal 1/16 binary64) x) #s(literal -1/8 binary64)) x) #s(literal 1/2 binary64)) (/.f64 #s(literal 5/128 binary64) (pow.f64 x #s(literal 3 binary64)))) x)
(/ (+ (* -1/8 (sqrt (/ 1 x))) (* 1/2 (sqrt x))) x)
(/.f64 (fma.f64 #s(literal -1/8 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) (*.f64 #s(literal 1/2 binary64) (sqrt.f64 x))) x)
(/ (+ (* -1/8 (sqrt (/ 1 x))) (+ (* 1/16 (sqrt (/ 1 (pow x 3)))) (* 1/2 (sqrt x)))) x)
(/.f64 (fma.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 3 binary64)))) #s(literal 1/16 binary64) (fma.f64 #s(literal -1/8 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) (*.f64 #s(literal 1/2 binary64) (sqrt.f64 x)))) x)
(/ (+ (* -1/8 (sqrt (/ 1 x))) (+ (* -5/128 (sqrt (/ 1 (pow x 5)))) (+ (* 1/16 (sqrt (/ 1 (pow x 3)))) (* 1/2 (sqrt x))))) x)
(/.f64 (fma.f64 #s(literal -5/128 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 5 binary64)))) (fma.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 3 binary64)))) #s(literal 1/16 binary64) (fma.f64 #s(literal -1/8 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) (*.f64 #s(literal 1/2 binary64) (sqrt.f64 x))))) x)
(* x (+ (sqrt (/ 1 x)) (* 1/2 (sqrt (/ 1 (pow x 3))))))
(*.f64 (fma.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 3 binary64)))) #s(literal 1/2 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) x))) x)
(* x (+ (sqrt (/ 1 x)) (+ (* -1/8 (sqrt (/ 1 (pow x 5)))) (* 1/2 (sqrt (/ 1 (pow x 3)))))))
(*.f64 (fma.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 5 binary64)))) #s(literal -1/8 binary64) (fma.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 3 binary64)))) #s(literal 1/2 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) x)))) x)
(* 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 (+.f64 (fma.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 7 binary64)))) #s(literal 1/16 binary64) (fma.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 5 binary64)))) #s(literal -1/8 binary64) (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 3 binary64)))) #s(literal 1/2 binary64)))) (sqrt.f64 (/.f64 #s(literal 1 binary64) x))) x)
(/ 5/16 (pow x 2))
(/.f64 #s(literal 5/16 binary64) (*.f64 x x))
(/ (- 5/16 (* 1/4 (/ 1 x))) (pow x 2))
(/.f64 (/.f64 (-.f64 #s(literal 5/16 binary64) (/.f64 #s(literal 1/4 binary64) x)) x) x)
(- (+ 1/2 (/ 5/16 (pow x 2))) (* 3/8 (/ 1 x)))
(+.f64 (/.f64 (-.f64 (/.f64 #s(literal 5/16 binary64) x) #s(literal 3/8 binary64)) x) #s(literal 1/2 binary64))
(- (+ 1/2 (/ 5/16 (pow x 2))) (+ (* 3/8 (/ 1 x)) (* 1/4 (/ 1 (pow x 3)))))
(-.f64 (+.f64 (/.f64 (-.f64 (/.f64 #s(literal 5/16 binary64) x) #s(literal 3/8 binary64)) x) #s(literal 1/2 binary64)) (/.f64 #s(literal 1/4 binary64) (pow.f64 x #s(literal 3 binary64))))
(/ (+ (* 1/4 (* (sqrt (/ 1 x)) (/ 1 (pow (sqrt -1) 2)))) (* 1/2 (sqrt x))) (pow x 2))
(/.f64 (fma.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) #s(literal -1/4 binary64) (*.f64 #s(literal 1/2 binary64) (sqrt.f64 x))) (*.f64 x x))
(/ (+ (* -1 (/ (+ (* -1 (/ (+ (* -1/4 (* (sqrt x) (/ (+ 1 (* 1/4 (/ 1 (pow (sqrt -1) 2)))) (pow (sqrt -1) 2)))) (* -1/8 (* (sqrt (pow x 3)) (/ 1 (pow (sqrt -1) 2))))) x)) (* -1/4 (* (sqrt x) (/ 1 (pow (sqrt -1) 2))))) x)) (* 1/2 (sqrt x))) (pow x 2))
(/.f64 (fma.f64 #s(literal 1/2 binary64) (sqrt.f64 x) (/.f64 (fma.f64 #s(literal 1/4 binary64) (sqrt.f64 x) (/.f64 (fma.f64 #s(literal 1/8 binary64) (sqrt.f64 (pow.f64 x #s(literal 3 binary64))) (*.f64 #s(literal 3/16 binary64) (sqrt.f64 x))) (neg.f64 x))) (neg.f64 x))) (*.f64 x x))
(/ (+ (* -1 (/ (+ (* -1 (/ (+ (* -1 (/ (+ (* -1/4 (* (sqrt x) (/ (+ 1 (* 1/2 (/ (+ 1 (* 1/4 (/ 1 (pow (sqrt -1) 2)))) (pow (sqrt -1) 2)))) (pow (sqrt -1) 2)))) (* 1/16 (* (sqrt (pow x 3)) (/ 1 (pow (sqrt -1) 4))))) x)) (+ (* -1/4 (* (sqrt x) (/ (+ 1 (* 1/4 (/ 1 (pow (sqrt -1) 2)))) (pow (sqrt -1) 2)))) (* -1/8 (* (sqrt (pow x 3)) (/ 1 (pow (sqrt -1) 2)))))) x)) (* -1/4 (* (sqrt x) (/ 1 (pow (sqrt -1) 2))))) x)) (* 1/2 (sqrt x))) (pow x 2))
(/.f64 (fma.f64 #s(literal 1/2 binary64) (sqrt.f64 x) (/.f64 (fma.f64 #s(literal 1/4 binary64) (sqrt.f64 x) (/.f64 (fma.f64 #s(literal 1/8 binary64) (sqrt.f64 (pow.f64 x #s(literal 3 binary64))) (fma.f64 #s(literal 3/16 binary64) (sqrt.f64 x) (/.f64 (fma.f64 (/.f64 (sqrt.f64 (pow.f64 x #s(literal 3 binary64))) (pow.f64 (sqrt.f64 #s(literal -1 binary64)) #s(literal 4 binary64))) #s(literal 1/16 binary64) (*.f64 #s(literal 5/32 binary64) (sqrt.f64 x))) (neg.f64 x)))) (neg.f64 x))) (neg.f64 x))) (*.f64 x x))
(/ -1/2 x)
(/.f64 #s(literal -1/2 binary64) x)
(* -1 (/ (+ 1/2 (* -1 (/ (+ (* -1/4 (/ x (pow (sqrt -1) 2))) (* -1/8 (/ x (pow (sqrt -1) 2)))) (pow x 2)))) x))
(/.f64 (-.f64 #s(literal 1/2 binary64) (*.f64 (/.f64 (/.f64 x #s(literal -1 binary64)) x) (/.f64 #s(literal -3/8 binary64) x))) (neg.f64 x))
(* -1 (/ (+ 1/2 (* -1 (/ (+ (* -1/4 (/ x (pow (sqrt -1) 2))) (+ (* -1/8 (/ x (pow (sqrt -1) 2))) (* 1/4 (/ 1 (pow (sqrt -1) 2))))) (pow x 2)))) x))
(/.f64 (-.f64 #s(literal 1/2 binary64) (/.f64 (/.f64 (fma.f64 (/.f64 x #s(literal -1 binary64)) #s(literal -3/8 binary64) #s(literal -1/4 binary64)) x) x)) (neg.f64 x))
(* -1 (/ (- (+ 1/2 (* -1 (/ (- (* -1 (/ (+ (* 1/8 (/ (pow x 2) (pow (sqrt -1) 4))) (* 1/4 (/ (* x (+ 1 (* -1/4 (/ x (pow (sqrt -1) 2))))) (pow (sqrt -1) 2)))) x)) (* -1/4 (/ x (pow (sqrt -1) 2)))) (pow x 3)))) (+ (/ -1/4 (* x (pow (sqrt -1) 2))) (/ -1/8 (* x (pow (sqrt -1) 2))))) x))
(/.f64 (-.f64 #s(literal 1/2 binary64) (+.f64 (/.f64 (fma.f64 (/.f64 x #s(literal -1 binary64)) #s(literal 1/4 binary64) (/.f64 (fma.f64 (/.f64 (*.f64 (fma.f64 (/.f64 x #s(literal -1 binary64)) #s(literal -1/4 binary64) #s(literal 1 binary64)) x) #s(literal -1 binary64)) #s(literal 1/4 binary64) (/.f64 (*.f64 (*.f64 #s(literal 1/8 binary64) x) x) (pow.f64 (sqrt.f64 #s(literal -1 binary64)) #s(literal 4 binary64)))) (neg.f64 x))) (pow.f64 x #s(literal 3 binary64))) (/.f64 #s(literal 3/8 binary64) x))) (neg.f64 x))
(* -1 (/ (- (* 3/8 (/ 1 x)) 1/2) x))
(/.f64 (-.f64 (/.f64 #s(literal 3/8 binary64) x) #s(literal 1/2 binary64)) (neg.f64 x))
(* -1 (/ (- (* -1 (/ (- (* 5/16 (/ 1 x)) 3/8) x)) 1/2) x))
(/.f64 (-.f64 (/.f64 (-.f64 (/.f64 #s(literal 5/16 binary64) x) #s(literal 3/8 binary64)) (neg.f64 x)) #s(literal 1/2 binary64)) (neg.f64 x))
(* -1 (/ (- (* -1 (/ (- (* -1 (/ (- (* 1/4 (/ 1 x)) 5/16) x)) 3/8) x)) 1/2) x))
(/.f64 (-.f64 (/.f64 (-.f64 (/.f64 (-.f64 (/.f64 #s(literal 1/4 binary64) x) #s(literal 5/16 binary64)) (neg.f64 x)) #s(literal 3/8 binary64)) (neg.f64 x)) #s(literal 1/2 binary64)) (neg.f64 x))
(- (sqrt (/ 1 x)) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)))
(+.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) (sqrt.f64 (/.f64 #s(literal 1 binary64) x)))
(- (+ (sqrt (/ 1 x)) (* 1/2 (sqrt (/ 1 (pow x 3))))) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)))
(fma.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 3 binary64)))) #s(literal 1/2 binary64) (+.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) (sqrt.f64 (/.f64 #s(literal 1 binary64) x))))
(- (+ (sqrt (/ 1 x)) (* -1/2 (sqrt (/ 1 (pow x 5))))) (+ (* -1/2 (sqrt (/ 1 (pow x 3)))) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))))
(fma.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 5 binary64)))) #s(literal -1/2 binary64) (fma.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 3 binary64)))) #s(literal 1/2 binary64) (+.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) (sqrt.f64 (/.f64 #s(literal 1 binary64) x)))))
