ENA, Section 1.4, Exercise 4d

Time bar (total: 2.9s)

start0.0ms (0%)

Memory
0.1MiB live, 0.1MiB allocated; 0ms collecting garbage

analyze11.0ms (0.4%)

Memory
15.3MiB live, 15.3MiB allocated; 0ms collecting garbage
Algorithm
1×search
Search
ProbabilityValidUnknownPreconditionInfiniteDomainCan'tIter
0%0%12.8%87.2%0%0%0%0
0%0%12.8%87.2%0%0%0%1
0%0%12.8%87.2%0%0%0%2
50%6.4%6.4%87.2%0%0%0%3
57.1%6.4%4.8%87.2%0%1.6%0%4
69.2%7.2%3.2%87.2%0%2.4%0%5
75%7.2%2.4%87.2%0%3.2%0%6
82.6%7.6%1.6%87.2%0%3.6%0%7
86.4%7.6%1.2%87.2%0%4%0%8
90.7%7.8%0.8%87.2%0%4.2%0%9
92.6%7.8%0.6%87.2%0%4.4%0%10
95%7.9%0.4%87.2%0%4.5%0%11
96.3%8%0.3%87.2%0%4.5%0%12
Compiler

Compiled 24 to 18 computations (25% saved)

sample1.3s (43.2%)

Memory
5.0MiB live, 1 741.0MiB allocated; 327ms collecting garbage
Samples
349.0ms2 782×1valid
269.0ms4 801×0valid
121.0ms673×2valid
30.0ms157×0invalid
Precisions
Click to see histograms. Total time spent on operations: 453.0ms
ival-sqrt: 166.0ms (36.7% of total)
ival-mult!: 119.0ms (26.3% of total)
adjust: 104.0ms (23% of total)
ival-sub!: 63.0ms (13.9% of total)
Bogosity

preprocess98.0ms (3.3%)

Memory
1.2MiB live, 44.7MiB allocated; 8ms collecting garbage
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
02154
14454
28054
313254
435254
5195154
6459854
Stop Event
1×node-limit
Alt Table
Click to see full alt table
StatusAccuracyProgram
▶61.5%
(-.f64 x (sqrt.f64 (-.f64 (*.f64 x x) eps)))
Compiler

Compiled 12 to 12 computations (0% saved)

series8.0ms (0.3%)

Memory
17.9MiB live, 17.9MiB allocated; 0ms collecting garbage
Counts
6 → 54
Calls
Call 1
Inputs
(-.f64 x (sqrt.f64 (-.f64 (*.f64 x x) eps)))
x
(sqrt.f64 (-.f64 (*.f64 x x) eps))
(-.f64 (*.f64 x x) eps)
(*.f64 x x)
eps
Outputs
#s(approx (- x (sqrt (- (* x x) eps))) #s(hole binary64 (* -1 (sqrt (neg eps)))))
#s(approx (- x (sqrt (- (* x x) eps))) #s(hole binary64 (- x (sqrt (neg eps)))))
#s(approx (- x (sqrt (- (* x x) eps))) #s(hole binary64 (- (* x (+ 1 (* -1/2 (/ x (sqrt (neg eps)))))) (sqrt (neg eps)))))
#s(approx (- x (sqrt (- (* x x) eps))) #s(hole binary64 (- (* x (+ 1 (* x (- (* 1/8 (/ (pow x 2) (pow (sqrt (neg eps)) 3))) (* 1/2 (/ 1 (sqrt (neg eps)))))))) (sqrt (neg eps)))))
#s(approx x #s(hole binary64 x))
#s(approx (sqrt (- (* x x) eps)) #s(hole binary64 (sqrt (neg eps))))
#s(approx (sqrt (- (* x x) eps)) #s(hole binary64 (+ (sqrt (neg eps)) (* 1/2 (/ (pow x 2) (sqrt (neg eps)))))))
#s(approx (sqrt (- (* x x) eps)) #s(hole binary64 (+ (sqrt (neg eps)) (* (pow x 2) (+ (* -1/8 (/ (pow x 2) (pow (sqrt (neg eps)) 3))) (* 1/2 (/ 1 (sqrt (neg eps)))))))))
#s(approx (sqrt (- (* x x) eps)) #s(hole binary64 (+ (sqrt (neg eps)) (* (pow x 2) (+ (* (pow x 2) (- (* 1/16 (/ (pow x 2) (pow (sqrt (neg eps)) 5))) (* 1/8 (/ 1 (pow (sqrt (neg eps)) 3))))) (* 1/2 (/ 1 (sqrt (neg eps)))))))))
#s(approx (- (* x x) eps) #s(hole binary64 (* -1 eps)))
#s(approx (- (* x x) eps) #s(hole binary64 (- (pow x 2) eps)))
#s(approx (* x x) #s(hole binary64 (pow x 2)))
#s(approx (- x (sqrt (- (* x x) eps))) #s(hole binary64 (* 1/2 (/ eps x))))
#s(approx (- x (sqrt (- (* x x) eps))) #s(hole binary64 (/ (- (* 1/8 (/ (pow eps 2) (pow x 2))) (* -1/2 eps)) x)))
#s(approx (- x (sqrt (- (* x x) eps))) #s(hole binary64 (/ (- (* 1/16 (/ (pow eps 3) (pow x 4))) (+ (* -1/2 eps) (* -1/8 (/ (pow eps 2) (pow x 2))))) x)))
#s(approx (- x (sqrt (- (* x x) eps))) #s(hole binary64 (/ (- (* 1/2 (/ (+ (* 1/64 (pow eps 4)) (* 1/16 (pow eps 4))) (pow x 6))) (+ (* -1/2 eps) (+ (* -1/8 (/ (pow eps 2) (pow x 2))) (* -1/16 (/ (pow eps 3) (pow x 4)))))) x)))
#s(approx (sqrt (- (* x x) eps)) #s(hole binary64 (* x (+ 1 (* -1/2 (/ eps (pow x 2)))))))
#s(approx (sqrt (- (* x x) eps)) #s(hole binary64 (* x (+ 1 (+ (* -1/2 (/ eps (pow x 2))) (* -1/8 (/ (pow eps 2) (pow x 4))))))))
#s(approx (sqrt (- (* x x) eps)) #s(hole binary64 (* x (+ 1 (+ (* -1/2 (/ eps (pow x 2))) (+ (* -1/8 (/ (pow eps 2) (pow x 4))) (* -1/16 (/ (pow eps 3) (pow x 6)))))))))
#s(approx (- (* x x) eps) #s(hole binary64 (* (pow x 2) (+ 1 (* -1 (/ eps (pow x 2)))))))
#s(approx (- x (sqrt (- (* x x) eps))) #s(hole binary64 (* 2 x)))
#s(approx (- x (sqrt (- (* x x) eps))) #s(hole binary64 (* -1 (* x (- (* 1/2 (/ eps (pow x 2))) 2)))))
#s(approx (- x (sqrt (- (* x x) eps))) #s(hole binary64 (* -1 (* x (- (* 1/8 (/ (pow eps 2) (pow x 4))) (+ 2 (* -1/2 (/ eps (pow x 2)))))))))
#s(approx (- x (sqrt (- (* x x) eps))) #s(hole binary64 (* -1 (* x (- (* 1/16 (/ (pow eps 3) (pow x 6))) (+ 2 (+ (* -1/2 (/ eps (pow x 2))) (* -1/8 (/ (pow eps 2) (pow x 4))))))))))
#s(approx (sqrt (- (* x x) eps)) #s(hole binary64 (* -1 x)))
#s(approx (sqrt (- (* x x) eps)) #s(hole binary64 (* -1 (* x (+ 1 (* -1/2 (/ eps (pow x 2))))))))
#s(approx (sqrt (- (* x x) eps)) #s(hole binary64 (* -1 (* x (+ 1 (+ (* -1/2 (/ eps (pow x 2))) (* -1/8 (/ (pow eps 2) (pow x 4)))))))))
#s(approx (sqrt (- (* x x) eps)) #s(hole binary64 (* -1 (* x (+ 1 (+ (* -1/2 (/ eps (pow x 2))) (+ (* -1/8 (/ (pow eps 2) (pow x 4))) (* -1/16 (/ (pow eps 3) (pow x 6))))))))))
#s(approx (- x (sqrt (- (* x x) eps))) #s(hole binary64 (- x (sqrt (pow x 2)))))
#s(approx (- x (sqrt (- (* x x) eps))) #s(hole binary64 (- (+ x (* 1/2 (/ eps (sqrt (pow x 2))))) (sqrt (pow x 2)))))
#s(approx (- x (sqrt (- (* x x) eps))) #s(hole binary64 (- (+ x (* eps (+ (* 1/8 (/ eps (pow (sqrt (pow x 2)) 3))) (* 1/2 (/ 1 (sqrt (pow x 2))))))) (sqrt (pow x 2)))))
#s(approx (- x (sqrt (- (* x x) eps))) #s(hole binary64 (- (+ x (* eps (+ (* eps (+ (* 1/16 (/ eps (pow (sqrt (pow x 2)) 5))) (* 1/8 (/ 1 (pow (sqrt (pow x 2)) 3))))) (* 1/2 (/ 1 (sqrt (pow x 2))))))) (sqrt (pow x 2)))))
#s(approx (sqrt (- (* x x) eps)) #s(hole binary64 (sqrt (pow x 2))))
#s(approx (sqrt (- (* x x) eps)) #s(hole binary64 (+ (sqrt (pow x 2)) (* -1/2 (/ eps (sqrt (pow x 2)))))))
#s(approx (sqrt (- (* x x) eps)) #s(hole binary64 (+ (sqrt (pow x 2)) (* eps (- (* -1/8 (/ eps (pow (sqrt (pow x 2)) 3))) (* 1/2 (/ 1 (sqrt (pow x 2)))))))))
#s(approx (sqrt (- (* x x) eps)) #s(hole binary64 (+ (sqrt (pow x 2)) (* eps (- (* eps (- (* -1/16 (/ eps (pow (sqrt (pow x 2)) 5))) (* 1/8 (/ 1 (pow (sqrt (pow x 2)) 3))))) (* 1/2 (/ 1 (sqrt (pow x 2)))))))))
#s(approx (- (* x x) eps) #s(hole binary64 (+ (* -1 eps) (pow x 2))))
#s(approx eps #s(hole binary64 eps))
#s(approx (- x (sqrt (- (* x x) eps))) #s(hole binary64 (* -1 (* eps (sqrt (/ -1 eps))))))
#s(approx (- x (sqrt (- (* x x) eps))) #s(hole binary64 (* eps (- (/ x eps) (sqrt (/ -1 eps))))))
#s(approx (- x (sqrt (- (* x x) eps))) #s(hole binary64 (* eps (- (+ (* -1/2 (/ (pow x 2) (* (pow eps 2) (sqrt (/ -1 eps))))) (/ x eps)) (sqrt (/ -1 eps))))))
#s(approx (- x (sqrt (- (* x x) eps))) #s(hole binary64 (* eps (- (+ (* 1/8 (/ (pow x 4) (* (pow eps 4) (pow (sqrt (/ -1 eps)) 3)))) (/ x eps)) (+ (sqrt (/ -1 eps)) (* 1/2 (/ (pow x 2) (* (pow eps 2) (sqrt (/ -1 eps))))))))))
#s(approx (sqrt (- (* x x) eps)) #s(hole binary64 (* eps (sqrt (/ -1 eps)))))
#s(approx (sqrt (- (* x x) eps)) #s(hole binary64 (* eps (+ (sqrt (/ -1 eps)) (* 1/2 (/ (pow x 2) (* (pow eps 2) (sqrt (/ -1 eps)))))))))
#s(approx (sqrt (- (* x x) eps)) #s(hole binary64 (* eps (+ (sqrt (/ -1 eps)) (+ (* -1/8 (/ (pow x 4) (* (pow eps 4) (pow (sqrt (/ -1 eps)) 3)))) (* 1/2 (/ (pow x 2) (* (pow eps 2) (sqrt (/ -1 eps))))))))))
#s(approx (sqrt (- (* x x) eps)) #s(hole binary64 (* eps (+ (sqrt (/ -1 eps)) (+ (* -1/8 (/ (pow x 4) (* (pow eps 4) (pow (sqrt (/ -1 eps)) 3)))) (+ (* 1/16 (/ (pow x 6) (* (pow eps 6) (pow (sqrt (/ -1 eps)) 5)))) (* 1/2 (/ (pow x 2) (* (pow eps 2) (sqrt (/ -1 eps)))))))))))
#s(approx (- (* x x) eps) #s(hole binary64 (* eps (- (/ (pow x 2) eps) 1))))
#s(approx (- x (sqrt (- (* x x) eps))) #s(hole binary64 (* -1 (* eps (- (* -1 (/ x eps)) (sqrt (/ -1 eps)))))))
#s(approx (- x (sqrt (- (* x x) eps))) #s(hole binary64 (* -1 (* eps (- (* -1 (/ (+ x (* 1/2 (/ (pow x 2) (* eps (sqrt (/ -1 eps)))))) eps)) (sqrt (/ -1 eps)))))))
#s(approx (- x (sqrt (- (* x x) eps))) #s(hole binary64 (* -1 (* eps (- (* -1 (/ (+ x (* -1 (/ (- (* 1/8 (/ (pow x 4) (* (pow eps 2) (pow (sqrt (/ -1 eps)) 3)))) (* 1/2 (/ (pow x 2) (sqrt (/ -1 eps))))) eps))) eps)) (sqrt (/ -1 eps)))))))
#s(approx (sqrt (- (* x x) eps)) #s(hole binary64 (* -1 (* eps (+ (sqrt (/ -1 eps)) (* 1/2 (/ (pow x 2) (* (pow eps 2) (sqrt (/ -1 eps))))))))))
#s(approx (sqrt (- (* x x) eps)) #s(hole binary64 (* -1 (* eps (+ (sqrt (/ -1 eps)) (+ (* -1/8 (/ (pow x 4) (* (pow eps 4) (pow (sqrt (/ -1 eps)) 3)))) (* 1/2 (/ (pow x 2) (* (pow eps 2) (sqrt (/ -1 eps)))))))))))
#s(approx (sqrt (- (* x x) eps)) #s(hole binary64 (* -1 (* eps (+ (sqrt (/ -1 eps)) (+ (* -1/8 (/ (pow x 4) (* (pow eps 4) (pow (sqrt (/ -1 eps)) 3)))) (+ (* 1/16 (/ (pow x 6) (* (pow eps 6) (pow (sqrt (/ -1 eps)) 5)))) (* 1/2 (/ (pow x 2) (* (pow eps 2) (sqrt (/ -1 eps))))))))))))
#s(approx (- (* x x) eps) #s(hole binary64 (* -1 (* eps (+ 1 (* -1 (/ (pow x 2) eps)))))))
Calls

6 calls:

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

rewrite186.0ms (6.3%)

Memory
-2.1MiB live, 284.0MiB allocated; 58ms collecting garbage
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
02931501
02981433
116211377
088151331
Stop Event
1×iter-limit
1×node-limit
1×iter-limit
Counts
60 → 99
Calls
Call 1
Inputs
(-.f64 x (sqrt.f64 (-.f64 (*.f64 x x) eps)))
x
(sqrt.f64 (-.f64 (*.f64 x x) eps))
(-.f64 (*.f64 x x) eps)
(*.f64 x x)
eps
#s(approx (- x (sqrt (- (* x x) eps))) #s(hole binary64 (* -1 (sqrt (neg eps)))))
#s(approx (- x (sqrt (- (* x x) eps))) #s(hole binary64 (- x (sqrt (neg eps)))))
#s(approx (- x (sqrt (- (* x x) eps))) #s(hole binary64 (- (* x (+ 1 (* -1/2 (/ x (sqrt (neg eps)))))) (sqrt (neg eps)))))
#s(approx (- x (sqrt (- (* x x) eps))) #s(hole binary64 (- (* x (+ 1 (* x (- (* 1/8 (/ (pow x 2) (pow (sqrt (neg eps)) 3))) (* 1/2 (/ 1 (sqrt (neg eps)))))))) (sqrt (neg eps)))))
#s(approx x #s(hole binary64 x))
#s(approx (sqrt (- (* x x) eps)) #s(hole binary64 (sqrt (neg eps))))
#s(approx (sqrt (- (* x x) eps)) #s(hole binary64 (+ (sqrt (neg eps)) (* 1/2 (/ (pow x 2) (sqrt (neg eps)))))))
#s(approx (sqrt (- (* x x) eps)) #s(hole binary64 (+ (sqrt (neg eps)) (* (pow x 2) (+ (* -1/8 (/ (pow x 2) (pow (sqrt (neg eps)) 3))) (* 1/2 (/ 1 (sqrt (neg eps)))))))))
#s(approx (sqrt (- (* x x) eps)) #s(hole binary64 (+ (sqrt (neg eps)) (* (pow x 2) (+ (* (pow x 2) (- (* 1/16 (/ (pow x 2) (pow (sqrt (neg eps)) 5))) (* 1/8 (/ 1 (pow (sqrt (neg eps)) 3))))) (* 1/2 (/ 1 (sqrt (neg eps)))))))))
#s(approx (- (* x x) eps) #s(hole binary64 (* -1 eps)))
#s(approx (- (* x x) eps) #s(hole binary64 (- (pow x 2) eps)))
#s(approx (* x x) #s(hole binary64 (pow x 2)))
#s(approx (- x (sqrt (- (* x x) eps))) #s(hole binary64 (* 1/2 (/ eps x))))
#s(approx (- x (sqrt (- (* x x) eps))) #s(hole binary64 (/ (- (* 1/8 (/ (pow eps 2) (pow x 2))) (* -1/2 eps)) x)))
#s(approx (- x (sqrt (- (* x x) eps))) #s(hole binary64 (/ (- (* 1/16 (/ (pow eps 3) (pow x 4))) (+ (* -1/2 eps) (* -1/8 (/ (pow eps 2) (pow x 2))))) x)))
#s(approx (- x (sqrt (- (* x x) eps))) #s(hole binary64 (/ (- (* 1/2 (/ (+ (* 1/64 (pow eps 4)) (* 1/16 (pow eps 4))) (pow x 6))) (+ (* -1/2 eps) (+ (* -1/8 (/ (pow eps 2) (pow x 2))) (* -1/16 (/ (pow eps 3) (pow x 4)))))) x)))
#s(approx (sqrt (- (* x x) eps)) #s(hole binary64 (* x (+ 1 (* -1/2 (/ eps (pow x 2)))))))
#s(approx (sqrt (- (* x x) eps)) #s(hole binary64 (* x (+ 1 (+ (* -1/2 (/ eps (pow x 2))) (* -1/8 (/ (pow eps 2) (pow x 4))))))))
#s(approx (sqrt (- (* x x) eps)) #s(hole binary64 (* x (+ 1 (+ (* -1/2 (/ eps (pow x 2))) (+ (* -1/8 (/ (pow eps 2) (pow x 4))) (* -1/16 (/ (pow eps 3) (pow x 6)))))))))
#s(approx (- (* x x) eps) #s(hole binary64 (* (pow x 2) (+ 1 (* -1 (/ eps (pow x 2)))))))
#s(approx (- x (sqrt (- (* x x) eps))) #s(hole binary64 (* 2 x)))
#s(approx (- x (sqrt (- (* x x) eps))) #s(hole binary64 (* -1 (* x (- (* 1/2 (/ eps (pow x 2))) 2)))))
#s(approx (- x (sqrt (- (* x x) eps))) #s(hole binary64 (* -1 (* x (- (* 1/8 (/ (pow eps 2) (pow x 4))) (+ 2 (* -1/2 (/ eps (pow x 2)))))))))
#s(approx (- x (sqrt (- (* x x) eps))) #s(hole binary64 (* -1 (* x (- (* 1/16 (/ (pow eps 3) (pow x 6))) (+ 2 (+ (* -1/2 (/ eps (pow x 2))) (* -1/8 (/ (pow eps 2) (pow x 4))))))))))
#s(approx (sqrt (- (* x x) eps)) #s(hole binary64 (* -1 x)))
#s(approx (sqrt (- (* x x) eps)) #s(hole binary64 (* -1 (* x (+ 1 (* -1/2 (/ eps (pow x 2))))))))
#s(approx (sqrt (- (* x x) eps)) #s(hole binary64 (* -1 (* x (+ 1 (+ (* -1/2 (/ eps (pow x 2))) (* -1/8 (/ (pow eps 2) (pow x 4)))))))))
#s(approx (sqrt (- (* x x) eps)) #s(hole binary64 (* -1 (* x (+ 1 (+ (* -1/2 (/ eps (pow x 2))) (+ (* -1/8 (/ (pow eps 2) (pow x 4))) (* -1/16 (/ (pow eps 3) (pow x 6))))))))))
#s(approx (- x (sqrt (- (* x x) eps))) #s(hole binary64 (- x (sqrt (pow x 2)))))
#s(approx (- x (sqrt (- (* x x) eps))) #s(hole binary64 (- (+ x (* 1/2 (/ eps (sqrt (pow x 2))))) (sqrt (pow x 2)))))
#s(approx (- x (sqrt (- (* x x) eps))) #s(hole binary64 (- (+ x (* eps (+ (* 1/8 (/ eps (pow (sqrt (pow x 2)) 3))) (* 1/2 (/ 1 (sqrt (pow x 2))))))) (sqrt (pow x 2)))))
#s(approx (- x (sqrt (- (* x x) eps))) #s(hole binary64 (- (+ x (* eps (+ (* eps (+ (* 1/16 (/ eps (pow (sqrt (pow x 2)) 5))) (* 1/8 (/ 1 (pow (sqrt (pow x 2)) 3))))) (* 1/2 (/ 1 (sqrt (pow x 2))))))) (sqrt (pow x 2)))))
#s(approx (sqrt (- (* x x) eps)) #s(hole binary64 (sqrt (pow x 2))))
#s(approx (sqrt (- (* x x) eps)) #s(hole binary64 (+ (sqrt (pow x 2)) (* -1/2 (/ eps (sqrt (pow x 2)))))))
#s(approx (sqrt (- (* x x) eps)) #s(hole binary64 (+ (sqrt (pow x 2)) (* eps (- (* -1/8 (/ eps (pow (sqrt (pow x 2)) 3))) (* 1/2 (/ 1 (sqrt (pow x 2)))))))))
#s(approx (sqrt (- (* x x) eps)) #s(hole binary64 (+ (sqrt (pow x 2)) (* eps (- (* eps (- (* -1/16 (/ eps (pow (sqrt (pow x 2)) 5))) (* 1/8 (/ 1 (pow (sqrt (pow x 2)) 3))))) (* 1/2 (/ 1 (sqrt (pow x 2)))))))))
#s(approx (- (* x x) eps) #s(hole binary64 (+ (* -1 eps) (pow x 2))))
#s(approx eps #s(hole binary64 eps))
#s(approx (- x (sqrt (- (* x x) eps))) #s(hole binary64 (* -1 (* eps (sqrt (/ -1 eps))))))
#s(approx (- x (sqrt (- (* x x) eps))) #s(hole binary64 (* eps (- (/ x eps) (sqrt (/ -1 eps))))))
#s(approx (- x (sqrt (- (* x x) eps))) #s(hole binary64 (* eps (- (+ (* -1/2 (/ (pow x 2) (* (pow eps 2) (sqrt (/ -1 eps))))) (/ x eps)) (sqrt (/ -1 eps))))))
#s(approx (- x (sqrt (- (* x x) eps))) #s(hole binary64 (* eps (- (+ (* 1/8 (/ (pow x 4) (* (pow eps 4) (pow (sqrt (/ -1 eps)) 3)))) (/ x eps)) (+ (sqrt (/ -1 eps)) (* 1/2 (/ (pow x 2) (* (pow eps 2) (sqrt (/ -1 eps))))))))))
#s(approx (sqrt (- (* x x) eps)) #s(hole binary64 (* eps (sqrt (/ -1 eps)))))
#s(approx (sqrt (- (* x x) eps)) #s(hole binary64 (* eps (+ (sqrt (/ -1 eps)) (* 1/2 (/ (pow x 2) (* (pow eps 2) (sqrt (/ -1 eps)))))))))
#s(approx (sqrt (- (* x x) eps)) #s(hole binary64 (* eps (+ (sqrt (/ -1 eps)) (+ (* -1/8 (/ (pow x 4) (* (pow eps 4) (pow (sqrt (/ -1 eps)) 3)))) (* 1/2 (/ (pow x 2) (* (pow eps 2) (sqrt (/ -1 eps))))))))))
#s(approx (sqrt (- (* x x) eps)) #s(hole binary64 (* eps (+ (sqrt (/ -1 eps)) (+ (* -1/8 (/ (pow x 4) (* (pow eps 4) (pow (sqrt (/ -1 eps)) 3)))) (+ (* 1/16 (/ (pow x 6) (* (pow eps 6) (pow (sqrt (/ -1 eps)) 5)))) (* 1/2 (/ (pow x 2) (* (pow eps 2) (sqrt (/ -1 eps)))))))))))
#s(approx (- (* x x) eps) #s(hole binary64 (* eps (- (/ (pow x 2) eps) 1))))
#s(approx (- x (sqrt (- (* x x) eps))) #s(hole binary64 (* -1 (* eps (- (* -1 (/ x eps)) (sqrt (/ -1 eps)))))))
#s(approx (- x (sqrt (- (* x x) eps))) #s(hole binary64 (* -1 (* eps (- (* -1 (/ (+ x (* 1/2 (/ (pow x 2) (* eps (sqrt (/ -1 eps)))))) eps)) (sqrt (/ -1 eps)))))))
#s(approx (- x (sqrt (- (* x x) eps))) #s(hole binary64 (* -1 (* eps (- (* -1 (/ (+ x (* -1 (/ (- (* 1/8 (/ (pow x 4) (* (pow eps 2) (pow (sqrt (/ -1 eps)) 3)))) (* 1/2 (/ (pow x 2) (sqrt (/ -1 eps))))) eps))) eps)) (sqrt (/ -1 eps)))))))
#s(approx (sqrt (- (* x x) eps)) #s(hole binary64 (* -1 (* eps (+ (sqrt (/ -1 eps)) (* 1/2 (/ (pow x 2) (* (pow eps 2) (sqrt (/ -1 eps))))))))))
#s(approx (sqrt (- (* x x) eps)) #s(hole binary64 (* -1 (* eps (+ (sqrt (/ -1 eps)) (+ (* -1/8 (/ (pow x 4) (* (pow eps 4) (pow (sqrt (/ -1 eps)) 3)))) (* 1/2 (/ (pow x 2) (* (pow eps 2) (sqrt (/ -1 eps)))))))))))
#s(approx (sqrt (- (* x x) eps)) #s(hole binary64 (* -1 (* eps (+ (sqrt (/ -1 eps)) (+ (* -1/8 (/ (pow x 4) (* (pow eps 4) (pow (sqrt (/ -1 eps)) 3)))) (+ (* 1/16 (/ (pow x 6) (* (pow eps 6) (pow (sqrt (/ -1 eps)) 5)))) (* 1/2 (/ (pow x 2) (* (pow eps 2) (sqrt (/ -1 eps))))))))))))
#s(approx (- (* x x) eps) #s(hole binary64 (* -1 (* eps (+ 1 (* -1 (/ (pow x 2) eps)))))))
Outputs
(/.f64 (neg.f64 (-.f64 (*.f64 x x) (-.f64 (*.f64 x x) eps))) (neg.f64 (+.f64 x (sqrt.f64 (-.f64 (*.f64 x x) eps)))))
(/.f64 (neg.f64 (-.f64 (*.f64 (*.f64 x x) x) (*.f64 (sqrt.f64 (-.f64 (*.f64 x x) eps)) (-.f64 (*.f64 x x) eps)))) (neg.f64 (fma.f64 x x (+.f64 (-.f64 (*.f64 x x) eps) (*.f64 x (sqrt.f64 (-.f64 (*.f64 x x) eps)))))))
(/.f64 (-.f64 (*.f64 x x) (-.f64 (*.f64 x x) eps)) (+.f64 x (sqrt.f64 (-.f64 (*.f64 x x) eps))))
(/.f64 (-.f64 (*.f64 (*.f64 x x) x) (*.f64 (sqrt.f64 (-.f64 (*.f64 x x) eps)) (-.f64 (*.f64 x x) eps))) (fma.f64 x x (+.f64 (-.f64 (*.f64 x x) eps) (*.f64 x (sqrt.f64 (-.f64 (*.f64 x x) eps))))))
(-.f64 (/.f64 (*.f64 x x) (+.f64 x (sqrt.f64 (-.f64 (*.f64 x x) eps)))) (/.f64 (-.f64 (*.f64 x x) eps) (+.f64 x (sqrt.f64 (-.f64 (*.f64 x x) eps)))))
(-.f64 (/.f64 (*.f64 (*.f64 x x) x) (fma.f64 x x (+.f64 (-.f64 (*.f64 x x) eps) (*.f64 x (sqrt.f64 (-.f64 (*.f64 x x) eps)))))) (/.f64 (*.f64 (sqrt.f64 (-.f64 (*.f64 x x) eps)) (-.f64 (*.f64 x x) eps)) (fma.f64 x x (+.f64 (-.f64 (*.f64 x x) eps) (*.f64 x (sqrt.f64 (-.f64 (*.f64 x x) eps)))))))
(-.f64 x (sqrt.f64 (-.f64 (*.f64 x x) eps)))
x
(pow.f64 (-.f64 (*.f64 x x) eps) #s(literal 1/2 binary64))
(/.f64 (sqrt.f64 (-.f64 (*.f64 (*.f64 x x) (*.f64 x x)) (*.f64 eps eps))) (sqrt.f64 (fma.f64 x x eps)))
(/.f64 (sqrt.f64 (-.f64 (*.f64 (*.f64 (*.f64 x x) x) (*.f64 (*.f64 x x) x)) (*.f64 (*.f64 eps eps) eps))) (sqrt.f64 (fma.f64 (*.f64 x x) (*.f64 x x) (fma.f64 eps eps (*.f64 (*.f64 x x) eps)))))
(/.f64 #s(literal 1 binary64) (pow.f64 (-.f64 (*.f64 x x) eps) #s(literal -1/2 binary64)))
(sqrt.f64 (-.f64 (*.f64 x x) eps))
(exp.f64 (*.f64 (log.f64 (-.f64 (*.f64 x x) eps)) #s(literal 1/2 binary64)))
(*.f64 (fabs.f64 (sqrt.f64 (-.f64 (*.f64 x x) eps))) (fabs.f64 (sqrt.f64 (-.f64 (*.f64 x x) eps))))
(*.f64 (neg.f64 (sqrt.f64 (-.f64 (*.f64 x x) eps))) (neg.f64 (sqrt.f64 (-.f64 (*.f64 x x) eps))))
(*.f64 (sqrt.f64 (-.f64 (*.f64 x x) eps)) (sqrt.f64 (-.f64 (*.f64 x x) eps)))
(pow.f64 (*.f64 (-.f64 (*.f64 x x) eps) (-.f64 (*.f64 x x) eps)) #s(literal 1/2 binary64))
(pow.f64 (sqrt.f64 (-.f64 (*.f64 x x) eps)) #s(literal 2 binary64))
(pow.f64 (-.f64 (*.f64 x x) eps) #s(literal 1 binary64))
(/.f64 (neg.f64 (-.f64 (*.f64 (*.f64 x x) (*.f64 x x)) (*.f64 eps eps))) (neg.f64 (fma.f64 x x eps)))
(/.f64 (neg.f64 (-.f64 (*.f64 (*.f64 (*.f64 x x) x) (*.f64 (*.f64 x x) x)) (*.f64 (*.f64 eps eps) eps))) (neg.f64 (fma.f64 (*.f64 x x) (*.f64 x x) (fma.f64 eps eps (*.f64 (*.f64 x x) eps)))))
(/.f64 (-.f64 (*.f64 (*.f64 x x) (*.f64 x x)) (*.f64 eps eps)) (fma.f64 x x eps))
(/.f64 (-.f64 (*.f64 (*.f64 (*.f64 x x) x) (*.f64 (*.f64 x x) x)) (*.f64 (*.f64 eps eps) eps)) (fma.f64 (*.f64 x x) (*.f64 x x) (fma.f64 eps eps (*.f64 (*.f64 x x) eps))))
(sqrt.f64 (*.f64 (-.f64 (*.f64 x x) eps) (-.f64 (*.f64 x x) eps)))
(-.f64 (/.f64 (*.f64 (*.f64 x x) (*.f64 x x)) (fma.f64 x x eps)) (/.f64 (*.f64 eps eps) (fma.f64 x x eps)))
(-.f64 (/.f64 (*.f64 (*.f64 (*.f64 x x) x) (*.f64 (*.f64 x x) x)) (fma.f64 (*.f64 x x) (*.f64 x x) (fma.f64 eps eps (*.f64 (*.f64 x x) eps)))) (/.f64 (*.f64 (*.f64 eps eps) eps) (fma.f64 (*.f64 x x) (*.f64 x x) (fma.f64 eps eps (*.f64 (*.f64 x x) eps)))))
(-.f64 (*.f64 x x) eps)
(*.f64 (neg.f64 (neg.f64 x)) (neg.f64 (neg.f64 x)))
(*.f64 (exp.f64 (log.f64 x)) (exp.f64 (log.f64 x)))
(*.f64 (neg.f64 (fabs.f64 x)) (neg.f64 (fabs.f64 x)))
(*.f64 (neg.f64 x) (neg.f64 x))
(*.f64 (fabs.f64 x) (fabs.f64 x))
(*.f64 x x)
(pow.f64 (exp.f64 (log.f64 x)) #s(literal 2 binary64))
(pow.f64 (neg.f64 x) #s(literal 2 binary64))
(pow.f64 (fabs.f64 x) #s(literal 2 binary64))
(pow.f64 (*.f64 (*.f64 x x) (*.f64 x x)) #s(literal 1/2 binary64))
(pow.f64 (*.f64 x x) #s(literal 1 binary64))
(pow.f64 x #s(literal 2 binary64))
(sqrt.f64 (*.f64 (*.f64 x x) (*.f64 x x)))
(fabs.f64 (*.f64 x x))
(exp.f64 (*.f64 (log.f64 x) #s(literal 2 binary64)))
(+.f64 (cosh.f64 (*.f64 (log.f64 x) #s(literal 2 binary64))) (sinh.f64 (*.f64 (log.f64 x) #s(literal 2 binary64))))
eps
#s(approx (- x (sqrt (- (* x x) eps))) (neg.f64 (sqrt.f64 (neg.f64 eps))))
#s(approx (- x (sqrt (- (* x x) eps))) (-.f64 x (sqrt.f64 (neg.f64 eps))))
#s(approx (- x (sqrt (- (* x x) eps))) (-.f64 (*.f64 (fma.f64 (/.f64 x (sqrt.f64 (neg.f64 eps))) #s(literal -1/2 binary64) #s(literal 1 binary64)) x) (sqrt.f64 (neg.f64 eps))))
#s(approx (- x (sqrt (- (* x x) eps))) (-.f64 (*.f64 (fma.f64 (-.f64 (/.f64 (*.f64 #s(literal 1/8 binary64) (*.f64 x x)) (*.f64 (sqrt.f64 (neg.f64 eps)) (neg.f64 eps))) (/.f64 #s(literal 1/2 binary64) (sqrt.f64 (neg.f64 eps)))) x #s(literal 1 binary64)) x) (sqrt.f64 (neg.f64 eps))))
#s(approx x x)
#s(approx (sqrt (- (* x x) eps)) (sqrt.f64 (neg.f64 eps)))
#s(approx (sqrt (- (* x x) eps)) (fma.f64 (/.f64 (*.f64 x x) (sqrt.f64 (neg.f64 eps))) #s(literal 1/2 binary64) (sqrt.f64 (neg.f64 eps))))
#s(approx (sqrt (- (* x x) eps)) (fma.f64 (fma.f64 #s(literal -1/8 binary64) (/.f64 (*.f64 x x) (*.f64 (sqrt.f64 (neg.f64 eps)) (neg.f64 eps))) (/.f64 #s(literal 1/2 binary64) (sqrt.f64 (neg.f64 eps)))) (*.f64 x x) (sqrt.f64 (neg.f64 eps))))
#s(approx (sqrt (- (* x x) eps)) (fma.f64 (fma.f64 (-.f64 (/.f64 (*.f64 #s(literal 1/16 binary64) (*.f64 x x)) (pow.f64 (neg.f64 eps) #s(literal 5/2 binary64))) (/.f64 #s(literal 1/8 binary64) (*.f64 (sqrt.f64 (neg.f64 eps)) (neg.f64 eps)))) (*.f64 x x) (/.f64 #s(literal 1/2 binary64) (sqrt.f64 (neg.f64 eps)))) (*.f64 x x) (sqrt.f64 (neg.f64 eps))))
#s(approx (- (* x x) eps) (neg.f64 eps))
#s(approx (- (* x x) eps) (-.f64 (*.f64 x x) eps))
#s(approx (* x x) (*.f64 x x))
#s(approx (- x (sqrt (- (* x x) eps))) (*.f64 (/.f64 eps x) #s(literal 1/2 binary64)))
#s(approx (- x (sqrt (- (* x x) eps))) (/.f64 (fma.f64 (/.f64 (*.f64 eps eps) (*.f64 x x)) #s(literal 1/8 binary64) (*.f64 #s(literal 1/2 binary64) eps)) x))
#s(approx (- x (sqrt (- (* x x) eps))) (/.f64 (-.f64 (/.f64 (*.f64 #s(literal 1/16 binary64) (*.f64 (*.f64 eps eps) eps)) (*.f64 (*.f64 x x) (*.f64 x x))) (fma.f64 (/.f64 (*.f64 eps eps) (*.f64 x x)) #s(literal -1/8 binary64) (*.f64 #s(literal -1/2 binary64) eps))) x))
#s(approx (- x (sqrt (- (* x x) eps))) (/.f64 (-.f64 (*.f64 (/.f64 (*.f64 (*.f64 (*.f64 eps eps) (*.f64 eps eps)) #s(literal 5/64 binary64)) (*.f64 (*.f64 (*.f64 x x) x) (*.f64 (*.f64 x x) x))) #s(literal 1/2 binary64)) (fma.f64 #s(literal -1/2 binary64) eps (fma.f64 #s(literal -1/16 binary64) (/.f64 (*.f64 (*.f64 eps eps) eps) (*.f64 (*.f64 x x) (*.f64 x x))) (/.f64 (*.f64 #s(literal -1/8 binary64) (*.f64 eps eps)) (*.f64 x x))))) x))
#s(approx (sqrt (- (* x x) eps)) (*.f64 (fma.f64 (/.f64 eps (*.f64 x x)) #s(literal -1/2 binary64) #s(literal 1 binary64)) x))
#s(approx (sqrt (- (* x x) eps)) (*.f64 (+.f64 (fma.f64 (/.f64 (*.f64 eps eps) (*.f64 (*.f64 x x) (*.f64 x x))) #s(literal -1/8 binary64) (*.f64 (/.f64 eps (*.f64 x x)) #s(literal -1/2 binary64))) #s(literal 1 binary64)) x))
#s(approx (sqrt (- (* x x) eps)) (*.f64 x (+.f64 (fma.f64 (/.f64 eps (*.f64 x x)) #s(literal -1/2 binary64) (fma.f64 (/.f64 (*.f64 (*.f64 eps eps) eps) (*.f64 (*.f64 (*.f64 x x) x) (*.f64 (*.f64 x x) x))) #s(literal -1/16 binary64) (*.f64 (/.f64 (*.f64 eps eps) (*.f64 (*.f64 x x) (*.f64 x x))) #s(literal -1/8 binary64)))) #s(literal 1 binary64))))
#s(approx (- (* x x) eps) (*.f64 (+.f64 (/.f64 (neg.f64 eps) (*.f64 x x)) #s(literal 1 binary64)) (*.f64 x x)))
#s(approx (- x (sqrt (- (* x x) eps))) (+.f64 x x))
#s(approx (- x (sqrt (- (* x x) eps))) (*.f64 (neg.f64 x) (-.f64 (*.f64 (/.f64 eps (*.f64 x x)) #s(literal 1/2 binary64)) #s(literal 2 binary64))))
#s(approx (- x (sqrt (- (* x x) eps))) (*.f64 (neg.f64 x) (-.f64 (*.f64 (/.f64 (*.f64 eps eps) (*.f64 (*.f64 x x) (*.f64 x x))) #s(literal 1/8 binary64)) (fma.f64 (/.f64 eps (*.f64 x x)) #s(literal -1/2 binary64) #s(literal 2 binary64)))))
#s(approx (- x (sqrt (- (* x x) eps))) (*.f64 (neg.f64 x) (-.f64 (-.f64 (/.f64 (*.f64 #s(literal 1/16 binary64) (*.f64 (*.f64 eps eps) eps)) (*.f64 (*.f64 (*.f64 x x) x) (*.f64 (*.f64 x x) x))) #s(literal 2 binary64)) (fma.f64 (/.f64 (*.f64 eps eps) (*.f64 (*.f64 x x) (*.f64 x x))) #s(literal -1/8 binary64) (*.f64 (/.f64 eps (*.f64 x x)) #s(literal -1/2 binary64))))))
#s(approx (sqrt (- (* x x) eps)) (neg.f64 x))
#s(approx (sqrt (- (* x x) eps)) (*.f64 (neg.f64 x) (fma.f64 (/.f64 eps (*.f64 x x)) #s(literal -1/2 binary64) #s(literal 1 binary64))))
#s(approx (sqrt (- (* x x) eps)) (*.f64 (neg.f64 x) (+.f64 (fma.f64 (/.f64 (*.f64 eps eps) (*.f64 (*.f64 x x) (*.f64 x x))) #s(literal -1/8 binary64) (*.f64 (/.f64 eps (*.f64 x x)) #s(literal -1/2 binary64))) #s(literal 1 binary64))))
#s(approx (sqrt (- (* x x) eps)) (neg.f64 (*.f64 x (+.f64 (fma.f64 (/.f64 eps (*.f64 x x)) #s(literal -1/2 binary64) (fma.f64 (/.f64 (*.f64 (*.f64 eps eps) eps) (*.f64 (*.f64 (*.f64 x x) x) (*.f64 (*.f64 x x) x))) #s(literal -1/16 binary64) (*.f64 (/.f64 (*.f64 eps eps) (*.f64 (*.f64 x x) (*.f64 x x))) #s(literal -1/8 binary64)))) #s(literal 1 binary64)))))
#s(approx (- x (sqrt (- (* x x) eps))) (-.f64 x (fabs.f64 x)))
#s(approx (- x (sqrt (- (* x x) eps))) (-.f64 (fma.f64 (/.f64 eps (fabs.f64 x)) #s(literal 1/2 binary64) x) (fabs.f64 x)))
#s(approx (- x (sqrt (- (* x x) eps))) (-.f64 (fma.f64 (fma.f64 (/.f64 eps (*.f64 (fabs.f64 x) (*.f64 x x))) #s(literal 1/8 binary64) (/.f64 #s(literal 1/2 binary64) (fabs.f64 x))) eps x) (fabs.f64 x)))
#s(approx (- x (sqrt (- (* x x) eps))) (-.f64 (fma.f64 (fma.f64 (fma.f64 (/.f64 eps (pow.f64 (fabs.f64 x) #s(literal 5 binary64))) #s(literal 1/16 binary64) (/.f64 #s(literal 1/8 binary64) (*.f64 (fabs.f64 x) (*.f64 x x)))) eps (/.f64 #s(literal 1/2 binary64) (fabs.f64 x))) eps x) (fabs.f64 x)))
#s(approx (sqrt (- (* x x) eps)) (fabs.f64 x))
#s(approx (sqrt (- (* x x) eps)) (fma.f64 (/.f64 eps (fabs.f64 x)) #s(literal -1/2 binary64) (fabs.f64 x)))
#s(approx (sqrt (- (* x x) eps)) (fma.f64 (-.f64 (*.f64 (/.f64 eps (*.f64 (fabs.f64 x) (*.f64 x x))) #s(literal -1/8 binary64)) (/.f64 #s(literal 1/2 binary64) (fabs.f64 x))) eps (fabs.f64 x)))
#s(approx (sqrt (- (* x x) eps)) (fma.f64 (-.f64 (*.f64 (-.f64 (*.f64 (/.f64 eps (pow.f64 (fabs.f64 x) #s(literal 5 binary64))) #s(literal -1/16 binary64)) (/.f64 #s(literal 1/8 binary64) (*.f64 (fabs.f64 x) (*.f64 x x)))) eps) (/.f64 #s(literal 1/2 binary64) (fabs.f64 x))) eps (fabs.f64 x)))
#s(approx (- (* x x) eps) (fma.f64 x x (neg.f64 eps)))
#s(approx eps eps)
#s(approx (- x (sqrt (- (* x x) eps))) (*.f64 (neg.f64 eps) (sqrt.f64 (/.f64 #s(literal -1 binary64) eps))))
#s(approx (- x (sqrt (- (* x x) eps))) (*.f64 (-.f64 (/.f64 x eps) (sqrt.f64 (/.f64 #s(literal -1 binary64) eps))) eps))
#s(approx (- x (sqrt (- (* x x) eps))) (*.f64 (-.f64 (fma.f64 (/.f64 (*.f64 x x) (*.f64 (sqrt.f64 (/.f64 #s(literal -1 binary64) eps)) (*.f64 eps eps))) #s(literal -1/2 binary64) (/.f64 x eps)) (sqrt.f64 (/.f64 #s(literal -1 binary64) eps))) eps))
#s(approx (- x (sqrt (- (* x x) eps))) (*.f64 (fma.f64 (/.f64 (*.f64 (*.f64 x x) (*.f64 x x)) (*.f64 (/.f64 #s(literal 1 binary64) (*.f64 (sqrt.f64 (neg.f64 eps)) (neg.f64 eps))) (*.f64 (*.f64 eps eps) (*.f64 eps eps)))) #s(literal 1/8 binary64) (-.f64 (/.f64 x eps) (fma.f64 (/.f64 (*.f64 x x) (*.f64 (sqrt.f64 (/.f64 #s(literal -1 binary64) eps)) (*.f64 eps eps))) #s(literal 1/2 binary64) (sqrt.f64 (/.f64 #s(literal -1 binary64) eps))))) eps))
#s(approx (sqrt (- (* x x) eps)) (*.f64 (sqrt.f64 (/.f64 #s(literal -1 binary64) eps)) eps))
#s(approx (sqrt (- (* x x) eps)) (*.f64 (fma.f64 (/.f64 (*.f64 x x) (*.f64 (sqrt.f64 (/.f64 #s(literal -1 binary64) eps)) (*.f64 eps eps))) #s(literal 1/2 binary64) (sqrt.f64 (/.f64 #s(literal -1 binary64) eps))) eps))
#s(approx (sqrt (- (* x x) eps)) (*.f64 (+.f64 (fma.f64 (/.f64 (*.f64 (*.f64 x x) (*.f64 x x)) (*.f64 (/.f64 #s(literal 1 binary64) (*.f64 (sqrt.f64 (neg.f64 eps)) (neg.f64 eps))) (*.f64 (*.f64 eps eps) (*.f64 eps eps)))) #s(literal -1/8 binary64) (/.f64 (*.f64 #s(literal 1/2 binary64) (*.f64 x x)) (*.f64 (sqrt.f64 (/.f64 #s(literal -1 binary64) eps)) (*.f64 eps eps)))) (sqrt.f64 (/.f64 #s(literal -1 binary64) eps))) eps))
#s(approx (sqrt (- (* x x) eps)) (*.f64 (+.f64 (fma.f64 (/.f64 (*.f64 (*.f64 x x) (*.f64 x x)) (*.f64 (/.f64 #s(literal 1 binary64) (*.f64 (sqrt.f64 (neg.f64 eps)) (neg.f64 eps))) (*.f64 (*.f64 eps eps) (*.f64 eps eps)))) #s(literal -1/8 binary64) (fma.f64 (/.f64 #s(literal 1/16 binary64) (pow.f64 (/.f64 #s(literal -1 binary64) eps) #s(literal 5/2 binary64))) (exp.f64 (-.f64 (*.f64 (log.f64 x) #s(literal 6 binary64)) (*.f64 (log.f64 eps) #s(literal 6 binary64)))) (/.f64 (*.f64 #s(literal 1/2 binary64) (*.f64 x x)) (*.f64 (sqrt.f64 (/.f64 #s(literal -1 binary64) eps)) (*.f64 eps eps))))) (sqrt.f64 (/.f64 #s(literal -1 binary64) eps))) eps))
#s(approx (- (* x x) eps) (*.f64 (-.f64 (/.f64 (*.f64 x x) eps) #s(literal 1 binary64)) eps))
#s(approx (- x (sqrt (- (* x x) eps))) (*.f64 (neg.f64 eps) (-.f64 (/.f64 (neg.f64 x) eps) (sqrt.f64 (/.f64 #s(literal -1 binary64) eps)))))
#s(approx (- x (sqrt (- (* x x) eps))) (*.f64 (neg.f64 eps) (-.f64 (neg.f64 (/.f64 (fma.f64 (/.f64 (*.f64 x x) (*.f64 (sqrt.f64 (/.f64 #s(literal -1 binary64) eps)) eps)) #s(literal 1/2 binary64) x) eps)) (sqrt.f64 (/.f64 #s(literal -1 binary64) eps)))))
#s(approx (- x (sqrt (- (* x x) eps))) (*.f64 (neg.f64 eps) (-.f64 (neg.f64 (/.f64 (+.f64 (neg.f64 (/.f64 (fma.f64 (/.f64 (*.f64 (*.f64 x x) (*.f64 x x)) (*.f64 (/.f64 #s(literal 1 binary64) (*.f64 (sqrt.f64 (neg.f64 eps)) (neg.f64 eps))) (*.f64 eps eps))) #s(literal 1/8 binary64) (*.f64 #s(literal -1/2 binary64) (/.f64 (*.f64 x x) (sqrt.f64 (/.f64 #s(literal -1 binary64) eps))))) eps)) x) eps)) (sqrt.f64 (/.f64 #s(literal -1 binary64) eps)))))
#s(approx (sqrt (- (* x x) eps)) (*.f64 (neg.f64 eps) (fma.f64 (/.f64 (*.f64 x x) (*.f64 (sqrt.f64 (/.f64 #s(literal -1 binary64) eps)) (*.f64 eps eps))) #s(literal 1/2 binary64) (sqrt.f64 (/.f64 #s(literal -1 binary64) eps)))))
#s(approx (sqrt (- (* x x) eps)) (*.f64 (neg.f64 eps) (+.f64 (fma.f64 (/.f64 (*.f64 (*.f64 x x) (*.f64 x x)) (*.f64 (/.f64 #s(literal 1 binary64) (*.f64 (sqrt.f64 (neg.f64 eps)) (neg.f64 eps))) (*.f64 (*.f64 eps eps) (*.f64 eps eps)))) #s(literal -1/8 binary64) (/.f64 (*.f64 #s(literal 1/2 binary64) (*.f64 x x)) (*.f64 (sqrt.f64 (/.f64 #s(literal -1 binary64) eps)) (*.f64 eps eps)))) (sqrt.f64 (/.f64 #s(literal -1 binary64) eps)))))
#s(approx (sqrt (- (* x x) eps)) (*.f64 (neg.f64 eps) (+.f64 (fma.f64 (/.f64 (*.f64 (*.f64 x x) (*.f64 x x)) (*.f64 (/.f64 #s(literal 1 binary64) (*.f64 (sqrt.f64 (neg.f64 eps)) (neg.f64 eps))) (*.f64 (*.f64 eps eps) (*.f64 eps eps)))) #s(literal -1/8 binary64) (fma.f64 (/.f64 #s(literal 1/16 binary64) (pow.f64 (/.f64 #s(literal -1 binary64) eps) #s(literal 5/2 binary64))) (exp.f64 (-.f64 (*.f64 (log.f64 x) #s(literal 6 binary64)) (*.f64 (log.f64 eps) #s(literal 6 binary64)))) (/.f64 (*.f64 #s(literal 1/2 binary64) (*.f64 x x)) (*.f64 (sqrt.f64 (/.f64 #s(literal -1 binary64) eps)) (*.f64 eps eps))))) (sqrt.f64 (/.f64 #s(literal -1 binary64) eps)))))
#s(approx (- (* x x) eps) (*.f64 (neg.f64 eps) (+.f64 (neg.f64 (/.f64 (*.f64 x x) eps)) #s(literal 1 binary64))))