(- (+ (sqrt (/ 1 x)) (* -1 (/ (- (* -1/2 (* (sqrt (/ 1 x)) (+ 1 (* -1/4 (/ x (pow (sqrt -1) 2)))))) (* -1/2 (sqrt x))) (pow x 3)))) (+ (* -1/2 (sqrt (/ 1 (pow x 3)))) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))))
(-.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) (fma.f64 #s(literal -1/2 binary64) (/.f64 (-.f64 (*.f64 (fma.f64 (/.f64 x #s(literal -1 binary64)) #s(literal -1/4 binary64) #s(literal 1 binary64)) (sqrt.f64 (/.f64 #s(literal 1 binary64) x))) (sqrt.f64 x)) (pow.f64 x #s(literal 3 binary64))) (-.f64 (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 3 binary64)))) #s(literal -1/2 binary64)) (sqrt.f64 (/.f64 #s(literal 1 binary64) x)))))
(* -1 (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)))
(sqrt.f64 (/.f64 #s(literal 1 binary64) x))
(* -1 (* (sqrt x) (pow (sqrt -1) 2)))
(sqrt.f64 x)
(* -1 (/ (- (* -1 (/ (- (* 1/4 (/ 1 x)) 3/8) x)) 1/2) x))
(/.f64 (-.f64 (/.f64 (-.f64 (/.f64 #s(literal 1/4 binary64) x) #s(literal 3/8 binary64)) (neg.f64 x)) #s(literal 1/2 binary64)) (neg.f64 x))
(+ 1/2 (* -1 (/ (- 3/8 (* 1/4 (/ 1 x))) x)))
(-.f64 #s(literal 1/2 binary64) (/.f64 (-.f64 #s(literal 3/8 binary64) (/.f64 #s(literal 1/4 binary64) x)) x))
(/ -1/2 (* x (pow (sqrt -1) 2)))
(/.f64 #s(literal 1/2 binary64) x)
(* -1 (/ (+ (* 1/8 (/ 1 (* x (pow (sqrt -1) 4)))) (* 1/2 (/ 1 (pow (sqrt -1) 2)))) x))
(/.f64 (fma.f64 (/.f64 #s(literal 1/8 binary64) (*.f64 (pow.f64 (sqrt.f64 #s(literal -1 binary64)) #s(literal 4 binary64)) x)) #s(literal -1 binary64) #s(literal 1/2 binary64)) x)
(* -1 (/ (- (+ (/ 1/16 (* (pow x 2) (pow (sqrt -1) 6))) (* 1/2 (/ 1 (pow (sqrt -1) 2)))) (/ -1/8 (* x (pow (sqrt -1) 4)))) x))
(/.f64 (-.f64 (/.f64 (/.f64 #s(literal 1/16 binary64) (pow.f64 (sqrt.f64 #s(literal -1 binary64)) #s(literal 6 binary64))) (*.f64 x x)) (+.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/8 binary64) (*.f64 (pow.f64 (sqrt.f64 #s(literal -1 binary64)) #s(literal 4 binary64)) x)))) (neg.f64 x))
(* -1 (/ (- (+ (* 1/16 (/ 1 (* (pow x 2) (pow (sqrt -1) 6)))) (+ (* 5/128 (/ 1 (* (pow x 3) (pow (sqrt -1) 8)))) (* 1/2 (/ 1 (pow (sqrt -1) 2))))) (/ -1/8 (* x (pow (sqrt -1) 4)))) x))
(/.f64 (+.f64 (-.f64 (/.f64 (/.f64 #s(literal 5/128 binary64) (pow.f64 (sqrt.f64 #s(literal -1 binary64)) #s(literal 8 binary64))) (pow.f64 x #s(literal 3 binary64))) (+.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/8 binary64) (*.f64 (pow.f64 (sqrt.f64 #s(literal -1 binary64)) #s(literal 4 binary64)) x)))) (/.f64 (/.f64 #s(literal 1/16 binary64) (pow.f64 (sqrt.f64 #s(literal -1 binary64)) #s(literal 6 binary64))) (*.f64 x x))) (neg.f64 x))
(* -1/2 (sqrt (/ 1 x)))
(*.f64 #s(literal -1/2 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) x)))
(* -1 (/ (+ (* -1/8 (* (sqrt (/ 1 x)) (/ 1 (pow (sqrt -1) 2)))) (* 1/2 (sqrt x))) x))
(/.f64 (fma.f64 #s(literal 1/8 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) (*.f64 #s(literal 1/2 binary64) (sqrt.f64 x))) (neg.f64 x))
(* -1 (/ (+ (* -1/8 (* (sqrt (/ 1 x)) (/ 1 (pow (sqrt -1) 2)))) (+ (* 1/16 (* (sqrt (/ 1 (pow x 3))) (/ 1 (pow (sqrt -1) 4)))) (* 1/2 (sqrt x)))) x))
(/.f64 (fma.f64 (/.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 3 binary64)))) (pow.f64 (sqrt.f64 #s(literal -1 binary64)) #s(literal 4 binary64))) #s(literal 1/16 binary64) (fma.f64 #s(literal 1/8 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) (*.f64 #s(literal 1/2 binary64) (sqrt.f64 x)))) (neg.f64 x))
(* -1 (/ (+ (* -1/8 (* (sqrt (/ 1 x)) (/ 1 (pow (sqrt -1) 2)))) (+ (* -5/128 (* (sqrt (/ 1 (pow x 5))) (/ 1 (pow (sqrt -1) 6)))) (+ (* 1/16 (* (sqrt (/ 1 (pow x 3))) (/ 1 (pow (sqrt -1) 4)))) (* 1/2 (sqrt x))))) x))
(/.f64 (fma.f64 (/.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 5 binary64)))) (pow.f64 (sqrt.f64 #s(literal -1 binary64)) #s(literal 6 binary64))) #s(literal -5/128 binary64) (fma.f64 (/.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 3 binary64)))) (pow.f64 (sqrt.f64 #s(literal -1 binary64)) #s(literal 4 binary64))) #s(literal 1/16 binary64) (fma.f64 #s(literal 1/8 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) (*.f64 #s(literal 1/2 binary64) (sqrt.f64 x))))) (neg.f64 x))
(* -1 (* x (+ (* 1/2 (sqrt (/ 1 (pow x 3)))) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)))))
(*.f64 (neg.f64 x) (-.f64 (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 3 binary64)))) #s(literal 1/2 binary64)) (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 (neg.f64 x) (fma.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 5 binary64)))) #s(literal 1/8 binary64) (-.f64 (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 3 binary64)))) #s(literal 1/2 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 (neg.f64 x) (fma.f64 (/.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))) #s(literal 1/16 binary64) (fma.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 5 binary64)))) #s(literal 1/8 binary64) (-.f64 (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 3 binary64)))) #s(literal 1/2 binary64)) (sqrt.f64 (/.f64 #s(literal 1 binary64) x))))))
(/ (+ (* 1/4 (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))) (* 1/2 (sqrt x))) (pow x 2))
(/.f64 (fma.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) #s(literal -1/4 binary64) (*.f64 #s(literal 1/2 binary64) (sqrt.f64 x))) (*.f64 x x))
(/ (+ (* -1 (/ (+ (* -1 (/ (+ (* -1/4 (* (sqrt x) (+ (* -1 (pow (sqrt -1) 4)) (* 1/4 (pow (sqrt -1) 4))))) (* -1/8 (* (sqrt (pow x 3)) (/ 1 (pow (sqrt -1) 2))))) x)) (* -1/4 (* (sqrt x) (pow (sqrt -1) 2)))) x)) (* 1/2 (sqrt x))) (pow x 2))
(/.f64 (fma.f64 #s(literal 1/2 binary64) (sqrt.f64 x) (/.f64 (fma.f64 #s(literal 1/4 binary64) (sqrt.f64 x) (/.f64 (fma.f64 (*.f64 (*.f64 #s(literal -1/4 binary64) (sqrt.f64 x)) (pow.f64 (sqrt.f64 #s(literal -1 binary64)) #s(literal 4 binary64))) #s(literal -3/4 binary64) (*.f64 #s(literal 1/8 binary64) (sqrt.f64 (pow.f64 x #s(literal 3 binary64))))) (neg.f64 x))) (neg.f64 x))) (*.f64 x x))
(/ (+ (* -1 (/ (+ (* -1 (/ (+ (* -1 (/ (+ (* -1/4 (* (sqrt x) (+ (* 1/2 (* (pow (sqrt -1) 2) (+ (* -1 (pow (sqrt -1) 4)) (* 1/4 (pow (sqrt -1) 4))))) (pow (sqrt -1) 6)))) (* 1/16 (sqrt (pow x 3)))) x)) (+ (* -1/4 (* (sqrt x) (+ (* -1 (pow (sqrt -1) 4)) (* 1/4 (pow (sqrt -1) 4))))) (* -1/8 (* (sqrt (pow x 3)) (/ 1 (pow (sqrt -1) 2)))))) x)) (* -1/4 (* (sqrt x) (pow (sqrt -1) 2)))) x)) (* 1/2 (sqrt x))) (pow x 2))
(/.f64 (fma.f64 #s(literal 1/2 binary64) (sqrt.f64 x) (/.f64 (fma.f64 #s(literal 1/4 binary64) (sqrt.f64 x) (/.f64 (fma.f64 (*.f64 (*.f64 #s(literal -1/4 binary64) (sqrt.f64 x)) (pow.f64 (sqrt.f64 #s(literal -1 binary64)) #s(literal 4 binary64))) #s(literal -3/4 binary64) (fma.f64 #s(literal 1/8 binary64) (sqrt.f64 (pow.f64 x #s(literal 3 binary64))) (/.f64 (fma.f64 (*.f64 (fma.f64 (*.f64 (pow.f64 (sqrt.f64 #s(literal -1 binary64)) #s(literal 4 binary64)) #s(literal 3/4 binary64)) #s(literal 1/2 binary64) (pow.f64 (sqrt.f64 #s(literal -1 binary64)) #s(literal 6 binary64))) (sqrt.f64 x)) #s(literal -1/4 binary64) (*.f64 #s(literal 1/16 binary64) (sqrt.f64 (pow.f64 x #s(literal 3 binary64))))) (neg.f64 x)))) (neg.f64 x))) (neg.f64 x))) (*.f64 x x))
(+ 1/2 (* -1 (/ (- 3/8 (* 5/16 (/ 1 x))) x)))
(-.f64 #s(literal 1/2 binary64) (/.f64 (-.f64 #s(literal 3/8 binary64) (/.f64 #s(literal 5/16 binary64) x)) x))
(+ 1/2 (* -1 (/ (+ 3/8 (* -1 (/ (- 5/16 (* 1/4 (/ 1 x))) x))) x)))
(-.f64 #s(literal 1/2 binary64) (/.f64 (-.f64 #s(literal 3/8 binary64) (/.f64 (-.f64 #s(literal 5/16 binary64) (/.f64 #s(literal 1/4 binary64) x)) x)) x))

rewrite128.0ms (1.9%)

Memory
18.4MiB live, 154.4MiB allocated
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
047313
077313
1284275
22239259
09349254
Stop Event
iter limit
node limit
iter limit
Counts
20 → 285
Calls
Call 1
Inputs
(*.f64 (fma.f64 #s(literal 1/4 binary64) x #s(literal 1 binary64)) #s(literal -1/4 binary64))
(/.f64 #s(approx (/ (- (sqrt (+ x 1)) (sqrt x)) (sqrt (+ x 1))) (/.f64 (-.f64 (+.f64 (/.f64 (+.f64 #s(literal 3/8 binary64) (/.f64 (*.f64 (fma.f64 #s(literal 1/4 binary64) x #s(literal 1 binary64)) #s(literal -1/4 binary64)) x)) (*.f64 x x)) #s(literal 1/2 binary64)) (/.f64 #s(literal 3/8 binary64) x)) x)) (sqrt.f64 x))
#s(approx (/ (- (sqrt (+ x 1)) (sqrt x)) (sqrt (+ x 1))) (/.f64 (-.f64 (+.f64 (/.f64 (+.f64 #s(literal 3/8 binary64) (/.f64 (*.f64 (fma.f64 #s(literal 1/4 binary64) x #s(literal 1 binary64)) #s(literal -1/4 binary64)) x)) (*.f64 x x)) #s(literal 1/2 binary64)) (/.f64 #s(literal 3/8 binary64) x)) x))
(/.f64 (-.f64 (+.f64 (/.f64 (+.f64 #s(literal 3/8 binary64) (/.f64 (*.f64 (fma.f64 #s(literal 1/4 binary64) x #s(literal 1 binary64)) #s(literal -1/4 binary64)) x)) (*.f64 x x)) #s(literal 1/2 binary64)) (/.f64 #s(literal 3/8 binary64) x)) x)
#s(approx (- (/ 1 (sqrt x)) (/ 1 (sqrt (+ x 1)))) (/.f64 (sqrt.f64 x) x))
(/.f64 (sqrt.f64 x) x)
(sqrt.f64 x)
(/.f64 #s(approx (/ (- (sqrt (+ x 1)) (sqrt x)) (sqrt (+ x 1))) (/.f64 #s(approx (- (+ (/ 1/4 (* x x)) 1/2) (/ 3/8 x)) #s(literal 1/2 binary64)) x)) (sqrt.f64 x))
#s(approx (/ (- (sqrt (+ x 1)) (sqrt x)) (sqrt (+ x 1))) (/.f64 #s(approx (- (+ (/ 1/4 (* x x)) 1/2) (/ 3/8 x)) #s(literal 1/2 binary64)) x))
(/.f64 #s(approx (- (+ (/ 1/4 (* x x)) 1/2) (/ 3/8 x)) #s(literal 1/2 binary64)) x)
#s(approx (- (+ (/ 1/4 (* x x)) 1/2) (/ 3/8 x)) #s(literal 1/2 binary64))
(/.f64 (/.f64 (-.f64 (sqrt.f64 (+.f64 x #s(literal 1 binary64))) (sqrt.f64 x)) (sqrt.f64 x)) (sqrt.f64 (+.f64 x #s(literal 1 binary64))))
(/.f64 (-.f64 (sqrt.f64 (+.f64 x #s(literal 1 binary64))) (sqrt.f64 x)) (sqrt.f64 x))
(-.f64 (sqrt.f64 (+.f64 x #s(literal 1 binary64))) (sqrt.f64 x))
(sqrt.f64 (+.f64 x #s(literal 1 binary64)))
(/.f64 #s(approx (- (sqrt (+ x 1)) (sqrt x)) (/.f64 #s(literal 1/2 binary64) (sqrt.f64 x))) (hypot.f64 (sqrt.f64 x) x))
#s(approx (- (sqrt (+ x 1)) (sqrt x)) (/.f64 #s(literal 1/2 binary64) (sqrt.f64 x)))
(/.f64 #s(literal 1/2 binary64) (sqrt.f64 x))
(/.f64 (+.f64 #s(literal 3/8 binary64) (/.f64 (*.f64 (fma.f64 #s(literal 1/4 binary64) x #s(literal 1 binary64)) #s(literal -1/4 binary64)) x)) (*.f64 x x))
(-.f64 (+.f64 (/.f64 (+.f64 #s(literal 3/8 binary64) (/.f64 (*.f64 (fma.f64 #s(literal 1/4 binary64) x #s(literal 1 binary64)) #s(literal -1/4 binary64)) x)) (*.f64 x x)) #s(literal 1/2 binary64)) (/.f64 #s(literal 3/8 binary64) x))
Outputs
(*.f64 #s(literal -1/4 binary64) (fma.f64 x #s(literal 1/4 binary64) #s(literal 1 binary64)))
(*.f64 (fma.f64 x #s(literal 1/4 binary64) #s(literal 1 binary64)) #s(literal -1/4 binary64))
(/.f64 (*.f64 #s(literal -1/4 binary64) (-.f64 (*.f64 #s(literal 1/16 binary64) (*.f64 x x)) #s(literal 1 binary64))) (-.f64 (*.f64 x #s(literal 1/4 binary64)) #s(literal 1 binary64)))
(/.f64 (*.f64 #s(literal -1/4 binary64) (fma.f64 #s(literal 1/64 binary64) (pow.f64 x #s(literal 3 binary64)) #s(literal 1 binary64))) (fma.f64 #s(literal 1/16 binary64) (*.f64 x x) (fma.f64 x #s(literal 1/4 binary64) #s(literal 1 binary64))))
(/.f64 (*.f64 (-.f64 (*.f64 #s(literal 1/16 binary64) (*.f64 x x)) #s(literal 1 binary64)) #s(literal -1/4 binary64)) (-.f64 (*.f64 x #s(literal 1/4 binary64)) #s(literal 1 binary64)))
(/.f64 (*.f64 (fma.f64 #s(literal 1/64 binary64) (pow.f64 x #s(literal 3 binary64)) #s(literal 1 binary64)) #s(literal -1/4 binary64)) (fma.f64 #s(literal 1/16 binary64) (*.f64 x x) (fma.f64 x #s(literal 1/4 binary64) #s(literal 1 binary64))))
(fma.f64 (*.f64 x #s(literal 1/4 binary64)) #s(literal -1/4 binary64) #s(literal -1/4 binary64))
(fma.f64 #s(literal -1/4 binary64) (*.f64 x #s(literal 1/4 binary64)) #s(literal -1/4 binary64))
(+.f64 (*.f64 (*.f64 x #s(literal 1/4 binary64)) #s(literal -1/4 binary64)) #s(literal -1/4 binary64))
(+.f64 (*.f64 #s(literal -1/4 binary64) (*.f64 x #s(literal 1/4 binary64))) #s(literal -1/4 binary64))
(+.f64 #s(literal -1/4 binary64) (*.f64 (*.f64 x #s(literal 1/4 binary64)) #s(literal -1/4 binary64)))
(+.f64 #s(literal -1/4 binary64) (*.f64 #s(literal -1/4 binary64) (*.f64 x #s(literal 1/4 binary64))))
(/.f64 (neg.f64 (neg.f64 #s(approx (/ (- (sqrt (+ x 1)) (sqrt x)) (sqrt (+ x 1))) (/.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 (-.f64 (/.f64 (fma.f64 (/.f64 #s(literal -1/4 binary64) x) (fma.f64 x #s(literal 1/4 binary64) #s(literal 1 binary64)) #s(literal -3/8 binary64)) x) #s(literal -3/8 binary64)) x)) x)))) (sqrt.f64 x))
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(/.f64 (neg.f64 (-.f64 (pow.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 (fma.f64 (/.f64 #s(literal -1/4 binary64) x) (fma.f64 x #s(literal 1/4 binary64) #s(literal 1 binary64)) #s(literal 3/8 binary64)) (*.f64 x x))) #s(literal 3 binary64)) (pow.f64 (/.f64 #s(literal -3/8 binary64) x) #s(literal 3 binary64)))) (neg.f64 (fma.f64 (/.f64 #s(literal -3/8 binary64) x) (+.f64 (/.f64 (fma.f64 (/.f64 #s(literal -1/4 binary64) x) (fma.f64 x #s(literal 1/4 binary64) #s(literal 1 binary64)) #s(literal 3/8 binary64)) (*.f64 x x)) (+.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -3/8 binary64) x))) (pow.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 (fma.f64 (/.f64 #s(literal -1/4 binary64) x) (fma.f64 x #s(literal 1/4 binary64) #s(literal 1 binary64)) #s(literal 3/8 binary64)) (*.f64 x x))) #s(literal 2 binary64)))))
(/.f64 (-.f64 (*.f64 (-.f64 (pow.f64 (/.f64 (fma.f64 (/.f64 #s(literal -1/4 binary64) x) (fma.f64 x #s(literal 1/4 binary64) #s(literal 1 binary64)) #s(literal 3/8 binary64)) (*.f64 x x)) #s(literal 2 binary64)) #s(literal 1/4 binary64)) x) (*.f64 (-.f64 (/.f64 (fma.f64 (/.f64 #s(literal -1/4 binary64) x) (fma.f64 x #s(literal 1/4 binary64) #s(literal 1 binary64)) #s(literal 3/8 binary64)) (*.f64 x x)) #s(literal 1/2 binary64)) #s(literal 3/8 binary64))) (*.f64 (-.f64 (/.f64 (fma.f64 (/.f64 #s(literal -1/4 binary64) x) (fma.f64 x #s(literal 1/4 binary64) #s(literal 1 binary64)) #s(literal 3/8 binary64)) (*.f64 x x)) #s(literal 1/2 binary64)) x))
(/.f64 (-.f64 (*.f64 (+.f64 #s(literal 1/8 binary64) (pow.f64 (/.f64 (fma.f64 (/.f64 #s(literal -1/4 binary64) x) (fma.f64 x #s(literal 1/4 binary64) #s(literal 1 binary64)) #s(literal 3/8 binary64)) (*.f64 x x)) #s(literal 3 binary64))) x) (*.f64 (-.f64 (+.f64 (pow.f64 (/.f64 (fma.f64 (/.f64 #s(literal -1/4 binary64) x) (fma.f64 x #s(literal 1/4 binary64) #s(literal 1 binary64)) #s(literal 3/8 binary64)) (*.f64 x x)) #s(literal 2 binary64)) #s(literal 1/4 binary64)) (*.f64 #s(literal 1/2 binary64) (/.f64 (fma.f64 (/.f64 #s(literal -1/4 binary64) x) (fma.f64 x #s(literal 1/4 binary64) #s(literal 1 binary64)) #s(literal 3/8 binary64)) (*.f64 x x)))) #s(literal 3/8 binary64))) (*.f64 (-.f64 (+.f64 (pow.f64 (/.f64 (fma.f64 (/.f64 #s(literal -1/4 binary64) x) (fma.f64 x #s(literal 1/4 binary64) #s(literal 1 binary64)) #s(literal 3/8 binary64)) (*.f64 x x)) #s(literal 2 binary64)) #s(literal 1/4 binary64)) (*.f64 #s(literal 1/2 binary64) (/.f64 (fma.f64 (/.f64 #s(literal -1/4 binary64) x) (fma.f64 x #s(literal 1/4 binary64) #s(literal 1 binary64)) #s(literal 3/8 binary64)) (*.f64 x x)))) x))
(/.f64 (-.f64 (pow.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 (fma.f64 (/.f64 #s(literal -1/4 binary64) x) (fma.f64 x #s(literal 1/4 binary64) #s(literal 1 binary64)) #s(literal 3/8 binary64)) (*.f64 x x))) #s(literal 2 binary64)) (pow.f64 (/.f64 #s(literal -3/8 binary64) x) #s(literal 2 binary64))) (+.f64 (/.f64 (fma.f64 (/.f64 #s(literal -1/4 binary64) x) (fma.f64 x #s(literal 1/4 binary64) #s(literal 1 binary64)) #s(literal 3/8 binary64)) (*.f64 x x)) (+.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -3/8 binary64) x))))
(/.f64 (-.f64 (pow.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 (fma.f64 (/.f64 #s(literal -1/4 binary64) x) (fma.f64 x #s(literal 1/4 binary64) #s(literal 1 binary64)) #s(literal 3/8 binary64)) (*.f64 x x))) #s(literal 3 binary64)) (pow.f64 (/.f64 #s(literal -3/8 binary64) x) #s(literal 3 binary64))) (fma.f64 (/.f64 #s(literal -3/8 binary64) x) (+.f64 (/.f64 (fma.f64 (/.f64 #s(literal -1/4 binary64) x) (fma.f64 x #s(literal 1/4 binary64) #s(literal 1 binary64)) #s(literal 3/8 binary64)) (*.f64 x x)) (+.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -3/8 binary64) x))) (pow.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 (fma.f64 (/.f64 #s(literal -1/4 binary64) x) (fma.f64 x #s(literal 1/4 binary64) #s(literal 1 binary64)) #s(literal 3/8 binary64)) (*.f64 x x))) #s(literal 2 binary64))))
(-.f64 (/.f64 (pow.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 (fma.f64 (/.f64 #s(literal -1/4 binary64) x) (fma.f64 x #s(literal 1/4 binary64) #s(literal 1 binary64)) #s(literal 3/8 binary64)) (*.f64 x x))) #s(literal 2 binary64)) (+.f64 (/.f64 (fma.f64 (/.f64 #s(literal -1/4 binary64) x) (fma.f64 x #s(literal 1/4 binary64) #s(literal 1 binary64)) #s(literal 3/8 binary64)) (*.f64 x x)) (+.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -3/8 binary64) x)))) (/.f64 (pow.f64 (/.f64 #s(literal -3/8 binary64) x) #s(literal 2 binary64)) (+.f64 (/.f64 (fma.f64 (/.f64 #s(literal -1/4 binary64) x) (fma.f64 x #s(literal 1/4 binary64) #s(literal 1 binary64)) #s(literal 3/8 binary64)) (*.f64 x x)) (+.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -3/8 binary64) x)))))
(-.f64 (/.f64 (pow.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 (fma.f64 (/.f64 #s(literal -1/4 binary64) x) (fma.f64 x #s(literal 1/4 binary64) #s(literal 1 binary64)) #s(literal 3/8 binary64)) (*.f64 x x))) #s(literal 3 binary64)) (fma.f64 (/.f64 #s(literal -3/8 binary64) x) (+.f64 (/.f64 (fma.f64 (/.f64 #s(literal -1/4 binary64) x) (fma.f64 x #s(literal 1/4 binary64) #s(literal 1 binary64)) #s(literal 3/8 binary64)) (*.f64 x x)) (+.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -3/8 binary64) x))) (pow.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 (fma.f64 (/.f64 #s(literal -1/4 binary64) x) (fma.f64 x #s(literal 1/4 binary64) #s(literal 1 binary64)) #s(literal 3/8 binary64)) (*.f64 x x))) #s(literal 2 binary64)))) (/.f64 (pow.f64 (/.f64 #s(literal -3/8 binary64) x) #s(literal 3 binary64)) (fma.f64 (/.f64 #s(literal -3/8 binary64) x) (+.f64 (/.f64 (fma.f64 (/.f64 #s(literal -1/4 binary64) x) (fma.f64 x #s(literal 1/4 binary64) #s(literal 1 binary64)) #s(literal 3/8 binary64)) (*.f64 x x)) (+.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -3/8 binary64) x))) (pow.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 (fma.f64 (/.f64 #s(literal -1/4 binary64) x) (fma.f64 x #s(literal 1/4 binary64) #s(literal 1 binary64)) #s(literal 3/8 binary64)) (*.f64 x x))) #s(literal 2 binary64)))))
(-.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 (fma.f64 (/.f64 #s(literal -1/4 binary64) x) (fma.f64 x #s(literal 1/4 binary64) #s(literal 1 binary64)) #s(literal 3/8 binary64)) (*.f64 x x))) (/.f64 #s(literal -3/8 binary64) x))
(+.f64 (-.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -3/8 binary64) x)) (/.f64 (fma.f64 (/.f64 #s(literal -1/4 binary64) x) (fma.f64 x #s(literal 1/4 binary64) #s(literal 1 binary64)) #s(literal 3/8 binary64)) (*.f64 x x)))
(+.f64 (/.f64 #s(literal -3/8 binary64) (*.f64 x x)) (+.f64 (/.f64 (*.f64 (fma.f64 x #s(literal 1/4 binary64) #s(literal 1 binary64)) #s(literal 1/4 binary64)) (pow.f64 x #s(literal 3 binary64))) (-.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -3/8 binary64) x))))
(+.f64 #s(literal 1/2 binary64) (/.f64 (-.f64 (/.f64 (fma.f64 (/.f64 #s(literal -1/4 binary64) x) (fma.f64 x #s(literal 1/4 binary64) #s(literal 1 binary64)) #s(literal -3/8 binary64)) x) #s(literal -3/8 binary64)) x))
(+.f64 (/.f64 (fma.f64 (/.f64 #s(literal -1/4 binary64) x) (fma.f64 x #s(literal 1/4 binary64) #s(literal 1 binary64)) #s(literal 3/8 binary64)) (*.f64 x x)) (-.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -3/8 binary64) x)))