eval10.0ms (0.3%)

Memory
29.7MiB live, 29.7MiB allocated; 0ms collecting garbage
Compiler

Compiled 1 232 to 464 computations (62.3% saved)

prune9.0ms (0.3%)

Memory
-24.4MiB live, 22.0MiB allocated; 2ms collecting garbage
Pruning

13 alts after pruning (12 fresh and 1 done)

PrunedKeptTotal
New811293
Fresh000
Picked011
Done000
Total811394
Accuracy
99.9%
Counts
94 → 13
Alt Table
Click to see full alt table
StatusAccuracyProgram
61.1%
(/.f64 (-.f64 (*.f64 x x) (-.f64 (*.f64 x x) eps)) (+.f64 x (sqrt.f64 (-.f64 (*.f64 x x) eps))))
✓61.5%
(-.f64 x (sqrt.f64 (-.f64 (*.f64 x x) eps)))
▶61.5%
(-.f64 x (sqrt.f64 #s(approx (- (* x x) eps) (fma.f64 x x (neg.f64 eps)))))
▶61.5%
(-.f64 x (sqrt.f64 #s(approx (- (* x x) eps) (*.f64 (-.f64 (/.f64 (*.f64 x x) eps) #s(literal 1 binary64)) eps))))
57.1%
(-.f64 x (sqrt.f64 #s(approx (- (* x x) eps) (neg.f64 eps))))
▶4.2%
(-.f64 x #s(approx (sqrt (- (* x x) eps)) (fabs.f64 x)))
42.5%
#s(approx (- x (sqrt (- (* x x) eps))) (/.f64 (fma.f64 (/.f64 (*.f64 eps eps) (*.f64 x x)) #s(literal 1/8 binary64) (*.f64 #s(literal 1/2 binary64) eps)) x))
37.2%
#s(approx (- x (sqrt (- (* x x) eps))) (/.f64 (-.f64 (/.f64 (*.f64 #s(literal 1/16 binary64) (*.f64 (*.f64 eps eps) eps)) (*.f64 (*.f64 x x) (*.f64 x x))) (fma.f64 (/.f64 (*.f64 eps eps) (*.f64 x x)) #s(literal -1/8 binary64) (*.f64 #s(literal -1/2 binary64) eps))) x))
28.2%
#s(approx (- x (sqrt (- (* x x) eps))) (/.f64 (-.f64 (*.f64 (/.f64 (*.f64 (*.f64 (*.f64 eps eps) (*.f64 eps eps)) #s(literal 5/64 binary64)) (*.f64 (*.f64 (*.f64 x x) x) (*.f64 (*.f64 x x) x))) #s(literal 1/2 binary64)) (fma.f64 #s(literal -1/2 binary64) eps (fma.f64 #s(literal -1/16 binary64) (/.f64 (*.f64 (*.f64 eps eps) eps) (*.f64 (*.f64 x x) (*.f64 x x))) (/.f64 (*.f64 #s(literal -1/8 binary64) (*.f64 eps eps)) (*.f64 x x))))) x))
▶3.7%
#s(approx (- x (sqrt (- (* x x) eps))) (+.f64 x x))
▶44.7%
#s(approx (- x (sqrt (- (* x x) eps))) (*.f64 (/.f64 eps x) #s(literal 1/2 binary64)))
56.9%
#s(approx (- x (sqrt (- (* x x) eps))) (*.f64 (neg.f64 eps) (-.f64 (/.f64 (neg.f64 x) eps) (sqrt.f64 (/.f64 #s(literal -1 binary64) eps)))))
56.9%
#s(approx (- x (sqrt (- (* x x) eps))) (neg.f64 (sqrt.f64 (neg.f64 eps))))
Compiler

Compiled 340 to 312 computations (8.2% saved)

series16.0ms (0.6%)

Memory
-6.6MiB live, 39.6MiB allocated; 2ms collecting garbage
Counts
24 → 61
Calls
Call 1
Inputs
(-.f64 x (sqrt.f64 #s(approx (- (* x x) eps) (fma.f64 x x (neg.f64 eps)))))
x
(sqrt.f64 #s(approx (- (* x x) eps) (fma.f64 x x (neg.f64 eps))))
#s(approx (- (* x x) eps) (fma.f64 x x (neg.f64 eps)))
(fma.f64 x x (neg.f64 eps))
(neg.f64 eps)
eps
#s(approx (- x (sqrt (- (* x x) eps))) (+.f64 x x))
(+.f64 x x)
(-.f64 x #s(approx (sqrt (- (* x x) eps)) (fabs.f64 x)))
#s(approx (sqrt (- (* x x) eps)) (fabs.f64 x))
(fabs.f64 x)
#s(approx (- x (sqrt (- (* x x) eps))) (*.f64 (/.f64 eps x) #s(literal 1/2 binary64)))
(*.f64 (/.f64 eps x) #s(literal 1/2 binary64))
(/.f64 eps x)
#s(literal 1/2 binary64)
(-.f64 x (sqrt.f64 #s(approx (- (* x x) eps) (*.f64 (-.f64 (/.f64 (*.f64 x x) eps) #s(literal 1 binary64)) eps))))
(sqrt.f64 #s(approx (- (* x x) eps) (*.f64 (-.f64 (/.f64 (*.f64 x x) eps) #s(literal 1 binary64)) eps)))
#s(approx (- (* x x) eps) (*.f64 (-.f64 (/.f64 (*.f64 x x) eps) #s(literal 1 binary64)) eps))
(*.f64 (-.f64 (/.f64 (*.f64 x x) eps) #s(literal 1 binary64)) eps)
(-.f64 (/.f64 (*.f64 x x) eps) #s(literal 1 binary64))
(/.f64 (*.f64 x x) eps)
(*.f64 x x)
#s(literal 1 binary64)
Outputs
#s(approx (- x (sqrt (- (* x x) eps))) #s(hole binary64 (* -1 (sqrt (neg eps)))))
#s(approx (- x (sqrt (- (* x x) eps))) #s(hole binary64 (- x (sqrt (neg eps)))))
#s(approx (- x (sqrt (- (* x x) eps))) #s(hole binary64 (- (* x (+ 1 (* -1/2 (/ x (sqrt (neg eps)))))) (sqrt (neg eps)))))
#s(approx (- x (sqrt (- (* x x) eps))) #s(hole binary64 (- (* x (+ 1 (* x (- (* 1/8 (/ (pow x 2) (pow (sqrt (neg eps)) 3))) (* 1/2 (/ 1 (sqrt (neg eps)))))))) (sqrt (neg eps)))))
#s(approx x #s(hole binary64 x))
#s(approx (sqrt (- (* x x) eps)) #s(hole binary64 (sqrt (neg eps))))
#s(approx (sqrt (- (* x x) eps)) #s(hole binary64 (+ (sqrt (neg eps)) (* 1/2 (/ (pow x 2) (sqrt (neg eps)))))))
#s(approx (sqrt (- (* x x) eps)) #s(hole binary64 (+ (sqrt (neg eps)) (* (pow x 2) (+ (* -1/8 (/ (pow x 2) (pow (sqrt (neg eps)) 3))) (* 1/2 (/ 1 (sqrt (neg eps)))))))))
#s(approx (sqrt (- (* x x) eps)) #s(hole binary64 (+ (sqrt (neg eps)) (* (pow x 2) (+ (* (pow x 2) (- (* 1/16 (/ (pow x 2) (pow (sqrt (neg eps)) 5))) (* 1/8 (/ 1 (pow (sqrt (neg eps)) 3))))) (* 1/2 (/ 1 (sqrt (neg eps)))))))))
#s(approx (- (* x x) eps) #s(hole binary64 (* -1 eps)))
#s(approx (- (* x x) eps) #s(hole binary64 (- (pow x 2) eps)))
#s(approx (+ x x) #s(hole binary64 (* 2 x)))
#s(approx (fabs x) #s(hole binary64 (fabs x)))
#s(approx (* (/ eps x) 1/2) #s(hole binary64 (* 1/2 (/ eps x))))
#s(approx (/ eps x) #s(hole binary64 (/ eps x)))
#s(approx (* (- (/ (* x x) eps) 1) eps) #s(hole binary64 (+ (* -1 eps) (pow x 2))))
#s(approx (- (/ (* x x) eps) 1) #s(hole binary64 -1))
#s(approx (- (/ (* x x) eps) 1) #s(hole binary64 (- (/ (pow x 2) eps) 1)))
#s(approx (/ (* x x) eps) #s(hole binary64 (/ (pow x 2) eps)))
#s(approx (* x x) #s(hole binary64 (pow x 2)))
#s(approx (- x (sqrt (- (* x x) eps))) #s(hole binary64 (/ (- (* 1/8 (/ (pow eps 2) (pow x 2))) (* -1/2 eps)) x)))
#s(approx (- x (sqrt (- (* x x) eps))) #s(hole binary64 (/ (- (* 1/16 (/ (pow eps 3) (pow x 4))) (+ (* -1/2 eps) (* -1/8 (/ (pow eps 2) (pow x 2))))) x)))
#s(approx (- x (sqrt (- (* x x) eps))) #s(hole binary64 (/ (- (* 1/2 (/ (+ (* 1/64 (pow eps 4)) (* 1/16 (pow eps 4))) (pow x 6))) (+ (* -1/2 eps) (+ (* -1/8 (/ (pow eps 2) (pow x 2))) (* -1/16 (/ (pow eps 3) (pow x 4)))))) x)))
#s(approx (sqrt (- (* x x) eps)) #s(hole binary64 (* x (+ 1 (* -1/2 (/ eps (pow x 2)))))))
#s(approx (sqrt (- (* x x) eps)) #s(hole binary64 (* x (+ 1 (+ (* -1/2 (/ eps (pow x 2))) (* -1/8 (/ (pow eps 2) (pow x 4))))))))
#s(approx (sqrt (- (* x x) eps)) #s(hole binary64 (* x (+ 1 (+ (* -1/2 (/ eps (pow x 2))) (+ (* -1/8 (/ (pow eps 2) (pow x 4))) (* -1/16 (/ (pow eps 3) (pow x 6)))))))))
#s(approx (- (* x x) eps) #s(hole binary64 (* (pow x 2) (+ 1 (* -1 (/ eps (pow x 2)))))))
#s(approx (- (/ (* x x) eps) 1) #s(hole binary64 (* (pow x 2) (- (/ 1 eps) (/ 1 (pow x 2))))))
#s(approx (- x (sqrt (- (* x x) eps))) #s(hole binary64 (* -1 (* x (- (* 1/2 (/ eps (pow x 2))) 2)))))
#s(approx (- x (sqrt (- (* x x) eps))) #s(hole binary64 (* -1 (* x (- (* 1/8 (/ (pow eps 2) (pow x 4))) (+ 2 (* -1/2 (/ eps (pow x 2)))))))))
#s(approx (- x (sqrt (- (* x x) eps))) #s(hole binary64 (* -1 (* x (- (* 1/16 (/ (pow eps 3) (pow x 6))) (+ 2 (+ (* -1/2 (/ eps (pow x 2))) (* -1/8 (/ (pow eps 2) (pow x 4))))))))))
#s(approx (sqrt (- (* x x) eps)) #s(hole binary64 (* -1 x)))
#s(approx (sqrt (- (* x x) eps)) #s(hole binary64 (* -1 (* x (+ 1 (* -1/2 (/ eps (pow x 2))))))))
#s(approx (sqrt (- (* x x) eps)) #s(hole binary64 (* -1 (* x (+ 1 (+ (* -1/2 (/ eps (pow x 2))) (* -1/8 (/ (pow eps 2) (pow x 4)))))))))
#s(approx (sqrt (- (* x x) eps)) #s(hole binary64 (* -1 (* x (+ 1 (+ (* -1/2 (/ eps (pow x 2))) (+ (* -1/8 (/ (pow eps 2) (pow x 4))) (* -1/16 (/ (pow eps 3) (pow x 6))))))))))
#s(approx (- x (sqrt (- (* x x) eps))) #s(hole binary64 (- x (sqrt (pow x 2)))))
#s(approx (- x (sqrt (- (* x x) eps))) #s(hole binary64 (- (+ x (* 1/2 (/ eps (sqrt (pow x 2))))) (sqrt (pow x 2)))))
#s(approx (- x (sqrt (- (* x x) eps))) #s(hole binary64 (- (+ x (* eps (+ (* 1/8 (/ eps (pow (sqrt (pow x 2)) 3))) (* 1/2 (/ 1 (sqrt (pow x 2))))))) (sqrt (pow x 2)))))
#s(approx (- x (sqrt (- (* x x) eps))) #s(hole binary64 (- (+ x (* eps (+ (* eps (+ (* 1/16 (/ eps (pow (sqrt (pow x 2)) 5))) (* 1/8 (/ 1 (pow (sqrt (pow x 2)) 3))))) (* 1/2 (/ 1 (sqrt (pow x 2))))))) (sqrt (pow x 2)))))
#s(approx (sqrt (- (* x x) eps)) #s(hole binary64 (sqrt (pow x 2))))
#s(approx (sqrt (- (* x x) eps)) #s(hole binary64 (+ (sqrt (pow x 2)) (* -1/2 (/ eps (sqrt (pow x 2)))))))
#s(approx (sqrt (- (* x x) eps)) #s(hole binary64 (+ (sqrt (pow x 2)) (* eps (- (* -1/8 (/ eps (pow (sqrt (pow x 2)) 3))) (* 1/2 (/ 1 (sqrt (pow x 2)))))))))
#s(approx (sqrt (- (* x x) eps)) #s(hole binary64 (+ (sqrt (pow x 2)) (* eps (- (* eps (- (* -1/16 (/ eps (pow (sqrt (pow x 2)) 5))) (* 1/8 (/ 1 (pow (sqrt (pow x 2)) 3))))) (* 1/2 (/ 1 (sqrt (pow x 2)))))))))
#s(approx eps #s(hole binary64 eps))
#s(approx (- (/ (* x x) eps) 1) #s(hole binary64 (/ (+ (* -1 eps) (pow x 2)) eps)))
#s(approx (- x (sqrt (- (* x x) eps))) #s(hole binary64 (* -1 (* eps (sqrt (/ -1 eps))))))
#s(approx (- x (sqrt (- (* x x) eps))) #s(hole binary64 (* eps (- (/ x eps) (sqrt (/ -1 eps))))))
#s(approx (- x (sqrt (- (* x x) eps))) #s(hole binary64 (* eps (- (+ (* -1/2 (/ (pow x 2) (* (pow eps 2) (sqrt (/ -1 eps))))) (/ x eps)) (sqrt (/ -1 eps))))))
#s(approx (- x (sqrt (- (* x x) eps))) #s(hole binary64 (* eps (- (+ (* 1/8 (/ (pow x 4) (* (pow eps 4) (pow (sqrt (/ -1 eps)) 3)))) (/ x eps)) (+ (sqrt (/ -1 eps)) (* 1/2 (/ (pow x 2) (* (pow eps 2) (sqrt (/ -1 eps))))))))))
#s(approx (sqrt (- (* x x) eps)) #s(hole binary64 (* eps (sqrt (/ -1 eps)))))
#s(approx (sqrt (- (* x x) eps)) #s(hole binary64 (* eps (+ (sqrt (/ -1 eps)) (* 1/2 (/ (pow x 2) (* (pow eps 2) (sqrt (/ -1 eps)))))))))
#s(approx (sqrt (- (* x x) eps)) #s(hole binary64 (* eps (+ (sqrt (/ -1 eps)) (+ (* -1/8 (/ (pow x 4) (* (pow eps 4) (pow (sqrt (/ -1 eps)) 3)))) (* 1/2 (/ (pow x 2) (* (pow eps 2) (sqrt (/ -1 eps))))))))))
#s(approx (sqrt (- (* x x) eps)) #s(hole binary64 (* eps (+ (sqrt (/ -1 eps)) (+ (* -1/8 (/ (pow x 4) (* (pow eps 4) (pow (sqrt (/ -1 eps)) 3)))) (+ (* 1/16 (/ (pow x 6) (* (pow eps 6) (pow (sqrt (/ -1 eps)) 5)))) (* 1/2 (/ (pow x 2) (* (pow eps 2) (sqrt (/ -1 eps)))))))))))
#s(approx (- (* x x) eps) #s(hole binary64 (* eps (- (/ (pow x 2) eps) 1))))
#s(approx (- x (sqrt (- (* x x) eps))) #s(hole binary64 (* -1 (* eps (- (* -1 (/ x eps)) (sqrt (/ -1 eps)))))))
#s(approx (- x (sqrt (- (* x x) eps))) #s(hole binary64 (* -1 (* eps (- (* -1 (/ (+ x (* 1/2 (/ (pow x 2) (* eps (sqrt (/ -1 eps)))))) eps)) (sqrt (/ -1 eps)))))))
#s(approx (- x (sqrt (- (* x x) eps))) #s(hole binary64 (* -1 (* eps (- (* -1 (/ (+ x (* -1 (/ (- (* 1/8 (/ (pow x 4) (* (pow eps 2) (pow (sqrt (/ -1 eps)) 3)))) (* 1/2 (/ (pow x 2) (sqrt (/ -1 eps))))) eps))) eps)) (sqrt (/ -1 eps)))))))
#s(approx (sqrt (- (* x x) eps)) #s(hole binary64 (* -1 (* eps (+ (sqrt (/ -1 eps)) (* 1/2 (/ (pow x 2) (* (pow eps 2) (sqrt (/ -1 eps))))))))))
#s(approx (sqrt (- (* x x) eps)) #s(hole binary64 (* -1 (* eps (+ (sqrt (/ -1 eps)) (+ (* -1/8 (/ (pow x 4) (* (pow eps 4) (pow (sqrt (/ -1 eps)) 3)))) (* 1/2 (/ (pow x 2) (* (pow eps 2) (sqrt (/ -1 eps)))))))))))
#s(approx (sqrt (- (* x x) eps)) #s(hole binary64 (* -1 (* eps (+ (sqrt (/ -1 eps)) (+ (* -1/8 (/ (pow x 4) (* (pow eps 4) (pow (sqrt (/ -1 eps)) 3)))) (+ (* 1/16 (/ (pow x 6) (* (pow eps 6) (pow (sqrt (/ -1 eps)) 5)))) (* 1/2 (/ (pow x 2) (* (pow eps 2) (sqrt (/ -1 eps))))))))))))
#s(approx (- (* x x) eps) #s(hole binary64 (* -1 (* eps (+ 1 (* -1 (/ (pow x 2) eps)))))))
Calls

6 calls:

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

rewrite228.0ms (7.8%)

Memory
5.0MiB live, 333.8MiB allocated; 87ms collecting garbage
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
03271738
03451631
117911609
093401564
Stop Event
1×iter-limit
1×node-limit
1×iter-limit
Counts
85 → 228
Calls
Call 1
Inputs
(-.f64 x (sqrt.f64 #s(approx (- (* x x) eps) (fma.f64 x x (neg.f64 eps)))))
x
(sqrt.f64 #s(approx (- (* x x) eps) (fma.f64 x x (neg.f64 eps))))
#s(approx (- (* x x) eps) (fma.f64 x x (neg.f64 eps)))
(fma.f64 x x (neg.f64 eps))
(neg.f64 eps)
eps
#s(approx (- x (sqrt (- (* x x) eps))) (+.f64 x x))
(+.f64 x x)
(-.f64 x #s(approx (sqrt (- (* x x) eps)) (fabs.f64 x)))
#s(approx (sqrt (- (* x x) eps)) (fabs.f64 x))
(fabs.f64 x)
#s(approx (- x (sqrt (- (* x x) eps))) (*.f64 (/.f64 eps x) #s(literal 1/2 binary64)))
(*.f64 (/.f64 eps x) #s(literal 1/2 binary64))
(/.f64 eps x)
#s(literal 1/2 binary64)
(-.f64 x (sqrt.f64 #s(approx (- (* x x) eps) (*.f64 (-.f64 (/.f64 (*.f64 x x) eps) #s(literal 1 binary64)) eps))))
(sqrt.f64 #s(approx (- (* x x) eps) (*.f64 (-.f64 (/.f64 (*.f64 x x) eps) #s(literal 1 binary64)) eps)))
#s(approx (- (* x x) eps) (*.f64 (-.f64 (/.f64 (*.f64 x x) eps) #s(literal 1 binary64)) eps))
(*.f64 (-.f64 (/.f64 (*.f64 x x) eps) #s(literal 1 binary64)) eps)
(-.f64 (/.f64 (*.f64 x x) eps) #s(literal 1 binary64))
(/.f64 (*.f64 x x) eps)
(*.f64 x x)
#s(literal 1 binary64)
#s(approx (- x (sqrt (- (* x x) eps))) #s(hole binary64 (* -1 (sqrt (neg eps)))))
#s(approx (- x (sqrt (- (* x x) eps))) #s(hole binary64 (- x (sqrt (neg eps)))))
#s(approx (- x (sqrt (- (* x x) eps))) #s(hole binary64 (- (* x (+ 1 (* -1/2 (/ x (sqrt (neg eps)))))) (sqrt (neg eps)))))
#s(approx (- x (sqrt (- (* x x) eps))) #s(hole binary64 (- (* x (+ 1 (* x (- (* 1/8 (/ (pow x 2) (pow (sqrt (neg eps)) 3))) (* 1/2 (/ 1 (sqrt (neg eps)))))))) (sqrt (neg eps)))))
#s(approx x #s(hole binary64 x))
#s(approx (sqrt (- (* x x) eps)) #s(hole binary64 (sqrt (neg eps))))
#s(approx (sqrt (- (* x x) eps)) #s(hole binary64 (+ (sqrt (neg eps)) (* 1/2 (/ (pow x 2) (sqrt (neg eps)))))))
#s(approx (sqrt (- (* x x) eps)) #s(hole binary64 (+ (sqrt (neg eps)) (* (pow x 2) (+ (* -1/8 (/ (pow x 2) (pow (sqrt (neg eps)) 3))) (* 1/2 (/ 1 (sqrt (neg eps)))))))))
#s(approx (sqrt (- (* x x) eps)) #s(hole binary64 (+ (sqrt (neg eps)) (* (pow x 2) (+ (* (pow x 2) (- (* 1/16 (/ (pow x 2) (pow (sqrt (neg eps)) 5))) (* 1/8 (/ 1 (pow (sqrt (neg eps)) 3))))) (* 1/2 (/ 1 (sqrt (neg eps)))))))))
#s(approx (- (* x x) eps) #s(hole binary64 (* -1 eps)))
#s(approx (- (* x x) eps) #s(hole binary64 (- (pow x 2) eps)))
#s(approx (+ x x) #s(hole binary64 (* 2 x)))
#s(approx (fabs x) #s(hole binary64 (fabs x)))
#s(approx (* (/ eps x) 1/2) #s(hole binary64 (* 1/2 (/ eps x))))
#s(approx (/ eps x) #s(hole binary64 (/ eps x)))
#s(approx (* (- (/ (* x x) eps) 1) eps) #s(hole binary64 (+ (* -1 eps) (pow x 2))))
#s(approx (- (/ (* x x) eps) 1) #s(hole binary64 -1))
#s(approx (- (/ (* x x) eps) 1) #s(hole binary64 (- (/ (pow x 2) eps) 1)))
#s(approx (/ (* x x) eps) #s(hole binary64 (/ (pow x 2) eps)))
#s(approx (* x x) #s(hole binary64 (pow x 2)))
#s(approx (- x (sqrt (- (* x x) eps))) #s(hole binary64 (/ (- (* 1/8 (/ (pow eps 2) (pow x 2))) (* -1/2 eps)) x)))
#s(approx (- x (sqrt (- (* x x) eps))) #s(hole binary64 (/ (- (* 1/16 (/ (pow eps 3) (pow x 4))) (+ (* -1/2 eps) (* -1/8 (/ (pow eps 2) (pow x 2))))) x)))
#s(approx (- x (sqrt (- (* x x) eps))) #s(hole binary64 (/ (- (* 1/2 (/ (+ (* 1/64 (pow eps 4)) (* 1/16 (pow eps 4))) (pow x 6))) (+ (* -1/2 eps) (+ (* -1/8 (/ (pow eps 2) (pow x 2))) (* -1/16 (/ (pow eps 3) (pow x 4)))))) x)))
#s(approx (sqrt (- (* x x) eps)) #s(hole binary64 (* x (+ 1 (* -1/2 (/ eps (pow x 2)))))))
#s(approx (sqrt (- (* x x) eps)) #s(hole binary64 (* x (+ 1 (+ (* -1/2 (/ eps (pow x 2))) (* -1/8 (/ (pow eps 2) (pow x 4))))))))
#s(approx (sqrt (- (* x x) eps)) #s(hole binary64 (* x (+ 1 (+ (* -1/2 (/ eps (pow x 2))) (+ (* -1/8 (/ (pow eps 2) (pow x 4))) (* -1/16 (/ (pow eps 3) (pow x 6)))))))))
#s(approx (- (* x x) eps) #s(hole binary64 (* (pow x 2) (+ 1 (* -1 (/ eps (pow x 2)))))))
#s(approx (- (/ (* x x) eps) 1) #s(hole binary64 (* (pow x 2) (- (/ 1 eps) (/ 1 (pow x 2))))))
#s(approx (- x (sqrt (- (* x x) eps))) #s(hole binary64 (* -1 (* x (- (* 1/2 (/ eps (pow x 2))) 2)))))
#s(approx (- x (sqrt (- (* x x) eps))) #s(hole binary64 (* -1 (* x (- (* 1/8 (/ (pow eps 2) (pow x 4))) (+ 2 (* -1/2 (/ eps (pow x 2)))))))))
#s(approx (- x (sqrt (- (* x x) eps))) #s(hole binary64 (* -1 (* x (- (* 1/16 (/ (pow eps 3) (pow x 6))) (+ 2 (+ (* -1/2 (/ eps (pow x 2))) (* -1/8 (/ (pow eps 2) (pow x 4))))))))))
#s(approx (sqrt (- (* x x) eps)) #s(hole binary64 (* -1 x)))
#s(approx (sqrt (- (* x x) eps)) #s(hole binary64 (* -1 (* x (+ 1 (* -1/2 (/ eps (pow x 2))))))))
#s(approx (sqrt (- (* x x) eps)) #s(hole binary64 (* -1 (* x (+ 1 (+ (* -1/2 (/ eps (pow x 2))) (* -1/8 (/ (pow eps 2) (pow x 4)))))))))
#s(approx (sqrt (- (* x x) eps)) #s(hole binary64 (* -1 (* x (+ 1 (+ (* -1/2 (/ eps (pow x 2))) (+ (* -1/8 (/ (pow eps 2) (pow x 4))) (* -1/16 (/ (pow eps 3) (pow x 6))))))))))
#s(approx (- x (sqrt (- (* x x) eps))) #s(hole binary64 (- x (sqrt (pow x 2)))))
#s(approx (- x (sqrt (- (* x x) eps))) #s(hole binary64 (- (+ x (* 1/2 (/ eps (sqrt (pow x 2))))) (sqrt (pow x 2)))))
#s(approx (- x (sqrt (- (* x x) eps))) #s(hole binary64 (- (+ x (* eps (+ (* 1/8 (/ eps (pow (sqrt (pow x 2)) 3))) (* 1/2 (/ 1 (sqrt (pow x 2))))))) (sqrt (pow x 2)))))
#s(approx (- x (sqrt (- (* x x) eps))) #s(hole binary64 (- (+ x (* eps (+ (* eps (+ (* 1/16 (/ eps (pow (sqrt (pow x 2)) 5))) (* 1/8 (/ 1 (pow (sqrt (pow x 2)) 3))))) (* 1/2 (/ 1 (sqrt (pow x 2))))))) (sqrt (pow x 2)))))
#s(approx (sqrt (- (* x x) eps)) #s(hole binary64 (sqrt (pow x 2))))
#s(approx (sqrt (- (* x x) eps)) #s(hole binary64 (+ (sqrt (pow x 2)) (* -1/2 (/ eps (sqrt (pow x 2)))))))
#s(approx (sqrt (- (* x x) eps)) #s(hole binary64 (+ (sqrt (pow x 2)) (* eps (- (* -1/8 (/ eps (pow (sqrt (pow x 2)) 3))) (* 1/2 (/ 1 (sqrt (pow x 2)))))))))
#s(approx (sqrt (- (* x x) eps)) #s(hole binary64 (+ (sqrt (pow x 2)) (* eps (- (* eps (- (* -1/16 (/ eps (pow (sqrt (pow x 2)) 5))) (* 1/8 (/ 1 (pow (sqrt (pow x 2)) 3))))) (* 1/2 (/ 1 (sqrt (pow x 2)))))))))
#s(approx eps #s(hole binary64 eps))
#s(approx (- (/ (* x x) eps) 1) #s(hole binary64 (/ (+ (* -1 eps) (pow x 2)) eps)))
#s(approx (- x (sqrt (- (* x x) eps))) #s(hole binary64 (* -1 (* eps (sqrt (/ -1 eps))))))
#s(approx (- x (sqrt (- (* x x) eps))) #s(hole binary64 (* eps (- (/ x eps) (sqrt (/ -1 eps))))))
#s(approx (- x (sqrt (- (* x x) eps))) #s(hole binary64 (* eps (- (+ (* -1/2 (/ (pow x 2) (* (pow eps 2) (sqrt (/ -1 eps))))) (/ x eps)) (sqrt (/ -1 eps))))))
#s(approx (- x (sqrt (- (* x x) eps))) #s(hole binary64 (* eps (- (+ (* 1/8 (/ (pow x 4) (* (pow eps 4) (pow (sqrt (/ -1 eps)) 3)))) (/ x eps)) (+ (sqrt (/ -1 eps)) (* 1/2 (/ (pow x 2) (* (pow eps 2) (sqrt (/ -1 eps))))))))))
#s(approx (sqrt (- (* x x) eps)) #s(hole binary64 (* eps (sqrt (/ -1 eps)))))
#s(approx (sqrt (- (* x x) eps)) #s(hole binary64 (* eps (+ (sqrt (/ -1 eps)) (* 1/2 (/ (pow x 2) (* (pow eps 2) (sqrt (/ -1 eps)))))))))
#s(approx (sqrt (- (* x x) eps)) #s(hole binary64 (* eps (+ (sqrt (/ -1 eps)) (+ (* -1/8 (/ (pow x 4) (* (pow eps 4) (pow (sqrt (/ -1 eps)) 3)))) (* 1/2 (/ (pow x 2) (* (pow eps 2) (sqrt (/ -1 eps))))))))))
#s(approx (sqrt (- (* x x) eps)) #s(hole binary64 (* eps (+ (sqrt (/ -1 eps)) (+ (* -1/8 (/ (pow x 4) (* (pow eps 4) (pow (sqrt (/ -1 eps)) 3)))) (+ (* 1/16 (/ (pow x 6) (* (pow eps 6) (pow (sqrt (/ -1 eps)) 5)))) (* 1/2 (/ (pow x 2) (* (pow eps 2) (sqrt (/ -1 eps)))))))))))
#s(approx (- (* x x) eps) #s(hole binary64 (* eps (- (/ (pow x 2) eps) 1))))
#s(approx (- x (sqrt (- (* x x) eps))) #s(hole binary64 (* -1 (* eps (- (* -1 (/ x eps)) (sqrt (/ -1 eps)))))))
#s(approx (- x (sqrt (- (* x x) eps))) #s(hole binary64 (* -1 (* eps (- (* -1 (/ (+ x (* 1/2 (/ (pow x 2) (* eps (sqrt (/ -1 eps)))))) eps)) (sqrt (/ -1 eps)))))))
#s(approx (- x (sqrt (- (* x x) eps))) #s(hole binary64 (* -1 (* eps (- (* -1 (/ (+ x (* -1 (/ (- (* 1/8 (/ (pow x 4) (* (pow eps 2) (pow (sqrt (/ -1 eps)) 3)))) (* 1/2 (/ (pow x 2) (sqrt (/ -1 eps))))) eps))) eps)) (sqrt (/ -1 eps)))))))
#s(approx (sqrt (- (* x x) eps)) #s(hole binary64 (* -1 (* eps (+ (sqrt (/ -1 eps)) (* 1/2 (/ (pow x 2) (* (pow eps 2) (sqrt (/ -1 eps))))))))))
#s(approx (sqrt (- (* x x) eps)) #s(hole binary64 (* -1 (* eps (+ (sqrt (/ -1 eps)) (+ (* -1/8 (/ (pow x 4) (* (pow eps 4) (pow (sqrt (/ -1 eps)) 3)))) (* 1/2 (/ (pow x 2) (* (pow eps 2) (sqrt (/ -1 eps)))))))))))
#s(approx (sqrt (- (* x x) eps)) #s(hole binary64 (* -1 (* eps (+ (sqrt (/ -1 eps)) (+ (* -1/8 (/ (pow x 4) (* (pow eps 4) (pow (sqrt (/ -1 eps)) 3)))) (+ (* 1/16 (/ (pow x 6) (* (pow eps 6) (pow (sqrt (/ -1 eps)) 5)))) (* 1/2 (/ (pow x 2) (* (pow eps 2) (sqrt (/ -1 eps))))))))))))
#s(approx (- (* x x) eps) #s(hole binary64 (* -1 (* eps (+ 1 (* -1 (/ (pow x 2) eps)))))))
Outputs
(/.f64 (neg.f64 (-.f64 (*.f64 x x) #s(approx (- (* x x) eps) (fma.f64 x x (neg.f64 eps))))) (neg.f64 (+.f64 x (sqrt.f64 #s(approx (- (* x x) eps) (fma.f64 x x (neg.f64 eps)))))))
(/.f64 (neg.f64 (-.f64 (*.f64 (*.f64 x x) x) (*.f64 (sqrt.f64 #s(approx (- (* x x) eps) (fma.f64 x x (neg.f64 eps)))) #s(approx (- (* x x) eps) (fma.f64 x x (neg.f64 eps)))))) (neg.f64 (fma.f64 x x (+.f64 #s(approx (- (* x x) eps) (fma.f64 x x (neg.f64 eps))) (*.f64 x (sqrt.f64 #s(approx (- (* x x) eps) (fma.f64 x x (neg.f64 eps)))))))))
(/.f64 (-.f64 (*.f64 x x) #s(approx (- (* x x) eps) (fma.f64 x x (neg.f64 eps)))) (+.f64 x (sqrt.f64 #s(approx (- (* x x) eps) (fma.f64 x x (neg.f64 eps))))))
(/.f64 (-.f64 (*.f64 (*.f64 x x) x) (*.f64 (sqrt.f64 #s(approx (- (* x x) eps) (fma.f64 x x (neg.f64 eps)))) #s(approx (- (* x x) eps) (fma.f64 x x (neg.f64 eps))))) (fma.f64 x x (+.f64 #s(approx (- (* x x) eps) (fma.f64 x x (neg.f64 eps))) (*.f64 x (sqrt.f64 #s(approx (- (* x x) eps) (fma.f64 x x (neg.f64 eps))))))))
(-.f64 (/.f64 (*.f64 x x) (+.f64 x (sqrt.f64 #s(approx (- (* x x) eps) (fma.f64 x x (neg.f64 eps)))))) (/.f64 #s(approx (- (* x x) eps) (fma.f64 x x (neg.f64 eps))) (+.f64 x (sqrt.f64 #s(approx (- (* x x) eps) (fma.f64 x x (neg.f64 eps)))))))
(-.f64 (/.f64 (*.f64 (*.f64 x x) x) (fma.f64 x x (+.f64 #s(approx (- (* x x) eps) (fma.f64 x x (neg.f64 eps))) (*.f64 x (sqrt.f64 #s(approx (- (* x x) eps) (fma.f64 x x (neg.f64 eps)))))))) (/.f64 (*.f64 (sqrt.f64 #s(approx (- (* x x) eps) (fma.f64 x x (neg.f64 eps)))) #s(approx (- (* x x) eps) (fma.f64 x x (neg.f64 eps)))) (fma.f64 x x (+.f64 #s(approx (- (* x x) eps) (fma.f64 x x (neg.f64 eps))) (*.f64 x (sqrt.f64 #s(approx (- (* x x) eps) (fma.f64 x x (neg.f64 eps)))))))))
(-.f64 x (sqrt.f64 #s(approx (- (* x x) eps) (fma.f64 x x (neg.f64 eps)))))
x
(pow.f64 #s(approx (- (* x x) eps) (fma.f64 x x (neg.f64 eps))) #s(literal 1/2 binary64))
(/.f64 #s(literal 1 binary64) (pow.f64 #s(approx (- (* x x) eps) (fma.f64 x x (neg.f64 eps))) #s(literal -1/2 binary64)))
(sqrt.f64 #s(approx (- (* x x) eps) (fma.f64 x x (neg.f64 eps))))
(exp.f64 (*.f64 (log.f64 #s(approx (- (* x x) eps) (fma.f64 x x (neg.f64 eps)))) #s(literal 1/2 binary64)))
(*.f64 (fabs.f64 (sqrt.f64 #s(approx (- (* x x) eps) (fma.f64 x x (neg.f64 eps))))) (fabs.f64 (sqrt.f64 #s(approx (- (* x x) eps) (fma.f64 x x (neg.f64 eps))))))
(*.f64 (neg.f64 (sqrt.f64 #s(approx (- (* x x) eps) (fma.f64 x x (neg.f64 eps))))) (neg.f64 (sqrt.f64 #s(approx (- (* x x) eps) (fma.f64 x x (neg.f64 eps))))))
(*.f64 (sqrt.f64 #s(approx (- (* x x) eps) (fma.f64 x x (neg.f64 eps)))) (sqrt.f64 #s(approx (- (* x x) eps) (fma.f64 x x (neg.f64 eps)))))
(pow.f64 (*.f64 #s(approx (- (* x x) eps) (fma.f64 x x (neg.f64 eps))) #s(approx (- (* x x) eps) (fma.f64 x x (neg.f64 eps)))) #s(literal 1/2 binary64))
(pow.f64 (sqrt.f64 #s(approx (- (* x x) eps) (fma.f64 x x (neg.f64 eps)))) #s(literal 2 binary64))
(pow.f64 #s(approx (- (* x x) eps) (fma.f64 x x (neg.f64 eps))) #s(literal 1 binary64))
#s(approx (- (* x x) eps) (fma.f64 x x (neg.f64 eps)))
(sqrt.f64 (*.f64 #s(approx (- (* x x) eps) (fma.f64 x x (neg.f64 eps))) #s(approx (- (* x x) eps) (fma.f64 x x (neg.f64 eps)))))
(/.f64 (fma.f64 (*.f64 eps eps) (neg.f64 eps) (*.f64 (*.f64 (*.f64 x x) x) (*.f64 (*.f64 x x) x))) (fma.f64 eps eps (-.f64 (*.f64 (*.f64 x x) (*.f64 x x)) (*.f64 (neg.f64 eps) (*.f64 x x)))))
(/.f64 (neg.f64 (-.f64 (*.f64 (*.f64 x x) (*.f64 x x)) (*.f64 eps eps))) (neg.f64 (-.f64 (*.f64 x x) (neg.f64 eps))))
(/.f64 (neg.f64 (-.f64 (*.f64 eps eps) (*.f64 (*.f64 x x) (*.f64 x x)))) (neg.f64 (-.f64 (neg.f64 eps) (*.f64 x x))))
(/.f64 (neg.f64 (fma.f64 (*.f64 (*.f64 x x) (*.f64 x x)) (*.f64 x x) (*.f64 (*.f64 eps eps) (neg.f64 eps)))) (neg.f64 (fma.f64 (*.f64 x x) (*.f64 x x) (-.f64 (*.f64 eps eps) (*.f64 (*.f64 x x) (neg.f64 eps))))))
(/.f64 (neg.f64 (fma.f64 (*.f64 eps eps) (neg.f64 eps) (*.f64 (*.f64 (*.f64 x x) x) (*.f64 (*.f64 x x) x)))) (neg.f64 (fma.f64 eps eps (-.f64 (*.f64 (*.f64 x x) (*.f64 x x)) (*.f64 (neg.f64 eps) (*.f64 x x))))))
(/.f64 (-.f64 (*.f64 eps eps) (*.f64 (*.f64 x x) (*.f64 x x))) (-.f64 (neg.f64 eps) (*.f64 x x)))
(/.f64 (-.f64 (*.f64 (*.f64 x x) (*.f64 x x)) (*.f64 eps eps)) (-.f64 (*.f64 x x) (neg.f64 eps)))
(/.f64 (fma.f64 (*.f64 (*.f64 x x) (*.f64 x x)) (*.f64 x x) (*.f64 (*.f64 eps eps) (neg.f64 eps))) (fma.f64 (*.f64 x x) (*.f64 x x) (-.f64 (*.f64 eps eps) (*.f64 (*.f64 x x) (neg.f64 eps)))))
(fma.f64 (fabs.f64 (sqrt.f64 (neg.f64 eps))) (fabs.f64 (sqrt.f64 (neg.f64 eps))) (*.f64 x x))
(fma.f64 (neg.f64 (neg.f64 x)) (neg.f64 (neg.f64 x)) (neg.f64 eps))
(fma.f64 (exp.f64 (log.f64 x)) (exp.f64 (log.f64 x)) (neg.f64 eps))
(fma.f64 (neg.f64 (sqrt.f64 (neg.f64 eps))) (neg.f64 (sqrt.f64 (neg.f64 eps))) (*.f64 x x))
(fma.f64 (neg.f64 (fabs.f64 x)) (neg.f64 (fabs.f64 x)) (neg.f64 eps))
(fma.f64 (neg.f64 x) (neg.f64 x) (neg.f64 eps))
(fma.f64 (fabs.f64 x) (fabs.f64 x) (neg.f64 eps))
(fma.f64 (sqrt.f64 (neg.f64 eps)) (sqrt.f64 (neg.f64 eps)) (*.f64 x x))
(fma.f64 #s(literal -1 binary64) eps (*.f64 x x))
(fma.f64 eps #s(literal -1 binary64) (*.f64 x x))
(fma.f64 x x (neg.f64 eps))
(-.f64 (/.f64 (*.f64 (*.f64 x x) (*.f64 x x)) (-.f64 (*.f64 x x) (neg.f64 eps))) (/.f64 (*.f64 eps eps) (-.f64 (*.f64 x x) (neg.f64 eps))))
(-.f64 (/.f64 (*.f64 eps eps) (-.f64 (neg.f64 eps) (*.f64 x x))) (/.f64 (*.f64 (*.f64 x x) (*.f64 x x)) (-.f64 (neg.f64 eps) (*.f64 x x))))
(+.f64 (/.f64 (*.f64 (*.f64 (*.f64 x x) x) (*.f64 (*.f64 x x) x)) (fma.f64 (*.f64 x x) (*.f64 x x) (-.f64 (*.f64 eps eps) (*.f64 (*.f64 x x) (neg.f64 eps))))) (/.f64 (*.f64 (*.f64 eps eps) (neg.f64 eps)) (fma.f64 (*.f64 x x) (*.f64 x x) (-.f64 (*.f64 eps eps) (*.f64 (*.f64 x x) (neg.f64 eps))))))
(+.f64 (/.f64 (*.f64 (*.f64 eps eps) (neg.f64 eps)) (fma.f64 eps eps (-.f64 (*.f64 (*.f64 x x) (*.f64 x x)) (*.f64 (neg.f64 eps) (*.f64 x x))))) (/.f64 (*.f64 (*.f64 (*.f64 x x) x) (*.f64 (*.f64 x x) x)) (fma.f64 eps eps (-.f64 (*.f64 (*.f64 x x) (*.f64 x x)) (*.f64 (neg.f64 eps) (*.f64 x x))))))
(+.f64 (*.f64 x x) (neg.f64 eps))
(+.f64 (neg.f64 eps) (*.f64 x x))
(*.f64 (fabs.f64 (sqrt.f64 (neg.f64 eps))) (fabs.f64 (sqrt.f64 (neg.f64 eps))))
(*.f64 (neg.f64 (sqrt.f64 (neg.f64 eps))) (neg.f64 (sqrt.f64 (neg.f64 eps))))
(*.f64 (sqrt.f64 (neg.f64 eps)) (sqrt.f64 (neg.f64 eps)))
(*.f64 #s(literal -1 binary64) eps)
(*.f64 eps #s(literal -1 binary64))
(pow.f64 (*.f64 eps eps) #s(literal 1/2 binary64))
(pow.f64 (sqrt.f64 (neg.f64 eps)) #s(literal 2 binary64))
(pow.f64 (neg.f64 eps) #s(literal 1 binary64))
(neg.f64 eps)
(sqrt.f64 (*.f64 eps eps))
eps
#s(approx (- x (sqrt (- (* x x) eps))) (+.f64 x x))
(*.f64 #s(literal 2 binary64) x)
(*.f64 x #s(literal 2 binary64))
(/.f64 (neg.f64 (fma.f64 (*.f64 x x) x (*.f64 (*.f64 x x) x))) (neg.f64 (fma.f64 x x (-.f64 (*.f64 x x) (*.f64 x x)))))
(/.f64 (neg.f64 (-.f64 (*.f64 x x) (*.f64 x x))) (neg.f64 (-.f64 x x)))
(/.f64 (-.f64 (*.f64 x x) (*.f64 x x)) (-.f64 x x))
(/.f64 (fma.f64 (*.f64 x x) x (*.f64 (*.f64 x x) x)) (fma.f64 x x (-.f64 (*.f64 x x) (*.f64 x x))))
(-.f64 (/.f64 (*.f64 x x) (-.f64 x x)) (/.f64 (*.f64 x x) (-.f64 x x)))
(+.f64 (/.f64 (*.f64 (*.f64 x x) x) (fma.f64 x x (-.f64 (*.f64 x x) (*.f64 x x)))) (/.f64 (*.f64 (*.f64 x x) x) (fma.f64 x x (-.f64 (*.f64 x x) (*.f64 x x)))))
(+.f64 x x)
(/.f64 (neg.f64 (-.f64 (*.f64 x x) (*.f64 #s(approx (sqrt (- (* x x) eps)) (fabs.f64 x)) #s(approx (sqrt (- (* x x) eps)) (fabs.f64 x))))) (neg.f64 (+.f64 x #s(approx (sqrt (- (* x x) eps)) (fabs.f64 x)))))
(/.f64 (neg.f64 (-.f64 (*.f64 (*.f64 x x) x) (*.f64 (*.f64 #s(approx (sqrt (- (* x x) eps)) (fabs.f64 x)) #s(approx (sqrt (- (* x x) eps)) (fabs.f64 x))) #s(approx (sqrt (- (* x x) eps)) (fabs.f64 x))))) (neg.f64 (fma.f64 x x (fma.f64 #s(approx (sqrt (- (* x x) eps)) (fabs.f64 x)) #s(approx (sqrt (- (* x x) eps)) (fabs.f64 x)) (*.f64 x #s(approx (sqrt (- (* x x) eps)) (fabs.f64 x)))))))
(/.f64 (-.f64 (*.f64 x x) (*.f64 #s(approx (sqrt (- (* x x) eps)) (fabs.f64 x)) #s(approx (sqrt (- (* x x) eps)) (fabs.f64 x)))) (+.f64 x #s(approx (sqrt (- (* x x) eps)) (fabs.f64 x))))
(/.f64 (-.f64 (*.f64 (*.f64 x x) x) (*.f64 (*.f64 #s(approx (sqrt (- (* x x) eps)) (fabs.f64 x)) #s(approx (sqrt (- (* x x) eps)) (fabs.f64 x))) #s(approx (sqrt (- (* x x) eps)) (fabs.f64 x)))) (fma.f64 x x (fma.f64 #s(approx (sqrt (- (* x x) eps)) (fabs.f64 x)) #s(approx (sqrt (- (* x x) eps)) (fabs.f64 x)) (*.f64 x #s(approx (sqrt (- (* x x) eps)) (fabs.f64 x))))))
(-.f64 (/.f64 (*.f64 x x) (+.f64 x #s(approx (sqrt (- (* x x) eps)) (fabs.f64 x)))) (/.f64 (*.f64 #s(approx (sqrt (- (* x x) eps)) (fabs.f64 x)) #s(approx (sqrt (- (* x x) eps)) (fabs.f64 x))) (+.f64 x #s(approx (sqrt (- (* x x) eps)) (fabs.f64 x)))))
(-.f64 (/.f64 (*.f64 (*.f64 x x) x) (fma.f64 x x (fma.f64 #s(approx (sqrt (- (* x x) eps)) (fabs.f64 x)) #s(approx (sqrt (- (* x x) eps)) (fabs.f64 x)) (*.f64 x #s(approx (sqrt (- (* x x) eps)) (fabs.f64 x)))))) (/.f64 (*.f64 (*.f64 #s(approx (sqrt (- (* x x) eps)) (fabs.f64 x)) #s(approx (sqrt (- (* x x) eps)) (fabs.f64 x))) #s(approx (sqrt (- (* x x) eps)) (fabs.f64 x))) (fma.f64 x x (fma.f64 #s(approx (sqrt (- (* x x) eps)) (fabs.f64 x)) #s(approx (sqrt (- (* x x) eps)) (fabs.f64 x)) (*.f64 x #s(approx (sqrt (- (* x x) eps)) (fabs.f64 x)))))))
(-.f64 x #s(approx (sqrt (- (* x x) eps)) (fabs.f64 x)))
#s(approx (sqrt (- (* x x) eps)) (fabs.f64 x))
(*.f64 (sqrt.f64 (neg.f64 x)) (sqrt.f64 (neg.f64 x)))
(*.f64 (sqrt.f64 (fabs.f64 x)) (sqrt.f64 (fabs.f64 x)))
(*.f64 (sqrt.f64 x) (sqrt.f64 x))
(*.f64 (pow.f64 (neg.f64 x) #s(literal 1/2 binary64)) (pow.f64 (neg.f64 x) #s(literal 1/2 binary64)))
(*.f64 (pow.f64 (fabs.f64 x) #s(literal 1/2 binary64)) (pow.f64 (fabs.f64 x) #s(literal 1/2 binary64)))
(*.f64 (pow.f64 x #s(literal 1/2 binary64)) (pow.f64 x #s(literal 1/2 binary64)))
(*.f64 (fabs.f64 x) #s(literal 1 binary64))
(*.f64 #s(literal 1 binary64) (fabs.f64 x))
(pow.f64 (*.f64 x x) #s(literal 1/2 binary64))
(/.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (fabs.f64 x)))
(sqrt.f64 (*.f64 x x))
(fabs.f64 (neg.f64 (neg.f64 x)))
(fabs.f64 (neg.f64 x))
(fabs.f64 (fabs.f64 x))
(fabs.f64 x)
(exp.f64 (/.f64 (*.f64 (log.f64 x) #s(literal 2 binary64)) #s(literal 2 binary64)))
(exp.f64 (*.f64 (*.f64 (log.f64 x) #s(literal 2 binary64)) #s(literal 1/2 binary64)))
(exp.f64 (*.f64 (log.f64 (*.f64 x x)) #s(literal 1/2 binary64)))
#s(approx (- x (sqrt (- (* x x) eps))) (*.f64 (/.f64 eps x) #s(literal 1/2 binary64)))
(*.f64 (/.f64 eps x) #s(literal 1/2 binary64))
(*.f64 #s(literal 1/2 binary64) (/.f64 eps x))
(/.f64 (neg.f64 (*.f64 eps #s(literal 1/2 binary64))) (neg.f64 x))
(/.f64 (neg.f64 (*.f64 #s(literal 1/2 binary64) eps)) (neg.f64 x))
(/.f64 (*.f64 eps #s(literal 1/2 binary64)) x)
(/.f64 (*.f64 #s(literal 1/2 binary64) eps) x)
(*.f64 (/.f64 eps #s(literal -1 binary64)) (/.f64 #s(literal -1 binary64) x))
(*.f64 (/.f64 #s(literal -1 binary64) x) (/.f64 eps #s(literal -1 binary64)))
(*.f64 (/.f64 eps x) #s(literal 1 binary64))
(*.f64 #s(literal 1 binary64) (/.f64 eps x))
(/.f64 (neg.f64 (neg.f64 eps)) (neg.f64 (neg.f64 x)))
(/.f64 (neg.f64 eps) (neg.f64 x))
(/.f64 eps x)
#s(literal 1/2 binary64)
(/.f64 (neg.f64 (-.f64 (*.f64 x x) #s(approx (- (* x x) eps) (*.f64 (-.f64 (/.f64 (*.f64 x x) eps) #s(literal 1 binary64)) eps)))) (neg.f64 (+.f64 x (sqrt.f64 #s(approx (- (* x x) eps) (*.f64 (-.f64 (/.f64 (*.f64 x x) eps) #s(literal 1 binary64)) eps))))))
(/.f64 (neg.f64 (-.f64 (*.f64 (*.f64 x x) x) (pow.f64 #s(approx (- (* x x) eps) (*.f64 (-.f64 (/.f64 (*.f64 x x) eps) #s(literal 1 binary64)) eps)) #s(literal 3/2 binary64)))) (neg.f64 (fma.f64 x x (+.f64 #s(approx (- (* x x) eps) (*.f64 (-.f64 (/.f64 (*.f64 x x) eps) #s(literal 1 binary64)) eps)) (*.f64 x (sqrt.f64 #s(approx (- (* x x) eps) (*.f64 (-.f64 (/.f64 (*.f64 x x) eps) #s(literal 1 binary64)) eps))))))))
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(*.f64 (neg.f64 (sqrt.f64 #s(approx (- (* x x) eps) (*.f64 (-.f64 (/.f64 (*.f64 x x) eps) #s(literal 1 binary64)) eps)))) (neg.f64 (sqrt.f64 #s(approx (- (* x x) eps) (*.f64 (-.f64 (/.f64 (*.f64 x x) eps) #s(literal 1 binary64)) eps)))))
(*.f64 (sqrt.f64 #s(approx (- (* x x) eps) (*.f64 (-.f64 (/.f64 (*.f64 x x) eps) #s(literal 1 binary64)) eps))) (sqrt.f64 #s(approx (- (* x x) eps) (*.f64 (-.f64 (/.f64 (*.f64 x x) eps) #s(literal 1 binary64)) eps))))
(pow.f64 (*.f64 #s(approx (- (* x x) eps) (*.f64 (-.f64 (/.f64 (*.f64 x x) eps) #s(literal 1 binary64)) eps)) #s(approx (- (* x x) eps) (*.f64 (-.f64 (/.f64 (*.f64 x x) eps) #s(literal 1 binary64)) eps))) #s(literal 1/2 binary64))
(pow.f64 (sqrt.f64 #s(approx (- (* x x) eps) (*.f64 (-.f64 (/.f64 (*.f64 x x) eps) #s(literal 1 binary64)) eps))) #s(literal 2 binary64))
(pow.f64 #s(approx (- (* x x) eps) (*.f64 (-.f64 (/.f64 (*.f64 x x) eps) #s(literal 1 binary64)) eps)) #s(literal 1 binary64))
#s(approx (- (* x x) eps) (*.f64 (-.f64 (/.f64 (*.f64 x x) eps) #s(literal 1 binary64)) eps))
(sqrt.f64 (*.f64 #s(approx (- (* x x) eps) (*.f64 (-.f64 (/.f64 (*.f64 x x) eps) #s(literal 1 binary64)) eps)) #s(approx (- (* x x) eps) (*.f64 (-.f64 (/.f64 (*.f64 x x) eps) #s(literal 1 binary64)) eps))))
#s(approx (- x (sqrt (- (* x x) eps))) (*.f64 (neg.f64 eps) (-.f64 (/.f64 (neg.f64 x) eps) (sqrt.f64 (/.f64 #s(literal -1 binary64) eps)))))
#s(approx (- x (sqrt (- (* x x) eps))) (*.f64 (neg.f64 eps) (-.f64 (neg.f64 (/.f64 (fma.f64 (/.f64 (*.f64 x x) (*.f64 (sqrt.f64 (/.f64 #s(literal -1 binary64) eps)) eps)) #s(literal 1/2 binary64) x) eps)) (sqrt.f64 (/.f64 #s(literal -1 binary64) eps)))))
#s(approx (- x (sqrt (- (* x x) eps))) (*.f64 (neg.f64 eps) (-.f64 (neg.f64 (/.f64 (+.f64 (neg.f64 (/.f64 (fma.f64 (/.f64 (*.f64 (*.f64 x x) (*.f64 x x)) (*.f64 (/.f64 #s(literal 1 binary64) (*.f64 (sqrt.f64 (neg.f64 eps)) (neg.f64 eps))) (*.f64 eps eps))) #s(literal 1/8 binary64) (*.f64 #s(literal -1/2 binary64) (/.f64 (*.f64 x x) (sqrt.f64 (/.f64 #s(literal -1 binary64) eps))))) eps)) x) eps)) (sqrt.f64 (/.f64 #s(literal -1 binary64) eps)))))
#s(approx (sqrt (- (* x x) eps)) (*.f64 (neg.f64 eps) (fma.f64 (/.f64 (*.f64 x x) (*.f64 (sqrt.f64 (/.f64 #s(literal -1 binary64) eps)) (*.f64 eps eps))) #s(literal 1/2 binary64) (sqrt.f64 (/.f64 #s(literal -1 binary64) eps)))))
#s(approx (sqrt (- (* x x) eps)) (*.f64 (neg.f64 eps) (+.f64 (fma.f64 (/.f64 (*.f64 (*.f64 x x) (*.f64 x x)) (*.f64 (/.f64 #s(literal 1 binary64) (*.f64 (sqrt.f64 (neg.f64 eps)) (neg.f64 eps))) (*.f64 (*.f64 eps eps) (*.f64 eps eps)))) #s(literal -1/8 binary64) (/.f64 (*.f64 #s(literal 1/2 binary64) (*.f64 x x)) (*.f64 (sqrt.f64 (/.f64 #s(literal -1 binary64) eps)) (*.f64 eps eps)))) (sqrt.f64 (/.f64 #s(literal -1 binary64) eps)))))
#s(approx (sqrt (- (* x x) eps)) (*.f64 (neg.f64 eps) (+.f64 (fma.f64 (/.f64 (*.f64 (*.f64 x x) (*.f64 x x)) (*.f64 (/.f64 #s(literal 1 binary64) (*.f64 (sqrt.f64 (neg.f64 eps)) (neg.f64 eps))) (*.f64 (*.f64 eps eps) (*.f64 eps eps)))) #s(literal -1/8 binary64) (fma.f64 (/.f64 #s(literal 1/16 binary64) (pow.f64 (/.f64 #s(literal -1 binary64) eps) #s(literal 5/2 binary64))) (exp.f64 (-.f64 (*.f64 (log.f64 x) #s(literal 6 binary64)) (*.f64 (log.f64 eps) #s(literal 6 binary64)))) (/.f64 (*.f64 #s(literal 1/2 binary64) (*.f64 x x)) (*.f64 (sqrt.f64 (/.f64 #s(literal -1 binary64) eps)) (*.f64 eps eps))))) (sqrt.f64 (/.f64 #s(literal -1 binary64) eps)))))
#s(approx (- (* x x) eps) (*.f64 (neg.f64 eps) (+.f64 (neg.f64 (/.f64 (*.f64 x x) eps)) #s(literal 1 binary64))))