eval106.0ms (1.6%)

Memory
-19.5MiB live, 81.2MiB allocated
Compiler

Compiled 18 440 to 2 281 computations (87.6% saved)

prune47.0ms (0.7%)

Memory
-6.3MiB live, 40.6MiB allocated
Pruning

25 alts after pruning (15 fresh and 10 done)

PrunedKeptTotal
New5604564
Fresh11112
Picked145
Done268
Total56425589
Accuracy
100.0%
Counts
589 → 25
Alt Table
Click to see full alt table
StatusAccuracyProgram
37.7%
(/.f64 (/.f64 (-.f64 (hypot.f64 (sqrt.f64 x) x) x) x) (sqrt.f64 (+.f64 x #s(literal 1 binary64))))
37.4%
(/.f64 (/.f64 (-.f64 (sqrt.f64 (+.f64 x #s(literal 1 binary64))) (sqrt.f64 x)) (sqrt.f64 x)) (sqrt.f64 (+.f64 x #s(literal 1 binary64))))
38.3%
(/.f64 (-.f64 (+.f64 x #s(literal 1 binary64)) x) (*.f64 (+.f64 (sqrt.f64 (+.f64 x #s(literal 1 binary64))) (sqrt.f64 x)) (hypot.f64 (sqrt.f64 x) x)))
37.4%
(/.f64 (-.f64 (sqrt.f64 (+.f64 x #s(literal 1 binary64))) (sqrt.f64 x)) (hypot.f64 (sqrt.f64 x) x))
81.9%
(/.f64 #s(approx (/ (- (sqrt (+ x 1)) (sqrt x)) (sqrt (+ x 1))) (/.f64 (fma.f64 (/.f64 #s(literal -1/4 binary64) (*.f64 x x)) x (*.f64 x (-.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -3/8 binary64) x)))) (*.f64 x x))) (sqrt.f64 x))
97.4%
(/.f64 #s(approx (/ (- (sqrt (+ x 1)) (sqrt x)) (sqrt (+ x 1))) (/.f64 (-.f64 (*.f64 (/.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/4 binary64) (*.f64 x x))) (sqrt.f64 x)) x) (*.f64 (sqrt.f64 x) (/.f64 #s(literal -3/8 binary64) x))) (pow.f64 x #s(literal 3/2 binary64)))) (sqrt.f64 x))
99.1%
(/.f64 #s(approx (/ (- (sqrt (+ x 1)) (sqrt x)) (sqrt (+ x 1))) (/.f64 #s(approx (- (+ (/ (+ 3/8 (/ (* (+ (* 1/4 x) 1) -1/4) x)) (* x x)) 1/2) (/ 3/8 x)) (-.f64 #s(literal 1/2 binary64) (/.f64 (-.f64 #s(literal 3/8 binary64) (/.f64 #s(literal 5/16 binary64) x)) x))) x)) (sqrt.f64 x))
98.8%
(/.f64 #s(approx (/ (- (sqrt (+ x 1)) (sqrt x)) (sqrt (+ x 1))) (/.f64 #s(approx (- (+ (/ 1/4 (* x x)) 1/2) (/ 3/8 x)) (-.f64 #s(literal 1/2 binary64) (/.f64 #s(literal 3/8 binary64) x))) x)) (sqrt.f64 x))
98.1%
(/.f64 #s(approx (/ (- (sqrt (+ x 1)) (sqrt x)) (sqrt (+ x 1))) (/.f64 #s(approx (- (+ (/ 1/4 (* x x)) 1/2) (/ 3/8 x)) #s(literal 1/2 binary64)) x)) (sqrt.f64 x))
98.9%
(/.f64 #s(approx (/ (- (sqrt (+ x 1)) (sqrt x)) (sqrt x)) (/.f64 (-.f64 #s(literal 1/2 binary64) (/.f64 #s(literal 1/8 binary64) x)) x)) (sqrt.f64 (+.f64 x #s(literal 1 binary64))))
98.2%
(/.f64 #s(approx (/ (- (sqrt (+ x 1)) (sqrt x)) (sqrt x)) (/.f64 #s(literal 1/2 binary64) x)) (sqrt.f64 (+.f64 x #s(literal 1 binary64))))
98.2%
(/.f64 #s(approx (- (sqrt (+ x 1)) (sqrt x)) (/.f64 #s(literal 1/2 binary64) (sqrt.f64 x))) (hypot.f64 (sqrt.f64 x) x))
98.3%
(/.f64 #s(approx (- (sqrt (+ x 1)) (sqrt x)) (*.f64 #s(literal 1/2 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) x)))) (hypot.f64 (sqrt.f64 x) x))
37.3%
(-.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 x)) (/.f64 #s(literal 1 binary64) (sqrt.f64 (+.f64 x #s(literal 1 binary64)))))
65.2%
#s(approx (/ (/ (- (sqrt (+ x 1)) (sqrt x)) (sqrt (+ x 1))) (sqrt x)) (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 3 binary64)))) #s(literal 1/2 binary64)))
34.5%
#s(approx (- (/ 1 (sqrt x)) (/ 1 (sqrt (+ x 1)))) (/.f64 (*.f64 #s(literal -1/2 binary64) #s(approx (- (sqrt (/ 1 x)) (sqrt x)) (sqrt.f64 x))) (*.f64 x x)))
5.5%
#s(approx (- (/ 1 (sqrt x)) (/ 1 (sqrt (+ x 1)))) (/.f64 (sqrt.f64 x) x))
5.5%
#s(approx (- (/ 1 (sqrt x)) (/ 1 (sqrt (+ x 1)))) (/.f64 #s(literal 1 binary64) (sqrt.f64 x)))
98.1%
#s(approx (- (/ 1 (sqrt x)) (/ 1 (sqrt (+ x 1)))) (*.f64 (/.f64 (neg.f64 (/.f64 #s(approx (- (sqrt (/ 1 x)) (sqrt x)) (sqrt.f64 x)) x)) x) #s(literal -1/2 binary64)))
82.0%
#s(approx (- (/ 1 (sqrt x)) (/ 1 (sqrt (+ x 1)))) (*.f64 (/.f64 #s(approx (- (sqrt (/ 1 x)) (sqrt x)) (neg.f64 (sqrt.f64 x))) (*.f64 x x)) #s(literal -1/2 binary64)))
82.1%
#s(approx (- (/ 1 (sqrt x)) (/ 1 (sqrt (+ x 1)))) (*.f64 (-.f64 (pow.f64 x #s(literal -1/2 binary64)) (sqrt.f64 x)) (/.f64 #s(literal -1/2 binary64) (*.f64 x x))))
98.6%
#s(approx (- (/ 1 (sqrt x)) (/ 1 (sqrt (+ x 1)))) (*.f64 (-.f64 (pow.f64 x #s(literal -5/2 binary64)) (pow.f64 x #s(literal -3/2 binary64))) #s(literal -1/2 binary64)))
34.5%
#s(approx (- (/ 1 (sqrt x)) (/ 1 (sqrt (+ x 1)))) (*.f64 #s(approx (- (sqrt (/ 1 x)) (sqrt x)) (sqrt.f64 x)) (/.f64 #s(literal -1/2 binary64) (*.f64 x x))))
36.4%
#s(approx (- (/ 1 (sqrt x)) (/ 1 (sqrt (+ x 1)))) (sqrt.f64 (/.f64 x (*.f64 x x))))
5.5%
#s(approx (- (/ 1 (sqrt x)) (/ 1 (sqrt (+ x 1)))) (sqrt.f64 (/.f64 #s(literal 1 binary64) x)))
Compiler