eval30.0ms (1%)

Memory
31.6MiB live, 74.0MiB allocated; 11ms collecting garbage
Compiler

Compiled 2 620 to 999 computations (61.9% saved)

prune63.0ms (2.1%)

Memory
-21.8MiB live, 36.6MiB allocated; 27ms collecting garbage
Pruning

13 alts after pruning (7 fresh and 6 done)

PrunedKeptTotal
New1960196
Fresh077
Picked055
Done011
Total19613209
Accuracy
99.9%
Counts
209 → 13
Alt Table
Click to see full alt table
StatusAccuracyProgram
▶61.1%
(/.f64 (-.f64 (*.f64 x x) (-.f64 (*.f64 x x) eps)) (+.f64 x (sqrt.f64 (-.f64 (*.f64 x x) eps))))
✓61.5%
(-.f64 x (sqrt.f64 (-.f64 (*.f64 x x) eps)))
✓61.5%
(-.f64 x (sqrt.f64 #s(approx (- (* x x) eps) (fma.f64 x x (neg.f64 eps)))))
✓61.5%
(-.f64 x (sqrt.f64 #s(approx (- (* x x) eps) (*.f64 (-.f64 (/.f64 (*.f64 x x) eps) #s(literal 1 binary64)) eps))))
▶57.1%
(-.f64 x (sqrt.f64 #s(approx (- (* x x) eps) (neg.f64 eps))))
✓4.2%
(-.f64 x #s(approx (sqrt (- (* x x) eps)) (fabs.f64 x)))
▶42.5%
#s(approx (- x (sqrt (- (* x x) eps))) (/.f64 (fma.f64 (/.f64 (*.f64 eps eps) (*.f64 x x)) #s(literal 1/8 binary64) (*.f64 #s(literal 1/2 binary64) eps)) x))
37.2%
#s(approx (- x (sqrt (- (* x x) eps))) (/.f64 (-.f64 (/.f64 (*.f64 #s(literal 1/16 binary64) (*.f64 (*.f64 eps eps) eps)) (*.f64 (*.f64 x x) (*.f64 x x))) (fma.f64 (/.f64 (*.f64 eps eps) (*.f64 x x)) #s(literal -1/8 binary64) (*.f64 #s(literal -1/2 binary64) eps))) x))
28.2%
#s(approx (- x (sqrt (- (* x x) eps))) (/.f64 (-.f64 (*.f64 (/.f64 (*.f64 (*.f64 (*.f64 eps eps) (*.f64 eps eps)) #s(literal 5/64 binary64)) (*.f64 (*.f64 (*.f64 x x) x) (*.f64 (*.f64 x x) x))) #s(literal 1/2 binary64)) (fma.f64 #s(literal -1/2 binary64) eps (fma.f64 #s(literal -1/16 binary64) (/.f64 (*.f64 (*.f64 eps eps) eps) (*.f64 (*.f64 x x) (*.f64 x x))) (/.f64 (*.f64 #s(literal -1/8 binary64) (*.f64 eps eps)) (*.f64 x x))))) x))
✓3.7%
#s(approx (- x (sqrt (- (* x x) eps))) (+.f64 x x))
✓44.7%
#s(approx (- x (sqrt (- (* x x) eps))) (*.f64 (/.f64 eps x) #s(literal 1/2 binary64)))
▶56.9%
#s(approx (- x (sqrt (- (* x x) eps))) (*.f64 (neg.f64 eps) (-.f64 (/.f64 (neg.f64 x) eps) (sqrt.f64 (/.f64 #s(literal -1 binary64) eps)))))
▶56.9%
#s(approx (- x (sqrt (- (* x x) eps))) (neg.f64 (sqrt.f64 (neg.f64 eps))))
Compiler

Compiled 293 to 265 computations (9.6% saved)

series49.0ms (1.7%)

Memory
15.3MiB live, 48.0MiB allocated; 23ms collecting garbage
Counts
31 → 122
Calls
Call 1
Inputs
(/.f64 (-.f64 (*.f64 x x) (-.f64 (*.f64 x x) eps)) (+.f64 x (sqrt.f64 (-.f64 (*.f64 x x) eps))))
(-.f64 (*.f64 x x) (-.f64 (*.f64 x x) eps))
(*.f64 x x)
x
(-.f64 (*.f64 x x) eps)
eps
(+.f64 x (sqrt.f64 (-.f64 (*.f64 x x) eps)))
(sqrt.f64 (-.f64 (*.f64 x x) eps))
#s(approx (- x (sqrt (- (* x x) eps))) (neg.f64 (sqrt.f64 (neg.f64 eps))))
(neg.f64 (sqrt.f64 (neg.f64 eps)))
(sqrt.f64 (neg.f64 eps))
(neg.f64 eps)
(-.f64 x (sqrt.f64 #s(approx (- (* x x) eps) (neg.f64 eps))))
(sqrt.f64 #s(approx (- (* x x) eps) (neg.f64 eps)))
#s(approx (- (* x x) eps) (neg.f64 eps))
#s(approx (- x (sqrt (- (* x x) eps))) (*.f64 (neg.f64 eps) (-.f64 (/.f64 (neg.f64 x) eps) (sqrt.f64 (/.f64 #s(literal -1 binary64) eps)))))
(*.f64 (neg.f64 eps) (-.f64 (/.f64 (neg.f64 x) eps) (sqrt.f64 (/.f64 #s(literal -1 binary64) eps))))
(-.f64 (/.f64 (neg.f64 x) eps) (sqrt.f64 (/.f64 #s(literal -1 binary64) eps)))
(/.f64 (neg.f64 x) eps)
(neg.f64 x)
(sqrt.f64 (/.f64 #s(literal -1 binary64) eps))
(/.f64 #s(literal -1 binary64) eps)
#s(literal -1 binary64)
#s(approx (- x (sqrt (- (* x x) eps))) (/.f64 (fma.f64 (/.f64 (*.f64 eps eps) (*.f64 x x)) #s(literal 1/8 binary64) (*.f64 #s(literal 1/2 binary64) eps)) x))
(/.f64 (fma.f64 (/.f64 (*.f64 eps eps) (*.f64 x x)) #s(literal 1/8 binary64) (*.f64 #s(literal 1/2 binary64) eps)) x)
(fma.f64 (/.f64 (*.f64 eps eps) (*.f64 x x)) #s(literal 1/8 binary64) (*.f64 #s(literal 1/2 binary64) eps))
(/.f64 (*.f64 eps eps) (*.f64 x x))
(*.f64 eps eps)
#s(literal 1/8 binary64)
(*.f64 #s(literal 1/2 binary64) eps)
#s(literal 1/2 binary64)
Outputs
#s(approx (/ (- (* x x) (- (* x x) eps)) (+ x (sqrt (- (* x x) eps)))) #s(hole binary64 (/ eps (sqrt (neg eps)))))
#s(approx (/ (- (* x x) (- (* x x) eps)) (+ x (sqrt (- (* x x) eps)))) #s(hole binary64 (+ (* -1 (/ (* eps x) (pow (sqrt (neg eps)) 2))) (/ eps (sqrt (neg eps))))))
#s(approx (/ (- (* x x) (- (* x x) eps)) (+ x (sqrt (- (* x x) eps)))) #s(hole binary64 (+ (* x (- (* -1 (* x (+ (* -1 (/ eps (pow (sqrt (neg eps)) 3))) (* 1/2 (/ eps (pow (sqrt (neg eps)) 3)))))) (/ eps (pow (sqrt (neg eps)) 2)))) (/ eps (sqrt (neg eps))))))
#s(approx (/ (- (* x x) (- (* x x) eps)) (+ x (sqrt (- (* x x) eps)))) #s(hole binary64 (+ (* x (- (* x (- (* -1 (* x (+ (* -1 (/ (+ (* -1 (/ eps (pow (sqrt (neg eps)) 3))) (* 1/2 (/ eps (pow (sqrt (neg eps)) 3)))) (sqrt (neg eps)))) (* -1/2 (/ eps (pow (sqrt (neg eps)) 4)))))) (+ (* -1 (/ eps (pow (sqrt (neg eps)) 3))) (* 1/2 (/ eps (pow (sqrt (neg eps)) 3)))))) (/ eps (pow (sqrt (neg eps)) 2)))) (/ eps (sqrt (neg eps))))))
#s(approx (- (* x x) (- (* x x) eps)) #s(hole binary64 eps))
#s(approx (* x x) #s(hole binary64 (pow x 2)))
#s(approx x #s(hole binary64 x))
#s(approx (- (* x x) eps) #s(hole binary64 (* -1 eps)))
#s(approx (- (* x x) eps) #s(hole binary64 (- (pow x 2) eps)))
#s(approx (+ x (sqrt (- (* x x) eps))) #s(hole binary64 (sqrt (neg eps))))
#s(approx (+ x (sqrt (- (* x x) eps))) #s(hole binary64 (+ x (sqrt (neg eps)))))
#s(approx (+ x (sqrt (- (* x x) eps))) #s(hole binary64 (+ (sqrt (neg eps)) (* x (+ 1 (* 1/2 (/ x (sqrt (neg eps)))))))))
#s(approx (+ x (sqrt (- (* x x) eps))) #s(hole binary64 (+ (sqrt (neg eps)) (* x (+ 1 (* x (+ (* -1/8 (/ (pow x 2) (pow (sqrt (neg eps)) 3))) (* 1/2 (/ 1 (sqrt (neg eps)))))))))))
#s(approx (sqrt (- (* x x) eps)) #s(hole binary64 (+ (sqrt (neg eps)) (* 1/2 (/ (pow x 2) (sqrt (neg eps)))))))
#s(approx (sqrt (- (* x x) eps)) #s(hole binary64 (+ (sqrt (neg eps)) (* (pow x 2) (+ (* -1/8 (/ (pow x 2) (pow (sqrt (neg eps)) 3))) (* 1/2 (/ 1 (sqrt (neg eps)))))))))
#s(approx (sqrt (- (* x x) eps)) #s(hole binary64 (+ (sqrt (neg eps)) (* (pow x 2) (+ (* (pow x 2) (- (* 1/16 (/ (pow x 2) (pow (sqrt (neg eps)) 5))) (* 1/8 (/ 1 (pow (sqrt (neg eps)) 3))))) (* 1/2 (/ 1 (sqrt (neg eps)))))))))
#s(approx (- x (sqrt (- (* x x) eps))) #s(hole binary64 (* -1 (sqrt (neg eps)))))
#s(approx (- x (sqrt (- (* x x) eps))) #s(hole binary64 (- x (sqrt (neg eps)))))
#s(approx (- x (sqrt (- (* x x) eps))) #s(hole binary64 (- (* x (+ 1 (* -1/2 (/ x (sqrt (neg eps)))))) (sqrt (neg eps)))))
#s(approx (- x (sqrt (- (* x x) eps))) #s(hole binary64 (- (* x (+ 1 (* x (- (* 1/8 (/ (pow x 2) (pow (sqrt (neg eps)) 3))) (* 1/2 (/ 1 (sqrt (neg eps)))))))) (sqrt (neg eps)))))
#s(approx (* (neg eps) (- (/ (neg x) eps) (sqrt (/ -1 eps)))) #s(hole binary64 (* eps (sqrt (/ -1 eps)))))
#s(approx (* (neg eps) (- (/ (neg x) eps) (sqrt (/ -1 eps)))) #s(hole binary64 (+ x (* eps (sqrt (/ -1 eps))))))
#s(approx (- (/ (neg x) eps) (sqrt (/ -1 eps))) #s(hole binary64 (* -1 (sqrt (/ -1 eps)))))
#s(approx (- (/ (neg x) eps) (sqrt (/ -1 eps))) #s(hole binary64 (- (* -1 (/ x eps)) (sqrt (/ -1 eps)))))
#s(approx (/ (neg x) eps) #s(hole binary64 (* -1 (/ x eps))))
#s(approx (neg x) #s(hole binary64 (* -1 x)))
#s(approx (/ (+ (* (/ (* eps eps) (* x x)) 1/8) (* 1/2 eps)) x) #s(hole binary64 (* 1/8 (/ (pow eps 2) (pow x 3)))))
#s(approx (/ (+ (* (/ (* eps eps) (* x x)) 1/8) (* 1/2 eps)) x) #s(hole binary64 (/ (+ (* 1/8 (pow eps 2)) (* 1/2 (* eps (pow x 2)))) (pow x 3))))
#s(approx (+ (* (/ (* eps eps) (* x x)) 1/8) (* 1/2 eps)) #s(hole binary64 (* 1/8 (/ (pow eps 2) (pow x 2)))))
#s(approx (+ (* (/ (* eps eps) (* x x)) 1/8) (* 1/2 eps)) #s(hole binary64 (/ (+ (* 1/8 (pow eps 2)) (* 1/2 (* eps (pow x 2)))) (pow x 2))))
#s(approx (/ (* eps eps) (* x x)) #s(hole binary64 (/ (pow eps 2) (pow x 2))))
#s(approx (/ (- (* x x) (- (* x x) eps)) (+ x (sqrt (- (* x x) eps)))) #s(hole binary64 (* 1/2 (/ eps x))))
#s(approx (/ (- (* x x) (- (* x x) eps)) (+ x (sqrt (- (* x x) eps)))) #s(hole binary64 (/ (+ (* 1/8 (/ (pow eps 2) (pow x 2))) (* 1/2 eps)) x)))
#s(approx (/ (- (* x x) (- (* x x) eps)) (+ x (sqrt (- (* x x) eps)))) #s(hole binary64 (/ (- (+ (* 1/16 (/ (pow eps 3) (pow x 4))) (* 1/2 eps)) (* -1/8 (/ (pow eps 2) (pow x 2)))) x)))
#s(approx (/ (- (* x x) (- (* x x) eps)) (+ x (sqrt (- (* x x) eps)))) #s(hole binary64 (/ (- (+ (* -1 (/ (+ (* -1/32 (pow eps 4)) (* -1/128 (pow eps 4))) (pow x 6))) (* 1/2 eps)) (+ (* -1/8 (/ (pow eps 2) (pow x 2))) (* -1/16 (/ (pow eps 3) (pow x 4))))) x)))
#s(approx (- (* x x) eps) #s(hole binary64 (* (pow x 2) (+ 1 (* -1 (/ eps (pow x 2)))))))
#s(approx (+ x (sqrt (- (* x x) eps))) #s(hole binary64 (* 2 x)))
#s(approx (+ x (sqrt (- (* x x) eps))) #s(hole binary64 (* x (+ 2 (* -1/2 (/ eps (pow x 2)))))))
#s(approx (+ x (sqrt (- (* x x) eps))) #s(hole binary64 (* x (+ 2 (+ (* -1/2 (/ eps (pow x 2))) (* -1/8 (/ (pow eps 2) (pow x 4))))))))
#s(approx (+ x (sqrt (- (* x x) eps))) #s(hole binary64 (* x (+ 2 (+ (* -1/2 (/ eps (pow x 2))) (+ (* -1/8 (/ (pow eps 2) (pow x 4))) (* -1/16 (/ (pow eps 3) (pow x 6)))))))))
#s(approx (sqrt (- (* x x) eps)) #s(hole binary64 (* x (+ 1 (* -1/2 (/ eps (pow x 2)))))))
#s(approx (sqrt (- (* x x) eps)) #s(hole binary64 (* x (+ 1 (+ (* -1/2 (/ eps (pow x 2))) (* -1/8 (/ (pow eps 2) (pow x 4))))))))
#s(approx (sqrt (- (* x x) eps)) #s(hole binary64 (* x (+ 1 (+ (* -1/2 (/ eps (pow x 2))) (+ (* -1/8 (/ (pow eps 2) (pow x 4))) (* -1/16 (/ (pow eps 3) (pow x 6)))))))))
#s(approx (- x (sqrt (- (* x x) eps))) #s(hole binary64 (/ (- (* 1/8 (/ (pow eps 2) (pow x 2))) (* -1/2 eps)) x)))
#s(approx (- x (sqrt (- (* x x) eps))) #s(hole binary64 (/ (- (* 1/16 (/ (pow eps 3) (pow x 4))) (+ (* -1/2 eps) (* -1/8 (/ (pow eps 2) (pow x 2))))) x)))
#s(approx (- x (sqrt (- (* x x) eps))) #s(hole binary64 (/ (- (* 1/2 (/ (+ (* 1/64 (pow eps 4)) (* 1/16 (pow eps 4))) (pow x 6))) (+ (* -1/2 eps) (+ (* -1/8 (/ (pow eps 2) (pow x 2))) (* -1/16 (/ (pow eps 3) (pow x 4)))))) x)))
#s(approx (* (neg eps) (- (/ (neg x) eps) (sqrt (/ -1 eps)))) #s(hole binary64 (* x (+ 1 (/ (* eps (sqrt (/ -1 eps))) x)))))
#s(approx (- (/ (neg x) eps) (sqrt (/ -1 eps))) #s(hole binary64 (* x (- (* -1 (/ (sqrt (/ -1 eps)) x)) (/ 1 eps)))))
#s(approx (+ (* (/ (* eps eps) (* x x)) 1/8) (* 1/2 eps)) #s(hole binary64 (* 1/2 eps)))
#s(approx (+ (* (/ (* eps eps) (* x x)) 1/8) (* 1/2 eps)) #s(hole binary64 (+ (* 1/8 (/ (pow eps 2) (pow x 2))) (* 1/2 eps))))
#s(approx (/ (- (* x x) (- (* x x) eps)) (+ x (sqrt (- (* x x) eps)))) #s(hole binary64 (* -1 (* x (- (* 1/2 (/ eps (pow x 2))) 2)))))
#s(approx (/ (- (* x x) (- (* x x) eps)) (+ x (sqrt (- (* x x) eps)))) #s(hole binary64 (* -1 (* x (- (* -1 (/ (+ (* -1/4 (pow eps 2)) (* 1/8 (pow eps 2))) (pow x 4))) (+ 2 (* -1/2 (/ eps (pow x 2)))))))))
#s(approx (/ (- (* x x) (- (* x x) eps)) (+ x (sqrt (- (* x x) eps)))) #s(hole binary64 (* -1 (* x (- (* -1 (/ (+ (* -2 (/ (+ (* 1/64 (pow eps 4)) (* 1/16 (pow eps 4))) eps)) (+ (* -1/4 (* eps (+ (* -1/4 (pow eps 2)) (* 1/8 (pow eps 2))))) (* 1/16 (pow eps 3)))) (pow x 6))) (+ 2 (+ (* -1/2 (/ eps (pow x 2))) (+ (* -1/4 (/ (pow eps 2) (pow x 4))) (* 1/8 (/ (pow eps 2) (pow x 4)))))))))))
#s(approx (+ x (sqrt (- (* x x) eps))) #s(hole binary64 (* -1 (/ (+ (* -1/2 eps) (* -1/8 (/ (pow eps 2) (pow x 2)))) x))))
#s(approx (+ x (sqrt (- (* x x) eps))) #s(hole binary64 (* -1 (/ (+ (* -1/2 eps) (+ (* -1/8 (/ (pow eps 2) (pow x 2))) (* -1/16 (/ (pow eps 3) (pow x 4))))) x))))
#s(approx (+ x (sqrt (- (* x x) eps))) #s(hole binary64 (* -1 (/ (+ (* -1/2 eps) (+ (* -1/2 (/ (+ (* 1/64 (pow eps 4)) (* 1/16 (pow eps 4))) (pow x 6))) (+ (* -1/8 (/ (pow eps 2) (pow x 2))) (* -1/16 (/ (pow eps 3) (pow x 4)))))) x))))
#s(approx (sqrt (- (* x x) eps)) #s(hole binary64 (* -1 (* x (+ 1 (* -1/2 (/ eps (pow x 2))))))))
#s(approx (sqrt (- (* x x) eps)) #s(hole binary64 (* -1 (* x (+ 1 (+ (* -1/2 (/ eps (pow x 2))) (* -1/8 (/ (pow eps 2) (pow x 4)))))))))
#s(approx (sqrt (- (* x x) eps)) #s(hole binary64 (* -1 (* x (+ 1 (+ (* -1/2 (/ eps (pow x 2))) (+ (* -1/8 (/ (pow eps 2) (pow x 4))) (* -1/16 (/ (pow eps 3) (pow x 6))))))))))
#s(approx (- x (sqrt (- (* x x) eps))) #s(hole binary64 (* -1 (* x (- (* 1/8 (/ (pow eps 2) (pow x 4))) (+ 2 (* -1/2 (/ eps (pow x 2)))))))))
#s(approx (- x (sqrt (- (* x x) eps))) #s(hole binary64 (* -1 (* x (- (* 1/16 (/ (pow eps 3) (pow x 6))) (+ 2 (+ (* -1/2 (/ eps (pow x 2))) (* -1/8 (/ (pow eps 2) (pow x 4))))))))))
#s(approx (* (neg eps) (- (/ (neg x) eps) (sqrt (/ -1 eps)))) #s(hole binary64 (* -1 (* x (- (* -1 (/ (* eps (sqrt (/ -1 eps))) x)) 1)))))
#s(approx (- (/ (neg x) eps) (sqrt (/ -1 eps))) #s(hole binary64 (* -1 (* x (+ (/ 1 eps) (/ (sqrt (/ -1 eps)) x))))))
#s(approx (/ (- (* x x) (- (* x x) eps)) (+ x (sqrt (- (* x x) eps)))) #s(hole binary64 (/ eps (+ x (sqrt (pow x 2))))))
#s(approx (/ (- (* x x) (- (* x x) eps)) (+ x (sqrt (- (* x x) eps)))) #s(hole binary64 (* eps (+ (* 1/2 (/ eps (* (sqrt (pow x 2)) (pow (+ x (sqrt (pow x 2))) 2)))) (/ 1 (+ x (sqrt (pow x 2))))))))
#s(approx (/ (- (* x x) (- (* x x) eps)) (+ x (sqrt (- (* x x) eps)))) #s(hole binary64 (* eps (+ (* eps (+ (* eps (+ (* 1/4 (/ 1 (* (pow (sqrt (pow x 2)) 2) (pow (+ x (sqrt (pow x 2))) 3)))) (* 1/8 (/ 1 (* (pow (sqrt (pow x 2)) 3) (pow (+ x (sqrt (pow x 2))) 2)))))) (* 1/2 (/ 1 (* (sqrt (pow x 2)) (pow (+ x (sqrt (pow x 2))) 2)))))) (/ 1 (+ x (sqrt (pow x 2))))))))
#s(approx (/ (- (* x x) (- (* x x) eps)) (+ x (sqrt (- (* x x) eps)))) #s(hole binary64 (* eps (+ (* eps (+ (* eps (+ (* 1/8 (/ 1 (* (pow (sqrt (pow x 2)) 3) (pow (+ x (sqrt (pow x 2))) 2)))) (+ (* 1/4 (/ 1 (* (pow (sqrt (pow x 2)) 2) (pow (+ x (sqrt (pow x 2))) 3)))) (* eps (- (+ (* 1/16 (/ 1 (* (pow (sqrt (pow x 2)) 4) (pow (+ x (sqrt (pow x 2))) 3)))) (* 1/16 (/ 1 (* (pow (sqrt (pow x 2)) 5) (pow (+ x (sqrt (pow x 2))) 2))))) (* -1/2 (/ (+ (* 1/4 (/ 1 (* (pow (sqrt (pow x 2)) 2) (pow (+ x (sqrt (pow x 2))) 3)))) (* 1/8 (/ 1 (* (pow (sqrt (pow x 2)) 3) (pow (+ x (sqrt (pow x 2))) 2))))) (* (sqrt (pow x 2)) (+ x (sqrt (pow x 2))))))))))) (* 1/2 (/ 1 (* (sqrt (pow x 2)) (pow (+ x (sqrt (pow x 2))) 2)))))) (/ 1 (+ x (sqrt (pow x 2))))))))
#s(approx (- (* x x) eps) #s(hole binary64 (+ (* -1 eps) (pow x 2))))
#s(approx (+ x (sqrt (- (* x x) eps))) #s(hole binary64 (+ x (sqrt (pow x 2)))))
#s(approx (+ x (sqrt (- (* x x) eps))) #s(hole binary64 (+ x (+ (sqrt (pow x 2)) (* -1/2 (/ eps (sqrt (pow x 2))))))))
#s(approx (+ x (sqrt (- (* x x) eps))) #s(hole binary64 (+ x (+ (sqrt (pow x 2)) (* eps (- (* -1/8 (/ eps (pow (sqrt (pow x 2)) 3))) (* 1/2 (/ 1 (sqrt (pow x 2))))))))))
#s(approx (+ x (sqrt (- (* x x) eps))) #s(hole binary64 (+ x (+ (sqrt (pow x 2)) (* eps (- (* eps (- (* -1/16 (/ eps (pow (sqrt (pow x 2)) 5))) (* 1/8 (/ 1 (pow (sqrt (pow x 2)) 3))))) (* 1/2 (/ 1 (sqrt (pow x 2))))))))))
#s(approx (sqrt (- (* x x) eps)) #s(hole binary64 (sqrt (pow x 2))))
#s(approx (sqrt (- (* x x) eps)) #s(hole binary64 (+ (sqrt (pow x 2)) (* -1/2 (/ eps (sqrt (pow x 2)))))))
#s(approx (sqrt (- (* x x) eps)) #s(hole binary64 (+ (sqrt (pow x 2)) (* eps (- (* -1/8 (/ eps (pow (sqrt (pow x 2)) 3))) (* 1/2 (/ 1 (sqrt (pow x 2)))))))))
#s(approx (sqrt (- (* x x) eps)) #s(hole binary64 (+ (sqrt (pow x 2)) (* eps (- (* eps (- (* -1/16 (/ eps (pow (sqrt (pow x 2)) 5))) (* 1/8 (/ 1 (pow (sqrt (pow x 2)) 3))))) (* 1/2 (/ 1 (sqrt (pow x 2)))))))))
#s(approx (- x (sqrt (- (* x x) eps))) #s(hole binary64 (- x (sqrt (pow x 2)))))
#s(approx (- x (sqrt (- (* x x) eps))) #s(hole binary64 (- (+ x (* 1/2 (/ eps (sqrt (pow x 2))))) (sqrt (pow x 2)))))
#s(approx (- x (sqrt (- (* x x) eps))) #s(hole binary64 (- (+ x (* eps (+ (* 1/8 (/ eps (pow (sqrt (pow x 2)) 3))) (* 1/2 (/ 1 (sqrt (pow x 2))))))) (sqrt (pow x 2)))))
#s(approx (- x (sqrt (- (* x x) eps))) #s(hole binary64 (- (+ x (* eps (+ (* eps (+ (* 1/16 (/ eps (pow (sqrt (pow x 2)) 5))) (* 1/8 (/ 1 (pow (sqrt (pow x 2)) 3))))) (* 1/2 (/ 1 (sqrt (pow x 2))))))) (sqrt (pow x 2)))))
#s(approx (neg (sqrt (neg eps))) #s(hole binary64 (* -1 (sqrt (* -1 eps)))))
#s(approx (sqrt (neg eps)) #s(hole binary64 (sqrt (* -1 eps))))
#s(approx (* (neg eps) (- (/ (neg x) eps) (sqrt (/ -1 eps)))) #s(hole binary64 (* -1 (- (* -1 x) (sqrt (* -1 eps))))))
#s(approx (- (/ (neg x) eps) (sqrt (/ -1 eps))) #s(hole binary64 (/ (- (* -1 x) (sqrt (* -1 eps))) eps)))
#s(approx (sqrt (/ -1 eps)) #s(hole binary64 (/ (sqrt (* -1 eps)) eps)))
#s(approx (/ -1 eps) #s(hole binary64 (/ -1 eps)))
#s(approx (/ (+ (* (/ (* eps eps) (* x x)) 1/8) (* 1/2 eps)) x) #s(hole binary64 (* eps (+ (* 1/8 (/ eps (pow x 3))) (* 1/2 (/ 1 x))))))
#s(approx (+ (* (/ (* eps eps) (* x x)) 1/8) (* 1/2 eps)) #s(hole binary64 (* eps (+ 1/2 (* 1/8 (/ eps (pow x 2)))))))
#s(approx (* eps eps) #s(hole binary64 (pow eps 2)))
#s(approx (/ (- (* x x) (- (* x x) eps)) (+ x (sqrt (- (* x x) eps)))) #s(hole binary64 (/ 1 (sqrt (/ -1 eps)))))
#s(approx (/ (- (* x x) (- (* x x) eps)) (+ x (sqrt (- (* x x) eps)))) #s(hole binary64 (+ (* -1 (/ x (* eps (pow (sqrt (/ -1 eps)) 2)))) (/ 1 (sqrt (/ -1 eps))))))
#s(approx (/ (- (* x x) (- (* x x) eps)) (+ x (sqrt (- (* x x) eps)))) #s(hole binary64 (- (+ (* -1 (/ (+ (* -1 (/ (pow x 2) (pow (sqrt (/ -1 eps)) 3))) (* 1/2 (/ (pow x 2) (pow (sqrt (/ -1 eps)) 3)))) (pow eps 2))) (/ 1 (sqrt (/ -1 eps)))) (/ x (* eps (pow (sqrt (/ -1 eps)) 2))))))
#s(approx (/ (- (* x x) (- (* x x) eps)) (+ x (sqrt (- (* x x) eps)))) #s(hole binary64 (- (+ (* -1 (/ (+ (* -1 (/ (* x (+ (* -1 (/ (pow x 2) (pow (sqrt (/ -1 eps)) 3))) (* 1/2 (/ (pow x 2) (pow (sqrt (/ -1 eps)) 3))))) (sqrt (/ -1 eps)))) (* -1/2 (/ (pow x 3) (pow (sqrt (/ -1 eps)) 4)))) (pow eps 3))) (/ 1 (sqrt (/ -1 eps)))) (+ (* -1 (/ (pow x 2) (* (pow eps 2) (pow (sqrt (/ -1 eps)) 3)))) (+ (* 1/2 (/ (pow x 2) (* (pow eps 2) (pow (sqrt (/ -1 eps)) 3)))) (/ x (* eps (pow (sqrt (/ -1 eps)) 2))))))))
#s(approx (- (* x x) eps) #s(hole binary64 (* eps (- (/ (pow x 2) eps) 1))))
#s(approx (+ x (sqrt (- (* x x) eps))) #s(hole binary64 (* eps (+ (sqrt (/ -1 eps)) (/ x eps)))))
#s(approx (+ x (sqrt (- (* x x) eps))) #s(hole binary64 (* eps (+ (sqrt (/ -1 eps)) (+ (* 1/2 (/ (pow x 2) (* (pow eps 2) (sqrt (/ -1 eps))))) (/ x eps))))))
#s(approx (+ x (sqrt (- (* x x) eps))) #s(hole binary64 (* eps (+ (sqrt (/ -1 eps)) (+ (* -1/8 (/ (pow x 4) (* (pow eps 4) (pow (sqrt (/ -1 eps)) 3)))) (+ (* 1/2 (/ (pow x 2) (* (pow eps 2) (sqrt (/ -1 eps))))) (/ x eps)))))))
#s(approx (sqrt (- (* x x) eps)) #s(hole binary64 (* eps (+ (sqrt (/ -1 eps)) (* 1/2 (/ (pow x 2) (* (pow eps 2) (sqrt (/ -1 eps)))))))))
#s(approx (sqrt (- (* x x) eps)) #s(hole binary64 (* eps (+ (sqrt (/ -1 eps)) (+ (* -1/8 (/ (pow x 4) (* (pow eps 4) (pow (sqrt (/ -1 eps)) 3)))) (* 1/2 (/ (pow x 2) (* (pow eps 2) (sqrt (/ -1 eps))))))))))
#s(approx (sqrt (- (* x x) eps)) #s(hole binary64 (* eps (+ (sqrt (/ -1 eps)) (+ (* -1/8 (/ (pow x 4) (* (pow eps 4) (pow (sqrt (/ -1 eps)) 3)))) (+ (* 1/16 (/ (pow x 6) (* (pow eps 6) (pow (sqrt (/ -1 eps)) 5)))) (* 1/2 (/ (pow x 2) (* (pow eps 2) (sqrt (/ -1 eps)))))))))))
#s(approx (- x (sqrt (- (* x x) eps))) #s(hole binary64 (* -1 (* eps (sqrt (/ -1 eps))))))
#s(approx (- x (sqrt (- (* x x) eps))) #s(hole binary64 (* eps (- (/ x eps) (sqrt (/ -1 eps))))))
#s(approx (- x (sqrt (- (* x x) eps))) #s(hole binary64 (* eps (- (+ (* -1/2 (/ (pow x 2) (* (pow eps 2) (sqrt (/ -1 eps))))) (/ x eps)) (sqrt (/ -1 eps))))))
#s(approx (- x (sqrt (- (* x x) eps))) #s(hole binary64 (* eps (- (+ (* 1/8 (/ (pow x 4) (* (pow eps 4) (pow (sqrt (/ -1 eps)) 3)))) (/ x eps)) (+ (sqrt (/ -1 eps)) (* 1/2 (/ (pow x 2) (* (pow eps 2) (sqrt (/ -1 eps))))))))))
#s(approx (sqrt (/ -1 eps)) #s(hole binary64 (sqrt (/ -1 eps))))
#s(approx (/ (+ (* (/ (* eps eps) (* x x)) 1/8) (* 1/2 eps)) x) #s(hole binary64 (* (pow eps 2) (+ (* 1/2 (/ 1 (* eps x))) (* 1/8 (/ 1 (pow x 3)))))))
#s(approx (+ (* (/ (* eps eps) (* x x)) 1/8) (* 1/2 eps)) #s(hole binary64 (* (pow eps 2) (+ (* 1/2 (/ 1 eps)) (* 1/8 (/ 1 (pow x 2)))))))
#s(approx (/ (- (* x x) (- (* x x) eps)) (+ x (sqrt (- (* x x) eps)))) #s(hole binary64 (/ -1 (sqrt (/ -1 eps)))))
#s(approx (/ (- (* x x) (- (* x x) eps)) (+ x (sqrt (- (* x x) eps)))) #s(hole binary64 (- (* -1 (/ x (* eps (pow (sqrt (/ -1 eps)) 2)))) (/ 1 (sqrt (/ -1 eps))))))
#s(approx (/ (- (* x x) (- (* x x) eps)) (+ x (sqrt (- (* x x) eps)))) #s(hole binary64 (- (* -1 (/ (- (+ (* -1/2 (/ (pow x 2) (* eps (pow (sqrt (/ -1 eps)) 3)))) (/ (pow x 2) (* eps (pow (sqrt (/ -1 eps)) 3)))) (* -1 (/ x (pow (sqrt (/ -1 eps)) 2)))) eps)) (/ 1 (sqrt (/ -1 eps))))))
#s(approx (/ (- (* x x) (- (* x x) eps)) (+ x (sqrt (- (* x x) eps)))) #s(hole binary64 (- (* -1 (/ (- (* -1 (/ (- (+ (* -1 (/ (* x (+ (* -1/2 (/ (pow x 2) (pow (sqrt (/ -1 eps)) 3))) (/ (pow x 2) (pow (sqrt (/ -1 eps)) 3)))) (* eps (sqrt (/ -1 eps))))) (* 1/2 (/ (pow x 3) (* eps (pow (sqrt (/ -1 eps)) 4))))) (+ (* -1/2 (/ (pow x 2) (pow (sqrt (/ -1 eps)) 3))) (/ (pow x 2) (pow (sqrt (/ -1 eps)) 3)))) eps)) (* -1 (/ x (pow (sqrt (/ -1 eps)) 2)))) eps)) (/ 1 (sqrt (/ -1 eps))))))
#s(approx (- (* x x) eps) #s(hole binary64 (* -1 (* eps (+ 1 (* -1 (/ (pow x 2) eps)))))))
#s(approx (+ x (sqrt (- (* x x) eps))) #s(hole binary64 (* -1 (* eps (+ (sqrt (/ -1 eps)) (* -1 (/ x eps)))))))
#s(approx (+ x (sqrt (- (* x x) eps))) #s(hole binary64 (* -1 (* eps (+ (sqrt (/ -1 eps)) (* -1 (/ (+ x (* -1/2 (/ (pow x 2) (* eps (sqrt (/ -1 eps)))))) eps)))))))
#s(approx (+ x (sqrt (- (* x x) eps))) #s(hole binary64 (* -1 (* eps (+ (sqrt (/ -1 eps)) (* -1 (/ (+ x (* -1 (/ (+ (* -1/8 (/ (pow x 4) (* (pow eps 2) (pow (sqrt (/ -1 eps)) 3)))) (* 1/2 (/ (pow x 2) (sqrt (/ -1 eps))))) eps))) eps)))))))
#s(approx (sqrt (- (* x x) eps)) #s(hole binary64 (* -1 (* eps (+ (sqrt (/ -1 eps)) (* 1/2 (/ (pow x 2) (* (pow eps 2) (sqrt (/ -1 eps))))))))))
#s(approx (sqrt (- (* x x) eps)) #s(hole binary64 (* -1 (* eps (+ (sqrt (/ -1 eps)) (+ (* -1/8 (/ (pow x 4) (* (pow eps 4) (pow (sqrt (/ -1 eps)) 3)))) (* 1/2 (/ (pow x 2) (* (pow eps 2) (sqrt (/ -1 eps)))))))))))
#s(approx (sqrt (- (* x x) eps)) #s(hole binary64 (* -1 (* eps (+ (sqrt (/ -1 eps)) (+ (* -1/8 (/ (pow x 4) (* (pow eps 4) (pow (sqrt (/ -1 eps)) 3)))) (+ (* 1/16 (/ (pow x 6) (* (pow eps 6) (pow (sqrt (/ -1 eps)) 5)))) (* 1/2 (/ (pow x 2) (* (pow eps 2) (sqrt (/ -1 eps))))))))))))
#s(approx (- x (sqrt (- (* x x) eps))) #s(hole binary64 (* -1 (* eps (- (* -1 (/ x eps)) (sqrt (/ -1 eps)))))))
#s(approx (- x (sqrt (- (* x x) eps))) #s(hole binary64 (* -1 (* eps (- (* -1 (/ (+ x (* 1/2 (/ (pow x 2) (* eps (sqrt (/ -1 eps)))))) eps)) (sqrt (/ -1 eps)))))))
#s(approx (- x (sqrt (- (* x x) eps))) #s(hole binary64 (* -1 (* eps (- (* -1 (/ (+ x (* -1 (/ (- (* 1/8 (/ (pow x 4) (* (pow eps 2) (pow (sqrt (/ -1 eps)) 3)))) (* 1/2 (/ (pow x 2) (sqrt (/ -1 eps))))) eps))) eps)) (sqrt (/ -1 eps)))))))
#s(approx (* (neg eps) (- (/ (neg x) eps) (sqrt (/ -1 eps)))) #s(hole binary64 (* -1 (* eps (+ (* -1 (sqrt (/ -1 eps))) (* -1 (/ x eps)))))))
Calls