Compiled 1 479 to 610 computations (58.8% saved)

regimes17.0ms (0.3%)

Memory
16.5MiB live, 16.5MiB allocated
Counts
37 → 1
Calls
Call 1
Inputs
#s(approx (- (/ 1 (sqrt x)) (/ 1 (sqrt (+ x 1)))) (sqrt.f64 (/.f64 #s(literal 1 binary64) x)))
#s(approx (- (/ 1 (sqrt x)) (/ 1 (sqrt (+ x 1)))) (/.f64 #s(literal 1 binary64) (sqrt.f64 x)))
#s(approx (- (/ 1 (sqrt x)) (/ 1 (sqrt (+ x 1)))) (/.f64 (sqrt.f64 x) x))
#s(approx (- (/ 1 (sqrt x)) (/ 1 (sqrt (+ x 1)))) (sqrt.f64 (/.f64 x (*.f64 x x))))
#s(approx (- (/ 1 (sqrt x)) (/ 1 (sqrt (+ x 1)))) (*.f64 #s(approx (- (sqrt (/ 1 x)) (sqrt x)) (sqrt.f64 x)) (/.f64 #s(literal -1/2 binary64) (*.f64 x x))))
#s(approx (- (/ 1 (sqrt x)) (/ 1 (sqrt (+ x 1)))) (/.f64 (*.f64 #s(literal -1/2 binary64) #s(approx (- (sqrt (/ 1 x)) (sqrt x)) (sqrt.f64 x))) (*.f64 x x)))
(/.f64 #s(approx (/ (- (sqrt (+ x 1)) (sqrt x)) (sqrt (+ x 1))) (/.f64 #s(literal 1/2 binary64) x)) (sqrt.f64 x))
(/.f64 #s(approx (/ (- (sqrt (+ x 1)) (sqrt x)) (sqrt (+ x 1))) (/.f64 #s(approx (- (+ (/ 1/4 (* x x)) 1/2) (/ 3/8 x)) #s(literal 1/2 binary64)) x)) (sqrt.f64 x))
#s(approx (- (/ 1 (sqrt x)) (/ 1 (sqrt (+ x 1)))) (*.f64 (/.f64 #s(approx (- (sqrt (/ 1 x)) (sqrt x)) (neg.f64 (sqrt.f64 x))) (*.f64 x x)) #s(literal -1/2 binary64)))
(/.f64 #s(approx (/ (- (sqrt (+ x 1)) (sqrt x)) (sqrt x)) (/.f64 #s(literal 1/2 binary64) x)) (sqrt.f64 (+.f64 x #s(literal 1 binary64))))
#s(approx (- (/ 1 (sqrt x)) (/ 1 (sqrt (+ x 1)))) (*.f64 (/.f64 (neg.f64 (/.f64 #s(approx (- (sqrt (/ 1 x)) (sqrt x)) (sqrt.f64 x)) x)) x) #s(literal -1/2 binary64)))
(/.f64 #s(approx (/ (- (sqrt (+ x 1)) (sqrt x)) (sqrt (+ x 1))) (/.f64 #s(approx (- (+ (/ 1/4 (* x x)) 1/2) (/ 3/8 x)) (-.f64 #s(literal 1/2 binary64) (/.f64 #s(literal 3/8 binary64) x))) x)) (sqrt.f64 x))
(-.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 x)) (/.f64 #s(literal 1 binary64) (sqrt.f64 (+.f64 x #s(literal 1 binary64)))))
(/.f64 #s(approx (/ (- (sqrt (+ x 1)) (sqrt x)) (sqrt x)) (/.f64 (-.f64 #s(literal 1/2 binary64) (/.f64 #s(literal 1/8 binary64) x)) x)) (sqrt.f64 (+.f64 x #s(literal 1 binary64))))
(/.f64 #s(approx (/ (- (sqrt (+ x 1)) (sqrt x)) (sqrt (+ x 1))) (/.f64 (-.f64 #s(literal 1/2 binary64) (*.f64 #s(literal 1 binary64) (/.f64 #s(literal 3/8 binary64) x))) x)) (sqrt.f64 x))
#s(approx (- (/ 1 (sqrt x)) (/ 1 (sqrt (+ x 1)))) (*.f64 (/.f64 (-.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) (sqrt.f64 x)) (*.f64 x x)) #s(literal -1/2 binary64)))
(/.f64 #s(approx (/ (- (sqrt (+ x 1)) (sqrt x)) (sqrt (+ x 1))) (/.f64 #s(approx (- (+ (/ (+ 3/8 (/ (* (+ (* 1/4 x) 1) -1/4) x)) (* x x)) 1/2) (/ 3/8 x)) (-.f64 #s(literal 1/2 binary64) (/.f64 (-.f64 #s(literal 3/8 binary64) (/.f64 #s(literal 5/16 binary64) x)) x))) x)) (sqrt.f64 x))
(/.f64 #s(approx (/ (- (sqrt (+ x 1)) (sqrt x)) (sqrt (+ x 1))) (/.f64 (+.f64 (/.f64 (-.f64 (/.f64 #s(literal 1/4 binary64) x) #s(literal 3/8 binary64)) x) #s(literal 1/2 binary64)) x)) (sqrt.f64 x))
(/.f64 #s(approx (/ (- (sqrt (+ x 1)) (sqrt x)) (sqrt (+ x 1))) (/.f64 (-.f64 (+.f64 (/.f64 #s(literal 1/4 binary64) (*.f64 x x)) #s(literal 1/2 binary64)) (/.f64 #s(literal 3/8 binary64) x)) x)) (sqrt.f64 x))
(/.f64 (/.f64 #s(approx (- (sqrt (+ x 1)) (sqrt x)) (*.f64 #s(literal 1/2 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) x)))) (sqrt.f64 (+.f64 x #s(literal 1 binary64)))) (sqrt.f64 x))
(/.f64 (/.f64 (-.f64 (sqrt.f64 (+.f64 x #s(literal 1 binary64))) (sqrt.f64 x)) (sqrt.f64 x)) (sqrt.f64 (+.f64 x #s(literal 1 binary64))))
(/.f64 (/.f64 (-.f64 (sqrt.f64 (+.f64 x #s(literal 1 binary64))) (sqrt.f64 x)) (sqrt.f64 (+.f64 x #s(literal 1 binary64)))) (sqrt.f64 x))
(/.f64 #s(approx (/ (- (sqrt (+ x 1)) (sqrt x)) (sqrt (+ x 1))) (/.f64 (fma.f64 (/.f64 #s(literal -1/4 binary64) (*.f64 x x)) x (*.f64 x (-.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -3/8 binary64) x)))) (*.f64 x x))) (sqrt.f64 x))
(/.f64 #s(approx (/ (- (sqrt (+ x 1)) (sqrt x)) (sqrt (+ x 1))) (/.f64 (-.f64 (+.f64 (/.f64 (+.f64 #s(literal 3/8 binary64) (/.f64 (*.f64 (fma.f64 #s(literal 1/4 binary64) x #s(literal 1 binary64)) #s(literal -1/4 binary64)) x)) (*.f64 x x)) #s(literal 1/2 binary64)) (/.f64 #s(literal 3/8 binary64) x)) x)) (sqrt.f64 x))
(/.f64 (/.f64 #s(approx (- (sqrt (+ x 1)) (sqrt x)) (/.f64 (fma.f64 #s(literal -1/8 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) (*.f64 #s(literal 1/2 binary64) (sqrt.f64 x))) x)) (sqrt.f64 (+.f64 x #s(literal 1 binary64)))) (sqrt.f64 x))
#s(approx (- (/ 1 (sqrt x)) (/ 1 (sqrt (+ x 1)))) (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 3 binary64)))) #s(literal 1/2 binary64)))
#s(approx (/ (/ (- (sqrt (+ x 1)) (sqrt x)) (sqrt (+ x 1))) (sqrt x)) (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 3 binary64)))) #s(literal 1/2 binary64)))
#s(approx (- (/ 1 (sqrt x)) (/ 1 (sqrt (+ x 1)))) (*.f64 (-.f64 (pow.f64 x #s(literal -1/2 binary64)) (sqrt.f64 x)) (/.f64 #s(literal -1/2 binary64) (*.f64 x x))))
#s(approx (- (/ 1 (sqrt x)) (/ 1 (sqrt (+ x 1)))) (/.f64 (/.f64 (*.f64 #s(literal -1/2 binary64) (-.f64 (pow.f64 x #s(literal -1/2 binary64)) (sqrt.f64 x))) x) x))
(/.f64 #s(approx (- (sqrt (+ x 1)) (sqrt x)) (/.f64 #s(literal 1/2 binary64) (sqrt.f64 x))) (hypot.f64 (sqrt.f64 x) x))
(/.f64 #s(approx (- (sqrt (+ x 1)) (sqrt x)) (*.f64 #s(literal 1/2 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) x)))) (hypot.f64 (sqrt.f64 x) x))
(/.f64 (-.f64 (sqrt.f64 (+.f64 x #s(literal 1 binary64))) (sqrt.f64 x)) (hypot.f64 (sqrt.f64 x) x))
(/.f64 (/.f64 (-.f64 (hypot.f64 (sqrt.f64 x) x) x) x) (sqrt.f64 (+.f64 x #s(literal 1 binary64))))
(/.f64 (-.f64 (+.f64 x #s(literal 1 binary64)) x) (*.f64 (+.f64 (sqrt.f64 (+.f64 x #s(literal 1 binary64))) (sqrt.f64 x)) (hypot.f64 (sqrt.f64 x) x)))
(/.f64 #s(approx (/ (- (sqrt (+ x 1)) (sqrt x)) (sqrt (+ x 1))) (/.f64 (-.f64 (*.f64 (/.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/4 binary64) (*.f64 x x))) (sqrt.f64 x)) x) (*.f64 (sqrt.f64 x) (/.f64 #s(literal -3/8 binary64) x))) (pow.f64 x #s(literal 3/2 binary64)))) (sqrt.f64 x))
#s(approx (- (/ 1 (sqrt x)) (/ 1 (sqrt (+ x 1)))) (*.f64 (-.f64 (pow.f64 x #s(literal -5/2 binary64)) (pow.f64 x #s(literal -3/2 binary64))) #s(literal -1/2 binary64)))
(/.f64 (-.f64 (pow.f64 (/.f64 (pow.f64 x #s(literal -1 binary64)) (-.f64 (pow.f64 x #s(literal -1/2 binary64)) (cos.f64 (atan.f64 (sqrt.f64 x))))) #s(literal 2 binary64)) (pow.f64 (/.f64 (exp.f64 (neg.f64 (log1p.f64 x))) (-.f64 (pow.f64 x #s(literal -1/2 binary64)) (cos.f64 (atan.f64 (sqrt.f64 x))))) #s(literal 2 binary64))) (-.f64 (pow.f64 x #s(literal -1/2 binary64)) (cos.f64 (atan.f64 (sqrt.f64 x)))))
Outputs
(/.f64 #s(approx (/ (- (sqrt (+ x 1)) (sqrt x)) (sqrt (+ x 1))) (/.f64 (-.f64 (+.f64 (/.f64 (+.f64 #s(literal 3/8 binary64) (/.f64 (*.f64 (fma.f64 #s(literal 1/4 binary64) x #s(literal 1 binary64)) #s(literal -1/4 binary64)) x)) (*.f64 x x)) #s(literal 1/2 binary64)) (/.f64 #s(literal 3/8 binary64) x)) x)) (sqrt.f64 x))
Calls

2 calls:

9.0ms
x
7.0ms
(-.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 x)) (/.f64 #s(literal 1 binary64) (sqrt.f64 (+.f64 x #s(literal 1 binary64)))))
Results
AccuracySegmentsBranch
99.1%1(-.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 x)) (/.f64 #s(literal 1 binary64) (sqrt.f64 (+.f64 x #s(literal 1 binary64)))))
99.1%1x
Compiler

Compiled 12 to 9 computations (25% saved)

regimes11.0ms (0.2%)

Memory
11.2MiB live, 11.2MiB allocated
Counts
23 → 1
Calls
Call 1
Inputs
#s(approx (- (/ 1 (sqrt x)) (/ 1 (sqrt (+ x 1)))) (sqrt.f64 (/.f64 #s(literal 1 binary64) x)))
#s(approx (- (/ 1 (sqrt x)) (/ 1 (sqrt (+ x 1)))) (/.f64 #s(literal 1 binary64) (sqrt.f64 x)))
#s(approx (- (/ 1 (sqrt x)) (/ 1 (sqrt (+ x 1)))) (/.f64 (sqrt.f64 x) x))
#s(approx (- (/ 1 (sqrt x)) (/ 1 (sqrt (+ x 1)))) (sqrt.f64 (/.f64 x (*.f64 x x))))
#s(approx (- (/ 1 (sqrt x)) (/ 1 (sqrt (+ x 1)))) (*.f64 #s(approx (- (sqrt (/ 1 x)) (sqrt x)) (sqrt.f64 x)) (/.f64 #s(literal -1/2 binary64) (*.f64 x x))))
#s(approx (- (/ 1 (sqrt x)) (/ 1 (sqrt (+ x 1)))) (/.f64 (*.f64 #s(literal -1/2 binary64) #s(approx (- (sqrt (/ 1 x)) (sqrt x)) (sqrt.f64 x))) (*.f64 x x)))
(/.f64 #s(approx (/ (- (sqrt (+ x 1)) (sqrt x)) (sqrt (+ x 1))) (/.f64 #s(literal 1/2 binary64) x)) (sqrt.f64 x))
(/.f64 #s(approx (/ (- (sqrt (+ x 1)) (sqrt x)) (sqrt (+ x 1))) (/.f64 #s(approx (- (+ (/ 1/4 (* x x)) 1/2) (/ 3/8 x)) #s(literal 1/2 binary64)) x)) (sqrt.f64 x))
#s(approx (- (/ 1 (sqrt x)) (/ 1 (sqrt (+ x 1)))) (*.f64 (/.f64 #s(approx (- (sqrt (/ 1 x)) (sqrt x)) (neg.f64 (sqrt.f64 x))) (*.f64 x x)) #s(literal -1/2 binary64)))
(/.f64 #s(approx (/ (- (sqrt (+ x 1)) (sqrt x)) (sqrt x)) (/.f64 #s(literal 1/2 binary64) x)) (sqrt.f64 (+.f64 x #s(literal 1 binary64))))
#s(approx (- (/ 1 (sqrt x)) (/ 1 (sqrt (+ x 1)))) (*.f64 (/.f64 (neg.f64 (/.f64 #s(approx (- (sqrt (/ 1 x)) (sqrt x)) (sqrt.f64 x)) x)) x) #s(literal -1/2 binary64)))
(/.f64 #s(approx (/ (- (sqrt (+ x 1)) (sqrt x)) (sqrt (+ x 1))) (/.f64 #s(approx (- (+ (/ 1/4 (* x x)) 1/2) (/ 3/8 x)) (-.f64 #s(literal 1/2 binary64) (/.f64 #s(literal 3/8 binary64) x))) x)) (sqrt.f64 x))
(-.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 x)) (/.f64 #s(literal 1 binary64) (sqrt.f64 (+.f64 x #s(literal 1 binary64)))))
(/.f64 #s(approx (/ (- (sqrt (+ x 1)) (sqrt x)) (sqrt x)) (/.f64 (-.f64 #s(literal 1/2 binary64) (/.f64 #s(literal 1/8 binary64) x)) x)) (sqrt.f64 (+.f64 x #s(literal 1 binary64))))
(/.f64 #s(approx (/ (- (sqrt (+ x 1)) (sqrt x)) (sqrt (+ x 1))) (/.f64 (-.f64 #s(literal 1/2 binary64) (*.f64 #s(literal 1 binary64) (/.f64 #s(literal 3/8 binary64) x))) x)) (sqrt.f64 x))
#s(approx (- (/ 1 (sqrt x)) (/ 1 (sqrt (+ x 1)))) (*.f64 (/.f64 (-.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) (sqrt.f64 x)) (*.f64 x x)) #s(literal -1/2 binary64)))
(/.f64 #s(approx (/ (- (sqrt (+ x 1)) (sqrt x)) (sqrt (+ x 1))) (/.f64 #s(approx (- (+ (/ (+ 3/8 (/ (* (+ (* 1/4 x) 1) -1/4) x)) (* x x)) 1/2) (/ 3/8 x)) (-.f64 #s(literal 1/2 binary64) (/.f64 (-.f64 #s(literal 3/8 binary64) (/.f64 #s(literal 5/16 binary64) x)) x))) x)) (sqrt.f64 x))
(/.f64 #s(approx (/ (- (sqrt (+ x 1)) (sqrt x)) (sqrt (+ x 1))) (/.f64 (+.f64 (/.f64 (-.f64 (/.f64 #s(literal 1/4 binary64) x) #s(literal 3/8 binary64)) x) #s(literal 1/2 binary64)) x)) (sqrt.f64 x))
(/.f64 #s(approx (/ (- (sqrt (+ x 1)) (sqrt x)) (sqrt (+ x 1))) (/.f64 (-.f64 (+.f64 (/.f64 #s(literal 1/4 binary64) (*.f64 x x)) #s(literal 1/2 binary64)) (/.f64 #s(literal 3/8 binary64) x)) x)) (sqrt.f64 x))
(/.f64 (/.f64 #s(approx (- (sqrt (+ x 1)) (sqrt x)) (*.f64 #s(literal 1/2 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) x)))) (sqrt.f64 (+.f64 x #s(literal 1 binary64)))) (sqrt.f64 x))
(/.f64 (/.f64 (-.f64 (sqrt.f64 (+.f64 x #s(literal 1 binary64))) (sqrt.f64 x)) (sqrt.f64 x)) (sqrt.f64 (+.f64 x #s(literal 1 binary64))))
(/.f64 (/.f64 (-.f64 (sqrt.f64 (+.f64 x #s(literal 1 binary64))) (sqrt.f64 x)) (sqrt.f64 (+.f64 x #s(literal 1 binary64)))) (sqrt.f64 x))
(/.f64 #s(approx (/ (- (sqrt (+ x 1)) (sqrt x)) (sqrt (+ x 1))) (/.f64 (fma.f64 (/.f64 #s(literal -1/4 binary64) (*.f64 x x)) x (*.f64 x (-.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -3/8 binary64) x)))) (*.f64 x x))) (sqrt.f64 x))
Outputs
(/.f64 #s(approx (/ (- (sqrt (+ x 1)) (sqrt x)) (sqrt (+ x 1))) (/.f64 #s(approx (- (+ (/ (+ 3/8 (/ (* (+ (* 1/4 x) 1) -1/4) x)) (* x x)) 1/2) (/ 3/8 x)) (-.f64 #s(literal 1/2 binary64) (/.f64 (-.f64 #s(literal 3/8 binary64) (/.f64 #s(literal 5/16 binary64) x)) x))) x)) (sqrt.f64 x))
Calls

2 calls:

6.0ms
x
4.0ms
(-.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 x)) (/.f64 #s(literal 1 binary64) (sqrt.f64 (+.f64 x #s(literal 1 binary64)))))
Results
AccuracySegmentsBranch
99.1%1(-.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 x)) (/.f64 #s(literal 1 binary64) (sqrt.f64 (+.f64 x #s(literal 1 binary64)))))
99.1%1x
Compiler

Compiled 12 to 9 computations (25% saved)

regimes14.0ms (0.2%)

Memory
-37.0MiB live, 9.3MiB allocated
Counts
16 → 1
Calls
Call 1
Inputs
#s(approx (- (/ 1 (sqrt x)) (/ 1 (sqrt (+ x 1)))) (sqrt.f64 (/.f64 #s(literal 1 binary64) x)))
#s(approx (- (/ 1 (sqrt x)) (/ 1 (sqrt (+ x 1)))) (/.f64 #s(literal 1 binary64) (sqrt.f64 x)))
#s(approx (- (/ 1 (sqrt x)) (/ 1 (sqrt (+ x 1)))) (/.f64 (sqrt.f64 x) x))
#s(approx (- (/ 1 (sqrt x)) (/ 1 (sqrt (+ x 1)))) (sqrt.f64 (/.f64 x (*.f64 x x))))
#s(approx (- (/ 1 (sqrt x)) (/ 1 (sqrt (+ x 1)))) (*.f64 #s(approx (- (sqrt (/ 1 x)) (sqrt x)) (sqrt.f64 x)) (/.f64 #s(literal -1/2 binary64) (*.f64 x x))))
#s(approx (- (/ 1 (sqrt x)) (/ 1 (sqrt (+ x 1)))) (/.f64 (*.f64 #s(literal -1/2 binary64) #s(approx (- (sqrt (/ 1 x)) (sqrt x)) (sqrt.f64 x))) (*.f64 x x)))
(/.f64 #s(approx (/ (- (sqrt (+ x 1)) (sqrt x)) (sqrt (+ x 1))) (/.f64 #s(literal 1/2 binary64) x)) (sqrt.f64 x))
(/.f64 #s(approx (/ (- (sqrt (+ x 1)) (sqrt x)) (sqrt (+ x 1))) (/.f64 #s(approx (- (+ (/ 1/4 (* x x)) 1/2) (/ 3/8 x)) #s(literal 1/2 binary64)) x)) (sqrt.f64 x))
#s(approx (- (/ 1 (sqrt x)) (/ 1 (sqrt (+ x 1)))) (*.f64 (/.f64 #s(approx (- (sqrt (/ 1 x)) (sqrt x)) (neg.f64 (sqrt.f64 x))) (*.f64 x x)) #s(literal -1/2 binary64)))
(/.f64 #s(approx (/ (- (sqrt (+ x 1)) (sqrt x)) (sqrt x)) (/.f64 #s(literal 1/2 binary64) x)) (sqrt.f64 (+.f64 x #s(literal 1 binary64))))
#s(approx (- (/ 1 (sqrt x)) (/ 1 (sqrt (+ x 1)))) (*.f64 (/.f64 (neg.f64 (/.f64 #s(approx (- (sqrt (/ 1 x)) (sqrt x)) (sqrt.f64 x)) x)) x) #s(literal -1/2 binary64)))
(/.f64 #s(approx (/ (- (sqrt (+ x 1)) (sqrt x)) (sqrt (+ x 1))) (/.f64 #s(approx (- (+ (/ 1/4 (* x x)) 1/2) (/ 3/8 x)) (-.f64 #s(literal 1/2 binary64) (/.f64 #s(literal 3/8 binary64) x))) x)) (sqrt.f64 x))
(-.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 x)) (/.f64 #s(literal 1 binary64) (sqrt.f64 (+.f64 x #s(literal 1 binary64)))))
(/.f64 #s(approx (/ (- (sqrt (+ x 1)) (sqrt x)) (sqrt x)) (/.f64 (-.f64 #s(literal 1/2 binary64) (/.f64 #s(literal 1/8 binary64) x)) x)) (sqrt.f64 (+.f64 x #s(literal 1 binary64))))
(/.f64 #s(approx (/ (- (sqrt (+ x 1)) (sqrt x)) (sqrt (+ x 1))) (/.f64 (-.f64 #s(literal 1/2 binary64) (*.f64 #s(literal 1 binary64) (/.f64 #s(literal 3/8 binary64) x))) x)) (sqrt.f64 x))
#s(approx (- (/ 1 (sqrt x)) (/ 1 (sqrt (+ x 1)))) (*.f64 (/.f64 (-.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) (sqrt.f64 x)) (*.f64 x x)) #s(literal -1/2 binary64)))
Outputs
(/.f64 #s(approx (/ (- (sqrt (+ x 1)) (sqrt x)) (sqrt x)) (/.f64 (-.f64 #s(literal 1/2 binary64) (/.f64 #s(literal 1/8 binary64) x)) x)) (sqrt.f64 (+.f64 x #s(literal 1 binary64))))
Calls