6 calls:

TimeVariablePointExpression
25.0ms
x
@-inf
((/ (- (* x x) (- (* x x) eps)) (+ x (sqrt (- (* x x) eps)))) (- (* x x) (- (* x x) eps)) (* x x) x (- (* x x) eps) eps (+ x (sqrt (- (* x x) eps))) (sqrt (- (* x x) eps)) (- x (sqrt (- (* x x) eps))) (neg (sqrt (neg eps))) (sqrt (neg eps)) (neg eps) (- x (sqrt (- (* x x) eps))) (sqrt (- (* x x) eps)) (- (* x x) eps) (- x (sqrt (- (* x x) eps))) (* (neg eps) (- (/ (neg x) eps) (sqrt (/ -1 eps)))) (- (/ (neg x) eps) (sqrt (/ -1 eps))) (/ (neg x) eps) (neg x) (sqrt (/ -1 eps)) (/ -1 eps) -1 (- x (sqrt (- (* x x) eps))) (/ (+ (* (/ (* eps eps) (* x x)) 1/8) (* 1/2 eps)) x) (+ (* (/ (* eps eps) (* x x)) 1/8) (* 1/2 eps)) (/ (* eps eps) (* x x)) (* eps eps) 1/8 (* 1/2 eps) 1/2)
5.0ms
x
@inf
((/ (- (* x x) (- (* x x) eps)) (+ x (sqrt (- (* x x) eps)))) (- (* x x) (- (* x x) eps)) (* x x) x (- (* x x) eps) eps (+ x (sqrt (- (* x x) eps))) (sqrt (- (* x x) eps)) (- x (sqrt (- (* x x) eps))) (neg (sqrt (neg eps))) (sqrt (neg eps)) (neg eps) (- x (sqrt (- (* x x) eps))) (sqrt (- (* x x) eps)) (- (* x x) eps) (- x (sqrt (- (* x x) eps))) (* (neg eps) (- (/ (neg x) eps) (sqrt (/ -1 eps)))) (- (/ (neg x) eps) (sqrt (/ -1 eps))) (/ (neg x) eps) (neg x) (sqrt (/ -1 eps)) (/ -1 eps) -1 (- x (sqrt (- (* x x) eps))) (/ (+ (* (/ (* eps eps) (* x x)) 1/8) (* 1/2 eps)) x) (+ (* (/ (* eps eps) (* x x)) 1/8) (* 1/2 eps)) (/ (* eps eps) (* x x)) (* eps eps) 1/8 (* 1/2 eps) 1/2)
4.0ms
eps
@0
((/ (- (* x x) (- (* x x) eps)) (+ x (sqrt (- (* x x) eps)))) (- (* x x) (- (* x x) eps)) (* x x) x (- (* x x) eps) eps (+ x (sqrt (- (* x x) eps))) (sqrt (- (* x x) eps)) (- x (sqrt (- (* x x) eps))) (neg (sqrt (neg eps))) (sqrt (neg eps)) (neg eps) (- x (sqrt (- (* x x) eps))) (sqrt (- (* x x) eps)) (- (* x x) eps) (- x (sqrt (- (* x x) eps))) (* (neg eps) (- (/ (neg x) eps) (sqrt (/ -1 eps)))) (- (/ (neg x) eps) (sqrt (/ -1 eps))) (/ (neg x) eps) (neg x) (sqrt (/ -1 eps)) (/ -1 eps) -1 (- x (sqrt (- (* x x) eps))) (/ (+ (* (/ (* eps eps) (* x x)) 1/8) (* 1/2 eps)) x) (+ (* (/ (* eps eps) (* x x)) 1/8) (* 1/2 eps)) (/ (* eps eps) (* x x)) (* eps eps) 1/8 (* 1/2 eps) 1/2)
4.0ms
eps
@inf
((/ (- (* x x) (- (* x x) eps)) (+ x (sqrt (- (* x x) eps)))) (- (* x x) (- (* x x) eps)) (* x x) x (- (* x x) eps) eps (+ x (sqrt (- (* x x) eps))) (sqrt (- (* x x) eps)) (- x (sqrt (- (* x x) eps))) (neg (sqrt (neg eps))) (sqrt (neg eps)) (neg eps) (- x (sqrt (- (* x x) eps))) (sqrt (- (* x x) eps)) (- (* x x) eps) (- x (sqrt (- (* x x) eps))) (* (neg eps) (- (/ (neg x) eps) (sqrt (/ -1 eps)))) (- (/ (neg x) eps) (sqrt (/ -1 eps))) (/ (neg x) eps) (neg x) (sqrt (/ -1 eps)) (/ -1 eps) -1 (- x (sqrt (- (* x x) eps))) (/ (+ (* (/ (* eps eps) (* x x)) 1/8) (* 1/2 eps)) x) (+ (* (/ (* eps eps) (* x x)) 1/8) (* 1/2 eps)) (/ (* eps eps) (* x x)) (* eps eps) 1/8 (* 1/2 eps) 1/2)
4.0ms
eps
@-inf
((/ (- (* x x) (- (* x x) eps)) (+ x (sqrt (- (* x x) eps)))) (- (* x x) (- (* x x) eps)) (* x x) x (- (* x x) eps) eps (+ x (sqrt (- (* x x) eps))) (sqrt (- (* x x) eps)) (- x (sqrt (- (* x x) eps))) (neg (sqrt (neg eps))) (sqrt (neg eps)) (neg eps) (- x (sqrt (- (* x x) eps))) (sqrt (- (* x x) eps)) (- (* x x) eps) (- x (sqrt (- (* x x) eps))) (* (neg eps) (- (/ (neg x) eps) (sqrt (/ -1 eps)))) (- (/ (neg x) eps) (sqrt (/ -1 eps))) (/ (neg x) eps) (neg x) (sqrt (/ -1 eps)) (/ -1 eps) -1 (- x (sqrt (- (* x x) eps))) (/ (+ (* (/ (* eps eps) (* x x)) 1/8) (* 1/2 eps)) x) (+ (* (/ (* eps eps) (* x x)) 1/8) (* 1/2 eps)) (/ (* eps eps) (* x x)) (* eps eps) 1/8 (* 1/2 eps) 1/2)

rewrite199.0ms (6.8%)