2 calls:

9.0ms
x
3.0ms
(-.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 x)) (/.f64 #s(literal 1 binary64) (sqrt.f64 (+.f64 x #s(literal 1 binary64)))))
Results
AccuracySegmentsBranch
98.9%1(-.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 x)) (/.f64 #s(literal 1 binary64) (sqrt.f64 (+.f64 x #s(literal 1 binary64)))))
98.9%1x
Compiler

Compiled 12 to 9 computations (25% saved)

regimes7.0ms (0.1%)

Memory
7.1MiB live, 7.1MiB allocated
Counts
13 → 1
Calls
Call 1
Inputs
#s(approx (- (/ 1 (sqrt x)) (/ 1 (sqrt (+ x 1)))) (sqrt.f64 (/.f64 #s(literal 1 binary64) x)))
#s(approx (- (/ 1 (sqrt x)) (/ 1 (sqrt (+ x 1)))) (/.f64 #s(literal 1 binary64) (sqrt.f64 x)))
#s(approx (- (/ 1 (sqrt x)) (/ 1 (sqrt (+ x 1)))) (/.f64 (sqrt.f64 x) x))
#s(approx (- (/ 1 (sqrt x)) (/ 1 (sqrt (+ x 1)))) (sqrt.f64 (/.f64 x (*.f64 x x))))
#s(approx (- (/ 1 (sqrt x)) (/ 1 (sqrt (+ x 1)))) (*.f64 #s(approx (- (sqrt (/ 1 x)) (sqrt x)) (sqrt.f64 x)) (/.f64 #s(literal -1/2 binary64) (*.f64 x x))))
#s(approx (- (/ 1 (sqrt x)) (/ 1 (sqrt (+ x 1)))) (/.f64 (*.f64 #s(literal -1/2 binary64) #s(approx (- (sqrt (/ 1 x)) (sqrt x)) (sqrt.f64 x))) (*.f64 x x)))
(/.f64 #s(approx (/ (- (sqrt (+ x 1)) (sqrt x)) (sqrt (+ x 1))) (/.f64 #s(literal 1/2 binary64) x)) (sqrt.f64 x))
(/.f64 #s(approx (/ (- (sqrt (+ x 1)) (sqrt x)) (sqrt (+ x 1))) (/.f64 #s(approx (- (+ (/ 1/4 (* x x)) 1/2) (/ 3/8 x)) #s(literal 1/2 binary64)) x)) (sqrt.f64 x))
#s(approx (- (/ 1 (sqrt x)) (/ 1 (sqrt (+ x 1)))) (*.f64 (/.f64 #s(approx (- (sqrt (/ 1 x)) (sqrt x)) (neg.f64 (sqrt.f64 x))) (*.f64 x x)) #s(literal -1/2 binary64)))
(/.f64 #s(approx (/ (- (sqrt (+ x 1)) (sqrt x)) (sqrt x)) (/.f64 #s(literal 1/2 binary64) x)) (sqrt.f64 (+.f64 x #s(literal 1 binary64))))
#s(approx (- (/ 1 (sqrt x)) (/ 1 (sqrt (+ x 1)))) (*.f64 (/.f64 (neg.f64 (/.f64 #s(approx (- (sqrt (/ 1 x)) (sqrt x)) (sqrt.f64 x)) x)) x) #s(literal -1/2 binary64)))
(/.f64 #s(approx (/ (- (sqrt (+ x 1)) (sqrt x)) (sqrt (+ x 1))) (/.f64 #s(approx (- (+ (/ 1/4 (* x x)) 1/2) (/ 3/8 x)) (-.f64 #s(literal 1/2 binary64) (/.f64 #s(literal 3/8 binary64) x))) x)) (sqrt.f64 x))
(-.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 x)) (/.f64 #s(literal 1 binary64) (sqrt.f64 (+.f64 x #s(literal 1 binary64)))))
Outputs
(/.f64 #s(approx (/ (- (sqrt (+ x 1)) (sqrt x)) (sqrt (+ x 1))) (/.f64 #s(approx (- (+ (/ 1/4 (* x x)) 1/2) (/ 3/8 x)) (-.f64 #s(literal 1/2 binary64) (/.f64 #s(literal 3/8 binary64) x))) x)) (sqrt.f64 x))
Calls

2 calls:

4.0ms
x
3.0ms
(-.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 x)) (/.f64 #s(literal 1 binary64) (sqrt.f64 (+.f64 x #s(literal 1 binary64)))))
Results
AccuracySegmentsBranch
98.8%1(-.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 x)) (/.f64 #s(literal 1 binary64) (sqrt.f64 (+.f64 x #s(literal 1 binary64)))))
98.8%1x
Compiler

Compiled 12 to 9 computations (25% saved)

regimes6.0ms (0.1%)

Memory
7.0MiB live, 7.0MiB allocated
Counts
11 → 1
Calls
Call 1
Inputs
#s(approx (- (/ 1 (sqrt x)) (/ 1 (sqrt (+ x 1)))) (sqrt.f64 (/.f64 #s(literal 1 binary64) x)))
#s(approx (- (/ 1 (sqrt x)) (/ 1 (sqrt (+ x 1)))) (/.f64 #s(literal 1 binary64) (sqrt.f64 x)))
#s(approx (- (/ 1 (sqrt x)) (/ 1 (sqrt (+ x 1)))) (/.f64 (sqrt.f64 x) x))
#s(approx (- (/ 1 (sqrt x)) (/ 1 (sqrt (+ x 1)))) (sqrt.f64 (/.f64 x (*.f64 x x))))
#s(approx (- (/ 1 (sqrt x)) (/ 1 (sqrt (+ x 1)))) (*.f64 #s(approx (- (sqrt (/ 1 x)) (sqrt x)) (sqrt.f64 x)) (/.f64 #s(literal -1/2 binary64) (*.f64 x x))))
#s(approx (- (/ 1 (sqrt x)) (/ 1 (sqrt (+ x 1)))) (/.f64 (*.f64 #s(literal -1/2 binary64) #s(approx (- (sqrt (/ 1 x)) (sqrt x)) (sqrt.f64 x))) (*.f64 x x)))
(/.f64 #s(approx (/ (- (sqrt (+ x 1)) (sqrt x)) (sqrt (+ x 1))) (/.f64 #s(literal 1/2 binary64) x)) (sqrt.f64 x))
(/.f64 #s(approx (/ (- (sqrt (+ x 1)) (sqrt x)) (sqrt (+ x 1))) (/.f64 #s(approx (- (+ (/ 1/4 (* x x)) 1/2) (/ 3/8 x)) #s(literal 1/2 binary64)) x)) (sqrt.f64 x))
#s(approx (- (/ 1 (sqrt x)) (/ 1 (sqrt (+ x 1)))) (*.f64 (/.f64 #s(approx (- (sqrt (/ 1 x)) (sqrt x)) (neg.f64 (sqrt.f64 x))) (*.f64 x x)) #s(literal -1/2 binary64)))
(/.f64 #s(approx (/ (- (sqrt (+ x 1)) (sqrt x)) (sqrt x)) (/.f64 #s(literal 1/2 binary64) x)) (sqrt.f64 (+.f64 x #s(literal 1 binary64))))
#s(approx (- (/ 1 (sqrt x)) (/ 1 (sqrt (+ x 1)))) (*.f64 (/.f64 (neg.f64 (/.f64 #s(approx (- (sqrt (/ 1 x)) (sqrt x)) (sqrt.f64 x)) x)) x) #s(literal -1/2 binary64)))
Outputs
(/.f64 #s(approx (/ (- (sqrt (+ x 1)) (sqrt x)) (sqrt x)) (/.f64 #s(literal 1/2 binary64) x)) (sqrt.f64 (+.f64 x #s(literal 1 binary64))))
Calls

2 calls:

3.0ms
x
2.0ms
(-.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 x)) (/.f64 #s(literal 1 binary64) (sqrt.f64 (+.f64 x #s(literal 1 binary64)))))
Results
AccuracySegmentsBranch
98.2%1(-.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 x)) (/.f64 #s(literal 1 binary64) (sqrt.f64 (+.f64 x #s(literal 1 binary64)))))
98.2%1x
Compiler

Compiled 12 to 9 computations (25% saved)

regimes6.0ms (0.1%)

Memory
6.1MiB live, 6.1MiB allocated
Counts
9 → 1
Calls
Call 1
Inputs
#s(approx (- (/ 1 (sqrt x)) (/ 1 (sqrt (+ x 1)))) (sqrt.f64 (/.f64 #s(literal 1 binary64) x)))
#s(approx (- (/ 1 (sqrt x)) (/ 1 (sqrt (+ x 1)))) (/.f64 #s(literal 1 binary64) (sqrt.f64 x)))
#s(approx (- (/ 1 (sqrt x)) (/ 1 (sqrt (+ x 1)))) (/.f64 (sqrt.f64 x) x))
#s(approx (- (/ 1 (sqrt x)) (/ 1 (sqrt (+ x 1)))) (sqrt.f64 (/.f64 x (*.f64 x x))))
#s(approx (- (/ 1 (sqrt x)) (/ 1 (sqrt (+ x 1)))) (*.f64 #s(approx (- (sqrt (/ 1 x)) (sqrt x)) (sqrt.f64 x)) (/.f64 #s(literal -1/2 binary64) (*.f64 x x))))
#s(approx (- (/ 1 (sqrt x)) (/ 1 (sqrt (+ x 1)))) (/.f64 (*.f64 #s(literal -1/2 binary64) #s(approx (- (sqrt (/ 1 x)) (sqrt x)) (sqrt.f64 x))) (*.f64 x x)))
(/.f64 #s(approx (/ (- (sqrt (+ x 1)) (sqrt x)) (sqrt (+ x 1))) (/.f64 #s(literal 1/2 binary64) x)) (sqrt.f64 x))
(/.f64 #s(approx (/ (- (sqrt (+ x 1)) (sqrt x)) (sqrt (+ x 1))) (/.f64 #s(approx (- (+ (/ 1/4 (* x x)) 1/2) (/ 3/8 x)) #s(literal 1/2 binary64)) x)) (sqrt.f64 x))
#s(approx (- (/ 1 (sqrt x)) (/ 1 (sqrt (+ x 1)))) (*.f64 (/.f64 #s(approx (- (sqrt (/ 1 x)) (sqrt x)) (neg.f64 (sqrt.f64 x))) (*.f64 x x)) #s(literal -1/2 binary64)))
Outputs
(/.f64 #s(approx (/ (- (sqrt (+ x 1)) (sqrt x)) (sqrt (+ x 1))) (/.f64 #s(literal 1/2 binary64) x)) (sqrt.f64 x))
Calls

2 calls:

3.0ms
x
2.0ms
(-.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 x)) (/.f64 #s(literal 1 binary64) (sqrt.f64 (+.f64 x #s(literal 1 binary64)))))
Results
AccuracySegmentsBranch
98.1%1(-.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 x)) (/.f64 #s(literal 1 binary64) (sqrt.f64 (+.f64 x #s(literal 1 binary64)))))
98.1%1x
Compiler

Compiled 12 to 9 computations (25% saved)

regimes4.0ms (0.1%)

Memory
5.3MiB live, 5.3MiB allocated
Counts
6 → 1
Calls
Call 1
Inputs
#s(approx (- (/ 1 (sqrt x)) (/ 1 (sqrt (+ x 1)))) (sqrt.f64 (/.f64 #s(literal 1 binary64) x)))
#s(approx (- (/ 1 (sqrt x)) (/ 1 (sqrt (+ x 1)))) (/.f64 #s(literal 1 binary64) (sqrt.f64 x)))
#s(approx (- (/ 1 (sqrt x)) (/ 1 (sqrt (+ x 1)))) (/.f64 (sqrt.f64 x) x))
#s(approx (- (/ 1 (sqrt x)) (/ 1 (sqrt (+ x 1)))) (sqrt.f64 (/.f64 x (*.f64 x x))))
#s(approx (- (/ 1 (sqrt x)) (/ 1 (sqrt (+ x 1)))) (*.f64 #s(approx (- (sqrt (/ 1 x)) (sqrt x)) (sqrt.f64 x)) (/.f64 #s(literal -1/2 binary64) (*.f64 x x))))
#s(approx (- (/ 1 (sqrt x)) (/ 1 (sqrt (+ x 1)))) (/.f64 (*.f64 #s(literal -1/2 binary64) #s(approx (- (sqrt (/ 1 x)) (sqrt x)) (sqrt.f64 x))) (*.f64 x x)))
Outputs
#s(approx (- (/ 1 (sqrt x)) (/ 1 (sqrt (+ x 1)))) (sqrt.f64 (/.f64 x (*.f64 x x))))
Calls

2 calls:

2.0ms
x
2.0ms
(-.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 x)) (/.f64 #s(literal 1 binary64) (sqrt.f64 (+.f64 x #s(literal 1 binary64)))))
Results
AccuracySegmentsBranch
36.4%1(-.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 x)) (/.f64 #s(literal 1 binary64) (sqrt.f64 (+.f64 x #s(literal 1 binary64)))))
36.4%1x
Compiler

Compiled 12 to 9 computations (25% saved)

regimes3.0ms (0%)

Memory
4.0MiB live, 4.0MiB allocated
Accuracy

Total -0.0b remaining (-0%)

Threshold costs -0b (-0%)

Counts
3 → 1
Calls
Call 1
Inputs
#s(approx (- (/ 1 (sqrt x)) (/ 1 (sqrt (+ x 1)))) (sqrt.f64 (/.f64 #s(literal 1 binary64) x)))
#s(approx (- (/ 1 (sqrt x)) (/ 1 (sqrt (+ x 1)))) (/.f64 #s(literal 1 binary64) (sqrt.f64 x)))
#s(approx (- (/ 1 (sqrt x)) (/ 1 (sqrt (+ x 1)))) (/.f64 (sqrt.f64 x) x))
Outputs
#s(approx (- (/ 1 (sqrt x)) (/ 1 (sqrt (+ x 1)))) (sqrt.f64 (/.f64 #s(literal 1 binary64) x)))
Calls

2 calls:

1.0ms
x
1.0ms
(-.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 x)) (/.f64 #s(literal 1 binary64) (sqrt.f64 (+.f64 x #s(literal 1 binary64)))))
Results
AccuracySegmentsBranch
5.5%1x
5.5%1(-.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 x)) (/.f64 #s(literal 1 binary64) (sqrt.f64 (+.f64 x #s(literal 1 binary64)))))
Compiler

Compiled 12 to 9 computations (25% saved)

simplify49.0ms (0.7%)

Memory
-32.4MiB live, 18.5MiB allocated
Algorithm
egg-herbie
Iterations

Useful iterations: 4 (0.0ms)

IterNodesCost
074217
1116203
2221203
3534203
41694201
57072201
Stop Event
node limit
Calls
Call 1
Inputs
(/.f64 #s(approx (/ (- (sqrt (+ x 1)) (sqrt x)) (sqrt (+ x 1))) (/.f64 (-.f64 (+.f64 (/.f64 (+.f64 #s(literal 3/8 binary64) (/.f64 (*.f64 (fma.f64 #s(literal 1/4 binary64) x #s(literal 1 binary64)) #s(literal -1/4 binary64)) x)) (*.f64 x x)) #s(literal 1/2 binary64)) (/.f64 #s(literal 3/8 binary64) x)) x)) (sqrt.f64 x))
(/.f64 #s(approx (/ (- (sqrt (+ x 1)) (sqrt x)) (sqrt (+ x 1))) (/.f64 #s(approx (- (+ (/ (+ 3/8 (/ (* (+ (* 1/4 x) 1) -1/4) x)) (* x x)) 1/2) (/ 3/8 x)) (-.f64 #s(literal 1/2 binary64) (/.f64 (-.f64 #s(literal 3/8 binary64) (/.f64 #s(literal 5/16 binary64) x)) x))) x)) (sqrt.f64 x))
(/.f64 #s(approx (/ (- (sqrt (+ x 1)) (sqrt x)) (sqrt x)) (/.f64 (-.f64 #s(literal 1/2 binary64) (/.f64 #s(literal 1/8 binary64) x)) x)) (sqrt.f64 (+.f64 x #s(literal 1 binary64))))
(/.f64 #s(approx (/ (- (sqrt (+ x 1)) (sqrt x)) (sqrt (+ x 1))) (/.f64 #s(approx (- (+ (/ 1/4 (* x x)) 1/2) (/ 3/8 x)) (-.f64 #s(literal 1/2 binary64) (/.f64 #s(literal 3/8 binary64) x))) x)) (sqrt.f64 x))
(/.f64 #s(approx (/ (- (sqrt (+ x 1)) (sqrt x)) (sqrt x)) (/.f64 #s(literal 1/2 binary64) x)) (sqrt.f64 (+.f64 x #s(literal 1 binary64))))
(/.f64 #s(approx (/ (- (sqrt (+ x 1)) (sqrt x)) (sqrt (+ x 1))) (/.f64 #s(literal 1/2 binary64) x)) (sqrt.f64 x))
#s(approx (- (/ 1 (sqrt x)) (/ 1 (sqrt (+ x 1)))) (sqrt.f64 (/.f64 x (*.f64 x x))))
#s(approx (- (/ 1 (sqrt x)) (/ 1 (sqrt (+ x 1)))) (sqrt.f64 (/.f64 #s(literal 1 binary64) x)))
Outputs
(/.f64 #s(approx (/ (- (sqrt (+ x 1)) (sqrt x)) (sqrt (+ x 1))) (/.f64 (-.f64 (+.f64 (/.f64 (+.f64 #s(literal 3/8 binary64) (/.f64 (*.f64 (fma.f64 #s(literal 1/4 binary64) x #s(literal 1 binary64)) #s(literal -1/4 binary64)) x)) (*.f64 x x)) #s(literal 1/2 binary64)) (/.f64 #s(literal 3/8 binary64) x)) x)) (sqrt.f64 x))
(/.f64 #s(approx (/ (- (sqrt (+ x 1)) (sqrt x)) (sqrt (+ x 1))) (/.f64 #s(approx (- (+ (/ (+ 3/8 (/ (* (+ (* 1/4 x) 1) -1/4) x)) (* x x)) 1/2) (/ 3/8 x)) (-.f64 #s(literal 1/2 binary64) (/.f64 (-.f64 #s(literal 3/8 binary64) (/.f64 #s(literal 5/16 binary64) x)) x))) x)) (sqrt.f64 x))
(/.f64 #s(approx (/ (- (sqrt (+ x 1)) (sqrt x)) (sqrt x)) (/.f64 (-.f64 #s(literal 1/2 binary64) (/.f64 #s(literal 1/8 binary64) x)) x)) (sqrt.f64 (+.f64 x #s(literal 1 binary64))))
(/.f64 #s(approx (/ (- (sqrt (+ x 1)) (sqrt x)) (sqrt (+ x 1))) (/.f64 #s(approx (- (+ (/ 1/4 (* x x)) 1/2) (/ 3/8 x)) (-.f64 #s(literal 1/2 binary64) (/.f64 #s(literal 3/8 binary64) x))) x)) (sqrt.f64 x))
(/.f64 #s(approx (/ (- (sqrt (+ x 1)) (sqrt x)) (sqrt x)) (/.f64 #s(literal 1/2 binary64) x)) (sqrt.f64 (+.f64 x #s(literal 1 binary64))))
(/.f64 #s(approx (/ (- (sqrt (+ x 1)) (sqrt x)) (sqrt (+ x 1))) (/.f64 #s(literal 1/2 binary64) x)) (sqrt.f64 x))
#s(approx (- (/ 1 (sqrt x)) (/ 1 (sqrt (+ x 1)))) (sqrt.f64 (/.f64 x (*.f64 x x))))
#s(approx (- (/ 1 (sqrt x)) (/ 1 (sqrt (+ x 1)))) (sqrt.f64 (/.f64 #s(literal 1 binary64) x)))
#s(approx (- (/ 1 (sqrt x)) (/ 1 (sqrt (+ x 1)))) (sqrt.f64 (pow.f64 x #s(literal -1 binary64))))

derivations834.0ms (12.2%)

Memory
25.7MiB live, 436.4MiB allocated
Iterations

Useful iterations: 3 (0.0ms)

IterNodesCost
04992021
116601744
267551738
080351630
03981672
113291399
256041397
080931311
06113964
120383206
086853068
0823
01423
15919
241619
3567917
0879117
041241
072247
1284212
21968177
09349177
0114457
1333395
21237369
36312369
08119348
Stop Event
fuel
iter limit
node limit
iter limit
node limit
iter limit
iter limit
node limit
iter limit
iter limit
node limit
iter limit
node limit
iter limit
node limit
Compiler

Compiled 217 to 80 computations (63.1% saved)

preprocess46.0ms (0.7%)

Memory
13.3MiB live, 58.2MiB allocated
Compiler

Compiled 474 to 190 computations (59.9% saved)

end0.0ms (0%)

Memory
0.0MiB live, 0.0MiB allocated

Profiling

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