Memory
3.0MiB live, 180.6MiB allocated; 49ms collecting garbage
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
06784289
07153963
139003501
088883401
Stop Event
1×iter-limit
1×node-limit
1×iter-limit
Counts
153 → 364
Calls
Call 1
Inputs
(/.f64 (-.f64 (*.f64 x x) (-.f64 (*.f64 x x) eps)) (+.f64 x (sqrt.f64 (-.f64 (*.f64 x x) eps))))
(-.f64 (*.f64 x x) (-.f64 (*.f64 x x) eps))
(*.f64 x x)
x
(-.f64 (*.f64 x x) eps)
eps
(+.f64 x (sqrt.f64 (-.f64 (*.f64 x x) eps)))
(sqrt.f64 (-.f64 (*.f64 x x) eps))
#s(approx (- x (sqrt (- (* x x) eps))) (neg.f64 (sqrt.f64 (neg.f64 eps))))
(neg.f64 (sqrt.f64 (neg.f64 eps)))
(sqrt.f64 (neg.f64 eps))
(neg.f64 eps)
(-.f64 x (sqrt.f64 #s(approx (- (* x x) eps) (neg.f64 eps))))
(sqrt.f64 #s(approx (- (* x x) eps) (neg.f64 eps)))
#s(approx (- (* x x) eps) (neg.f64 eps))
#s(approx (- x (sqrt (- (* x x) eps))) (*.f64 (neg.f64 eps) (-.f64 (/.f64 (neg.f64 x) eps) (sqrt.f64 (/.f64 #s(literal -1 binary64) eps)))))
(*.f64 (neg.f64 eps) (-.f64 (/.f64 (neg.f64 x) eps) (sqrt.f64 (/.f64 #s(literal -1 binary64) eps))))
(-.f64 (/.f64 (neg.f64 x) eps) (sqrt.f64 (/.f64 #s(literal -1 binary64) eps)))
(/.f64 (neg.f64 x) eps)
(neg.f64 x)
(sqrt.f64 (/.f64 #s(literal -1 binary64) eps))
(/.f64 #s(literal -1 binary64) eps)
#s(literal -1 binary64)
#s(approx (- x (sqrt (- (* x x) eps))) (/.f64 (fma.f64 (/.f64 (*.f64 eps eps) (*.f64 x x)) #s(literal 1/8 binary64) (*.f64 #s(literal 1/2 binary64) eps)) x))
(/.f64 (fma.f64 (/.f64 (*.f64 eps eps) (*.f64 x x)) #s(literal 1/8 binary64) (*.f64 #s(literal 1/2 binary64) eps)) x)
(fma.f64 (/.f64 (*.f64 eps eps) (*.f64 x x)) #s(literal 1/8 binary64) (*.f64 #s(literal 1/2 binary64) eps))
(/.f64 (*.f64 eps eps) (*.f64 x x))
(*.f64 eps eps)
#s(literal 1/8 binary64)
(*.f64 #s(literal 1/2 binary64) eps)
#s(literal 1/2 binary64)
#s(approx (/ (- (* x x) (- (* x x) eps)) (+ x (sqrt (- (* x x) eps)))) #s(hole binary64 (/ eps (sqrt (neg eps)))))
#s(approx (/ (- (* x x) (- (* x x) eps)) (+ x (sqrt (- (* x x) eps)))) #s(hole binary64 (+ (* -1 (/ (* eps x) (pow (sqrt (neg eps)) 2))) (/ eps (sqrt (neg eps))))))
#s(approx (/ (- (* x x) (- (* x x) eps)) (+ x (sqrt (- (* x x) eps)))) #s(hole binary64 (+ (* x (- (* -1 (* x (+ (* -1 (/ eps (pow (sqrt (neg eps)) 3))) (* 1/2 (/ eps (pow (sqrt (neg eps)) 3)))))) (/ eps (pow (sqrt (neg eps)) 2)))) (/ eps (sqrt (neg eps))))))
#s(approx (/ (- (* x x) (- (* x x) eps)) (+ x (sqrt (- (* x x) eps)))) #s(hole binary64 (+ (* x (- (* x (- (* -1 (* x (+ (* -1 (/ (+ (* -1 (/ eps (pow (sqrt (neg eps)) 3))) (* 1/2 (/ eps (pow (sqrt (neg eps)) 3)))) (sqrt (neg eps)))) (* -1/2 (/ eps (pow (sqrt (neg eps)) 4)))))) (+ (* -1 (/ eps (pow (sqrt (neg eps)) 3))) (* 1/2 (/ eps (pow (sqrt (neg eps)) 3)))))) (/ eps (pow (sqrt (neg eps)) 2)))) (/ eps (sqrt (neg eps))))))
#s(approx (- (* x x) (- (* x x) eps)) #s(hole binary64 eps))
#s(approx (* x x) #s(hole binary64 (pow x 2)))
#s(approx x #s(hole binary64 x))
#s(approx (- (* x x) eps) #s(hole binary64 (* -1 eps)))
#s(approx (- (* x x) eps) #s(hole binary64 (- (pow x 2) eps)))
#s(approx (+ x (sqrt (- (* x x) eps))) #s(hole binary64 (sqrt (neg eps))))
#s(approx (+ x (sqrt (- (* x x) eps))) #s(hole binary64 (+ x (sqrt (neg eps)))))
#s(approx (+ x (sqrt (- (* x x) eps))) #s(hole binary64 (+ (sqrt (neg eps)) (* x (+ 1 (* 1/2 (/ x (sqrt (neg eps)))))))))
#s(approx (+ x (sqrt (- (* x x) eps))) #s(hole binary64 (+ (sqrt (neg eps)) (* x (+ 1 (* x (+ (* -1/8 (/ (pow x 2) (pow (sqrt (neg eps)) 3))) (* 1/2 (/ 1 (sqrt (neg eps)))))))))))
#s(approx (sqrt (- (* x x) eps)) #s(hole binary64 (+ (sqrt (neg eps)) (* 1/2 (/ (pow x 2) (sqrt (neg eps)))))))
#s(approx (sqrt (- (* x x) eps)) #s(hole binary64 (+ (sqrt (neg eps)) (* (pow x 2) (+ (* -1/8 (/ (pow x 2) (pow (sqrt (neg eps)) 3))) (* 1/2 (/ 1 (sqrt (neg eps)))))))))
#s(approx (sqrt (- (* x x) eps)) #s(hole binary64 (+ (sqrt (neg eps)) (* (pow x 2) (+ (* (pow x 2) (- (* 1/16 (/ (pow x 2) (pow (sqrt (neg eps)) 5))) (* 1/8 (/ 1 (pow (sqrt (neg eps)) 3))))) (* 1/2 (/ 1 (sqrt (neg eps)))))))))
#s(approx (- x (sqrt (- (* x x) eps))) #s(hole binary64 (* -1 (sqrt (neg eps)))))
#s(approx (- x (sqrt (- (* x x) eps))) #s(hole binary64 (- x (sqrt (neg eps)))))
#s(approx (- x (sqrt (- (* x x) eps))) #s(hole binary64 (- (* x (+ 1 (* -1/2 (/ x (sqrt (neg eps)))))) (sqrt (neg eps)))))
#s(approx (- x (sqrt (- (* x x) eps))) #s(hole binary64 (- (* x (+ 1 (* x (- (* 1/8 (/ (pow x 2) (pow (sqrt (neg eps)) 3))) (* 1/2 (/ 1 (sqrt (neg eps)))))))) (sqrt (neg eps)))))
#s(approx (* (neg eps) (- (/ (neg x) eps) (sqrt (/ -1 eps)))) #s(hole binary64 (* eps (sqrt (/ -1 eps)))))
#s(approx (* (neg eps) (- (/ (neg x) eps) (sqrt (/ -1 eps)))) #s(hole binary64 (+ x (* eps (sqrt (/ -1 eps))))))
#s(approx (- (/ (neg x) eps) (sqrt (/ -1 eps))) #s(hole binary64 (* -1 (sqrt (/ -1 eps)))))
#s(approx (- (/ (neg x) eps) (sqrt (/ -1 eps))) #s(hole binary64 (- (* -1 (/ x eps)) (sqrt (/ -1 eps)))))
#s(approx (/ (neg x) eps) #s(hole binary64 (* -1 (/ x eps))))
#s(approx (neg x) #s(hole binary64 (* -1 x)))
#s(approx (/ (+ (* (/ (* eps eps) (* x x)) 1/8) (* 1/2 eps)) x) #s(hole binary64 (* 1/8 (/ (pow eps 2) (pow x 3)))))
#s(approx (/ (+ (* (/ (* eps eps) (* x x)) 1/8) (* 1/2 eps)) x) #s(hole binary64 (/ (+ (* 1/8 (pow eps 2)) (* 1/2 (* eps (pow x 2)))) (pow x 3))))
#s(approx (+ (* (/ (* eps eps) (* x x)) 1/8) (* 1/2 eps)) #s(hole binary64 (* 1/8 (/ (pow eps 2) (pow x 2)))))
#s(approx (+ (* (/ (* eps eps) (* x x)) 1/8) (* 1/2 eps)) #s(hole binary64 (/ (+ (* 1/8 (pow eps 2)) (* 1/2 (* eps (pow x 2)))) (pow x 2))))
#s(approx (/ (* eps eps) (* x x)) #s(hole binary64 (/ (pow eps 2) (pow x 2))))
#s(approx (/ (- (* x x) (- (* x x) eps)) (+ x (sqrt (- (* x x) eps)))) #s(hole binary64 (* 1/2 (/ eps x))))
#s(approx (/ (- (* x x) (- (* x x) eps)) (+ x (sqrt (- (* x x) eps)))) #s(hole binary64 (/ (+ (* 1/8 (/ (pow eps 2) (pow x 2))) (* 1/2 eps)) x)))
#s(approx (/ (- (* x x) (- (* x x) eps)) (+ x (sqrt (- (* x x) eps)))) #s(hole binary64 (/ (- (+ (* 1/16 (/ (pow eps 3) (pow x 4))) (* 1/2 eps)) (* -1/8 (/ (pow eps 2) (pow x 2)))) x)))
#s(approx (/ (- (* x x) (- (* x x) eps)) (+ x (sqrt (- (* x x) eps)))) #s(hole binary64 (/ (- (+ (* -1 (/ (+ (* -1/32 (pow eps 4)) (* -1/128 (pow eps 4))) (pow x 6))) (* 1/2 eps)) (+ (* -1/8 (/ (pow eps 2) (pow x 2))) (* -1/16 (/ (pow eps 3) (pow x 4))))) x)))
#s(approx (- (* x x) eps) #s(hole binary64 (* (pow x 2) (+ 1 (* -1 (/ eps (pow x 2)))))))
#s(approx (+ x (sqrt (- (* x x) eps))) #s(hole binary64 (* 2 x)))
#s(approx (+ x (sqrt (- (* x x) eps))) #s(hole binary64 (* x (+ 2 (* -1/2 (/ eps (pow x 2)))))))
#s(approx (+ x (sqrt (- (* x x) eps))) #s(hole binary64 (* x (+ 2 (+ (* -1/2 (/ eps (pow x 2))) (* -1/8 (/ (pow eps 2) (pow x 4))))))))
#s(approx (+ x (sqrt (- (* x x) eps))) #s(hole binary64 (* x (+ 2 (+ (* -1/2 (/ eps (pow x 2))) (+ (* -1/8 (/ (pow eps 2) (pow x 4))) (* -1/16 (/ (pow eps 3) (pow x 6)))))))))
#s(approx (sqrt (- (* x x) eps)) #s(hole binary64 (* x (+ 1 (* -1/2 (/ eps (pow x 2)))))))
#s(approx (sqrt (- (* x x) eps)) #s(hole binary64 (* x (+ 1 (+ (* -1/2 (/ eps (pow x 2))) (* -1/8 (/ (pow eps 2) (pow x 4))))))))
#s(approx (sqrt (- (* x x) eps)) #s(hole binary64 (* x (+ 1 (+ (* -1/2 (/ eps (pow x 2))) (+ (* -1/8 (/ (pow eps 2) (pow x 4))) (* -1/16 (/ (pow eps 3) (pow x 6)))))))))
#s(approx (- x (sqrt (- (* x x) eps))) #s(hole binary64 (/ (- (* 1/8 (/ (pow eps 2) (pow x 2))) (* -1/2 eps)) x)))
#s(approx (- x (sqrt (- (* x x) eps))) #s(hole binary64 (/ (- (* 1/16 (/ (pow eps 3) (pow x 4))) (+ (* -1/2 eps) (* -1/8 (/ (pow eps 2) (pow x 2))))) x)))
#s(approx (- x (sqrt (- (* x x) eps))) #s(hole binary64 (/ (- (* 1/2 (/ (+ (* 1/64 (pow eps 4)) (* 1/16 (pow eps 4))) (pow x 6))) (+ (* -1/2 eps) (+ (* -1/8 (/ (pow eps 2) (pow x 2))) (* -1/16 (/ (pow eps 3) (pow x 4)))))) x)))
#s(approx (* (neg eps) (- (/ (neg x) eps) (sqrt (/ -1 eps)))) #s(hole binary64 (* x (+ 1 (/ (* eps (sqrt (/ -1 eps))) x)))))
#s(approx (- (/ (neg x) eps) (sqrt (/ -1 eps))) #s(hole binary64 (* x (- (* -1 (/ (sqrt (/ -1 eps)) x)) (/ 1 eps)))))
#s(approx (+ (* (/ (* eps eps) (* x x)) 1/8) (* 1/2 eps)) #s(hole binary64 (* 1/2 eps)))
#s(approx (+ (* (/ (* eps eps) (* x x)) 1/8) (* 1/2 eps)) #s(hole binary64 (+ (* 1/8 (/ (pow eps 2) (pow x 2))) (* 1/2 eps))))
#s(approx (/ (- (* x x) (- (* x x) eps)) (+ x (sqrt (- (* x x) eps)))) #s(hole binary64 (* -1 (* x (- (* 1/2 (/ eps (pow x 2))) 2)))))
#s(approx (/ (- (* x x) (- (* x x) eps)) (+ x (sqrt (- (* x x) eps)))) #s(hole binary64 (* -1 (* x (- (* -1 (/ (+ (* -1/4 (pow eps 2)) (* 1/8 (pow eps 2))) (pow x 4))) (+ 2 (* -1/2 (/ eps (pow x 2)))))))))
#s(approx (/ (- (* x x) (- (* x x) eps)) (+ x (sqrt (- (* x x) eps)))) #s(hole binary64 (* -1 (* x (- (* -1 (/ (+ (* -2 (/ (+ (* 1/64 (pow eps 4)) (* 1/16 (pow eps 4))) eps)) (+ (* -1/4 (* eps (+ (* -1/4 (pow eps 2)) (* 1/8 (pow eps 2))))) (* 1/16 (pow eps 3)))) (pow x 6))) (+ 2 (+ (* -1/2 (/ eps (pow x 2))) (+ (* -1/4 (/ (pow eps 2) (pow x 4))) (* 1/8 (/ (pow eps 2) (pow x 4)))))))))))
#s(approx (+ x (sqrt (- (* x x) eps))) #s(hole binary64 (* -1 (/ (+ (* -1/2 eps) (* -1/8 (/ (pow eps 2) (pow x 2)))) x))))
#s(approx (+ x (sqrt (- (* x x) eps))) #s(hole binary64 (* -1 (/ (+ (* -1/2 eps) (+ (* -1/8 (/ (pow eps 2) (pow x 2))) (* -1/16 (/ (pow eps 3) (pow x 4))))) x))))
#s(approx (+ x (sqrt (- (* x x) eps))) #s(hole binary64 (* -1 (/ (+ (* -1/2 eps) (+ (* -1/2 (/ (+ (* 1/64 (pow eps 4)) (* 1/16 (pow eps 4))) (pow x 6))) (+ (* -1/8 (/ (pow eps 2) (pow x 2))) (* -1/16 (/ (pow eps 3) (pow x 4)))))) x))))
#s(approx (sqrt (- (* x x) eps)) #s(hole binary64 (* -1 (* x (+ 1 (* -1/2 (/ eps (pow x 2))))))))
#s(approx (sqrt (- (* x x) eps)) #s(hole binary64 (* -1 (* x (+ 1 (+ (* -1/2 (/ eps (pow x 2))) (* -1/8 (/ (pow eps 2) (pow x 4)))))))))
#s(approx (sqrt (- (* x x) eps)) #s(hole binary64 (* -1 (* x (+ 1 (+ (* -1/2 (/ eps (pow x 2))) (+ (* -1/8 (/ (pow eps 2) (pow x 4))) (* -1/16 (/ (pow eps 3) (pow x 6))))))))))
#s(approx (- x (sqrt (- (* x x) eps))) #s(hole binary64 (* -1 (* x (- (* 1/8 (/ (pow eps 2) (pow x 4))) (+ 2 (* -1/2 (/ eps (pow x 2)))))))))
#s(approx (- x (sqrt (- (* x x) eps))) #s(hole binary64 (* -1 (* x (- (* 1/16 (/ (pow eps 3) (pow x 6))) (+ 2 (+ (* -1/2 (/ eps (pow x 2))) (* -1/8 (/ (pow eps 2) (pow x 4))))))))))
#s(approx (* (neg eps) (- (/ (neg x) eps) (sqrt (/ -1 eps)))) #s(hole binary64 (* -1 (* x (- (* -1 (/ (* eps (sqrt (/ -1 eps))) x)) 1)))))
#s(approx (- (/ (neg x) eps) (sqrt (/ -1 eps))) #s(hole binary64 (* -1 (* x (+ (/ 1 eps) (/ (sqrt (/ -1 eps)) x))))))
#s(approx (/ (- (* x x) (- (* x x) eps)) (+ x (sqrt (- (* x x) eps)))) #s(hole binary64 (/ eps (+ x (sqrt (pow x 2))))))
#s(approx (/ (- (* x x) (- (* x x) eps)) (+ x (sqrt (- (* x x) eps)))) #s(hole binary64 (* eps (+ (* 1/2 (/ eps (* (sqrt (pow x 2)) (pow (+ x (sqrt (pow x 2))) 2)))) (/ 1 (+ x (sqrt (pow x 2))))))))
#s(approx (/ (- (* x x) (- (* x x) eps)) (+ x (sqrt (- (* x x) eps)))) #s(hole binary64 (* eps (+ (* eps (+ (* eps (+ (* 1/4 (/ 1 (* (pow (sqrt (pow x 2)) 2) (pow (+ x (sqrt (pow x 2))) 3)))) (* 1/8 (/ 1 (* (pow (sqrt (pow x 2)) 3) (pow (+ x (sqrt (pow x 2))) 2)))))) (* 1/2 (/ 1 (* (sqrt (pow x 2)) (pow (+ x (sqrt (pow x 2))) 2)))))) (/ 1 (+ x (sqrt (pow x 2))))))))
#s(approx (/ (- (* x x) (- (* x x) eps)) (+ x (sqrt (- (* x x) eps)))) #s(hole binary64 (* eps (+ (* eps (+ (* eps (+ (* 1/8 (/ 1 (* (pow (sqrt (pow x 2)) 3) (pow (+ x (sqrt (pow x 2))) 2)))) (+ (* 1/4 (/ 1 (* (pow (sqrt (pow x 2)) 2) (pow (+ x (sqrt (pow x 2))) 3)))) (* eps (- (+ (* 1/16 (/ 1 (* (pow (sqrt (pow x 2)) 4) (pow (+ x (sqrt (pow x 2))) 3)))) (* 1/16 (/ 1 (* (pow (sqrt (pow x 2)) 5) (pow (+ x (sqrt (pow x 2))) 2))))) (* -1/2 (/ (+ (* 1/4 (/ 1 (* (pow (sqrt (pow x 2)) 2) (pow (+ x (sqrt (pow x 2))) 3)))) (* 1/8 (/ 1 (* (pow (sqrt (pow x 2)) 3) (pow (+ x (sqrt (pow x 2))) 2))))) (* (sqrt (pow x 2)) (+ x (sqrt (pow x 2))))))))))) (* 1/2 (/ 1 (* (sqrt (pow x 2)) (pow (+ x (sqrt (pow x 2))) 2)))))) (/ 1 (+ x (sqrt (pow x 2))))))))
#s(approx (- (* x x) eps) #s(hole binary64 (+ (* -1 eps) (pow x 2))))
#s(approx (+ x (sqrt (- (* x x) eps))) #s(hole binary64 (+ x (sqrt (pow x 2)))))
#s(approx (+ x (sqrt (- (* x x) eps))) #s(hole binary64 (+ x (+ (sqrt (pow x 2)) (* -1/2 (/ eps (sqrt (pow x 2))))))))
#s(approx (+ x (sqrt (- (* x x) eps))) #s(hole binary64 (+ x (+ (sqrt (pow x 2)) (* eps (- (* -1/8 (/ eps (pow (sqrt (pow x 2)) 3))) (* 1/2 (/ 1 (sqrt (pow x 2))))))))))
#s(approx (+ x (sqrt (- (* x x) eps))) #s(hole binary64 (+ x (+ (sqrt (pow x 2)) (* eps (- (* eps (- (* -1/16 (/ eps (pow (sqrt (pow x 2)) 5))) (* 1/8 (/ 1 (pow (sqrt (pow x 2)) 3))))) (* 1/2 (/ 1 (sqrt (pow x 2))))))))))
#s(approx (sqrt (- (* x x) eps)) #s(hole binary64 (sqrt (pow x 2))))
#s(approx (sqrt (- (* x x) eps)) #s(hole binary64 (+ (sqrt (pow x 2)) (* -1/2 (/ eps (sqrt (pow x 2)))))))
#s(approx (sqrt (- (* x x) eps)) #s(hole binary64 (+ (sqrt (pow x 2)) (* eps (- (* -1/8 (/ eps (pow (sqrt (pow x 2)) 3))) (* 1/2 (/ 1 (sqrt (pow x 2)))))))))
#s(approx (sqrt (- (* x x) eps)) #s(hole binary64 (+ (sqrt (pow x 2)) (* eps (- (* eps (- (* -1/16 (/ eps (pow (sqrt (pow x 2)) 5))) (* 1/8 (/ 1 (pow (sqrt (pow x 2)) 3))))) (* 1/2 (/ 1 (sqrt (pow x 2)))))))))
#s(approx (- x (sqrt (- (* x x) eps))) #s(hole binary64 (- x (sqrt (pow x 2)))))
#s(approx (- x (sqrt (- (* x x) eps))) #s(hole binary64 (- (+ x (* 1/2 (/ eps (sqrt (pow x 2))))) (sqrt (pow x 2)))))
#s(approx (- x (sqrt (- (* x x) eps))) #s(hole binary64 (- (+ x (* eps (+ (* 1/8 (/ eps (pow (sqrt (pow x 2)) 3))) (* 1/2 (/ 1 (sqrt (pow x 2))))))) (sqrt (pow x 2)))))
#s(approx (- x (sqrt (- (* x x) eps))) #s(hole binary64 (- (+ x (* eps (+ (* eps (+ (* 1/16 (/ eps (pow (sqrt (pow x 2)) 5))) (* 1/8 (/ 1 (pow (sqrt (pow x 2)) 3))))) (* 1/2 (/ 1 (sqrt (pow x 2))))))) (sqrt (pow x 2)))))
#s(approx (neg (sqrt (neg eps))) #s(hole binary64 (* -1 (sqrt (* -1 eps)))))
#s(approx (sqrt (neg eps)) #s(hole binary64 (sqrt (* -1 eps))))
#s(approx (* (neg eps) (- (/ (neg x) eps) (sqrt (/ -1 eps)))) #s(hole binary64 (* -1 (- (* -1 x) (sqrt (* -1 eps))))))
#s(approx (- (/ (neg x) eps) (sqrt (/ -1 eps))) #s(hole binary64 (/ (- (* -1 x) (sqrt (* -1 eps))) eps)))
#s(approx (sqrt (/ -1 eps)) #s(hole binary64 (/ (sqrt (* -1 eps)) eps)))
#s(approx (/ -1 eps) #s(hole binary64 (/ -1 eps)))
#s(approx (/ (+ (* (/ (* eps eps) (* x x)) 1/8) (* 1/2 eps)) x) #s(hole binary64 (* eps (+ (* 1/8 (/ eps (pow x 3))) (* 1/2 (/ 1 x))))))
#s(approx (+ (* (/ (* eps eps) (* x x)) 1/8) (* 1/2 eps)) #s(hole binary64 (* eps (+ 1/2 (* 1/8 (/ eps (pow x 2)))))))
#s(approx (* eps eps) #s(hole binary64 (pow eps 2)))
#s(approx (/ (- (* x x) (- (* x x) eps)) (+ x (sqrt (- (* x x) eps)))) #s(hole binary64 (/ 1 (sqrt (/ -1 eps)))))
#s(approx (/ (- (* x x) (- (* x x) eps)) (+ x (sqrt (- (* x x) eps)))) #s(hole binary64 (+ (* -1 (/ x (* eps (pow (sqrt (/ -1 eps)) 2)))) (/ 1 (sqrt (/ -1 eps))))))
#s(approx (/ (- (* x x) (- (* x x) eps)) (+ x (sqrt (- (* x x) eps)))) #s(hole binary64 (- (+ (* -1 (/ (+ (* -1 (/ (pow x 2) (pow (sqrt (/ -1 eps)) 3))) (* 1/2 (/ (pow x 2) (pow (sqrt (/ -1 eps)) 3)))) (pow eps 2))) (/ 1 (sqrt (/ -1 eps)))) (/ x (* eps (pow (sqrt (/ -1 eps)) 2))))))
#s(approx (/ (- (* x x) (- (* x x) eps)) (+ x (sqrt (- (* x x) eps)))) #s(hole binary64 (- (+ (* -1 (/ (+ (* -1 (/ (* x (+ (* -1 (/ (pow x 2) (pow (sqrt (/ -1 eps)) 3))) (* 1/2 (/ (pow x 2) (pow (sqrt (/ -1 eps)) 3))))) (sqrt (/ -1 eps)))) (* -1/2 (/ (pow x 3) (pow (sqrt (/ -1 eps)) 4)))) (pow eps 3))) (/ 1 (sqrt (/ -1 eps)))) (+ (* -1 (/ (pow x 2) (* (pow eps 2) (pow (sqrt (/ -1 eps)) 3)))) (+ (* 1/2 (/ (pow x 2) (* (pow eps 2) (pow (sqrt (/ -1 eps)) 3)))) (/ x (* eps (pow (sqrt (/ -1 eps)) 2))))))))
#s(approx (- (* x x) eps) #s(hole binary64 (* eps (- (/ (pow x 2) eps) 1))))
#s(approx (+ x (sqrt (- (* x x) eps))) #s(hole binary64 (* eps (+ (sqrt (/ -1 eps)) (/ x eps)))))
#s(approx (+ x (sqrt (- (* x x) eps))) #s(hole binary64 (* eps (+ (sqrt (/ -1 eps)) (+ (* 1/2 (/ (pow x 2) (* (pow eps 2) (sqrt (/ -1 eps))))) (/ x eps))))))
#s(approx (+ x (sqrt (- (* x x) eps))) #s(hole binary64 (* eps (+ (sqrt (/ -1 eps)) (+ (* -1/8 (/ (pow x 4) (* (pow eps 4) (pow (sqrt (/ -1 eps)) 3)))) (+ (* 1/2 (/ (pow x 2) (* (pow eps 2) (sqrt (/ -1 eps))))) (/ x eps)))))))
#s(approx (sqrt (- (* x x) eps)) #s(hole binary64 (* eps (+ (sqrt (/ -1 eps)) (* 1/2 (/ (pow x 2) (* (pow eps 2) (sqrt (/ -1 eps)))))))))
#s(approx (sqrt (- (* x x) eps)) #s(hole binary64 (* eps (+ (sqrt (/ -1 eps)) (+ (* -1/8 (/ (pow x 4) (* (pow eps 4) (pow (sqrt (/ -1 eps)) 3)))) (* 1/2 (/ (pow x 2) (* (pow eps 2) (sqrt (/ -1 eps))))))))))
#s(approx (sqrt (- (* x x) eps)) #s(hole binary64 (* eps (+ (sqrt (/ -1 eps)) (+ (* -1/8 (/ (pow x 4) (* (pow eps 4) (pow (sqrt (/ -1 eps)) 3)))) (+ (* 1/16 (/ (pow x 6) (* (pow eps 6) (pow (sqrt (/ -1 eps)) 5)))) (* 1/2 (/ (pow x 2) (* (pow eps 2) (sqrt (/ -1 eps)))))))))))
#s(approx (- x (sqrt (- (* x x) eps))) #s(hole binary64 (* -1 (* eps (sqrt (/ -1 eps))))))
#s(approx (- x (sqrt (- (* x x) eps))) #s(hole binary64 (* eps (- (/ x eps) (sqrt (/ -1 eps))))))
#s(approx (- x (sqrt (- (* x x) eps))) #s(hole binary64 (* eps (- (+ (* -1/2 (/ (pow x 2) (* (pow eps 2) (sqrt (/ -1 eps))))) (/ x eps)) (sqrt (/ -1 eps))))))
#s(approx (- x (sqrt (- (* x x) eps))) #s(hole binary64 (* eps (- (+ (* 1/8 (/ (pow x 4) (* (pow eps 4) (pow (sqrt (/ -1 eps)) 3)))) (/ x eps)) (+ (sqrt (/ -1 eps)) (* 1/2 (/ (pow x 2) (* (pow eps 2) (sqrt (/ -1 eps))))))))))
#s(approx (sqrt (/ -1 eps)) #s(hole binary64 (sqrt (/ -1 eps))))
#s(approx (/ (+ (* (/ (* eps eps) (* x x)) 1/8) (* 1/2 eps)) x) #s(hole binary64 (* (pow eps 2) (+ (* 1/2 (/ 1 (* eps x))) (* 1/8 (/ 1 (pow x 3)))))))
#s(approx (+ (* (/ (* eps eps) (* x x)) 1/8) (* 1/2 eps)) #s(hole binary64 (* (pow eps 2) (+ (* 1/2 (/ 1 eps)) (* 1/8 (/ 1 (pow x 2)))))))
#s(approx (/ (- (* x x) (- (* x x) eps)) (+ x (sqrt (- (* x x) eps)))) #s(hole binary64 (/ -1 (sqrt (/ -1 eps)))))
#s(approx (/ (- (* x x) (- (* x x) eps)) (+ x (sqrt (- (* x x) eps)))) #s(hole binary64 (- (* -1 (/ x (* eps (pow (sqrt (/ -1 eps)) 2)))) (/ 1 (sqrt (/ -1 eps))))))
#s(approx (/ (- (* x x) (- (* x x) eps)) (+ x (sqrt (- (* x x) eps)))) #s(hole binary64 (- (* -1 (/ (- (+ (* -1/2 (/ (pow x 2) (* eps (pow (sqrt (/ -1 eps)) 3)))) (/ (pow x 2) (* eps (pow (sqrt (/ -1 eps)) 3)))) (* -1 (/ x (pow (sqrt (/ -1 eps)) 2)))) eps)) (/ 1 (sqrt (/ -1 eps))))))
#s(approx (/ (- (* x x) (- (* x x) eps)) (+ x (sqrt (- (* x x) eps)))) #s(hole binary64 (- (* -1 (/ (- (* -1 (/ (- (+ (* -1 (/ (* x (+ (* -1/2 (/ (pow x 2) (pow (sqrt (/ -1 eps)) 3))) (/ (pow x 2) (pow (sqrt (/ -1 eps)) 3)))) (* eps (sqrt (/ -1 eps))))) (* 1/2 (/ (pow x 3) (* eps (pow (sqrt (/ -1 eps)) 4))))) (+ (* -1/2 (/ (pow x 2) (pow (sqrt (/ -1 eps)) 3))) (/ (pow x 2) (pow (sqrt (/ -1 eps)) 3)))) eps)) (* -1 (/ x (pow (sqrt (/ -1 eps)) 2)))) eps)) (/ 1 (sqrt (/ -1 eps))))))
#s(approx (- (* x x) eps) #s(hole binary64 (* -1 (* eps (+ 1 (* -1 (/ (pow x 2) eps)))))))
#s(approx (+ x (sqrt (- (* x x) eps))) #s(hole binary64 (* -1 (* eps (+ (sqrt (/ -1 eps)) (* -1 (/ x eps)))))))
#s(approx (+ x (sqrt (- (* x x) eps))) #s(hole binary64 (* -1 (* eps (+ (sqrt (/ -1 eps)) (* -1 (/ (+ x (* -1/2 (/ (pow x 2) (* eps (sqrt (/ -1 eps)))))) eps)))))))
#s(approx (+ x (sqrt (- (* x x) eps))) #s(hole binary64 (* -1 (* eps (+ (sqrt (/ -1 eps)) (* -1 (/ (+ x (* -1 (/ (+ (* -1/8 (/ (pow x 4) (* (pow eps 2) (pow (sqrt (/ -1 eps)) 3)))) (* 1/2 (/ (pow x 2) (sqrt (/ -1 eps))))) eps))) eps)))))))
#s(approx (sqrt (- (* x x) eps)) #s(hole binary64 (* -1 (* eps (+ (sqrt (/ -1 eps)) (* 1/2 (/ (pow x 2) (* (pow eps 2) (sqrt (/ -1 eps))))))))))
#s(approx (sqrt (- (* x x) eps)) #s(hole binary64 (* -1 (* eps (+ (sqrt (/ -1 eps)) (+ (* -1/8 (/ (pow x 4) (* (pow eps 4) (pow (sqrt (/ -1 eps)) 3)))) (* 1/2 (/ (pow x 2) (* (pow eps 2) (sqrt (/ -1 eps)))))))))))
#s(approx (sqrt (- (* x x) eps)) #s(hole binary64 (* -1 (* eps (+ (sqrt (/ -1 eps)) (+ (* -1/8 (/ (pow x 4) (* (pow eps 4) (pow (sqrt (/ -1 eps)) 3)))) (+ (* 1/16 (/ (pow x 6) (* (pow eps 6) (pow (sqrt (/ -1 eps)) 5)))) (* 1/2 (/ (pow x 2) (* (pow eps 2) (sqrt (/ -1 eps))))))))))))
#s(approx (- x (sqrt (- (* x x) eps))) #s(hole binary64 (* -1 (* eps (- (* -1 (/ x eps)) (sqrt (/ -1 eps)))))))
#s(approx (- x (sqrt (- (* x x) eps))) #s(hole binary64 (* -1 (* eps (- (* -1 (/ (+ x (* 1/2 (/ (pow x 2) (* eps (sqrt (/ -1 eps)))))) eps)) (sqrt (/ -1 eps)))))))
#s(approx (- x (sqrt (- (* x x) eps))) #s(hole binary64 (* -1 (* eps (- (* -1 (/ (+ x (* -1 (/ (- (* 1/8 (/ (pow x 4) (* (pow eps 2) (pow (sqrt (/ -1 eps)) 3)))) (* 1/2 (/ (pow x 2) (sqrt (/ -1 eps))))) eps))) eps)) (sqrt (/ -1 eps)))))))
#s(approx (* (neg eps) (- (/ (neg x) eps) (sqrt (/ -1 eps)))) #s(hole binary64 (* -1 (* eps (+ (* -1 (sqrt (/ -1 eps))) (* -1 (/ x eps)))))))
Outputs
(/.f64 (neg.f64 (neg.f64 (-.f64 (*.f64 x x) (-.f64 (*.f64 x x) eps)))) (neg.f64 (neg.f64 (+.f64 (sqrt.f64 (-.f64 (*.f64 x x) eps)) x))))
(/.f64 (neg.f64 (-.f64 (*.f64 (*.f64 x x) x) (*.f64 (sqrt.f64 (-.f64 (*.f64 x x) eps)) (-.f64 (*.f64 x x) eps)))) (neg.f64 (fma.f64 x x (+.f64 (-.f64 (*.f64 x x) eps) (*.f64 x (sqrt.f64 (-.f64 (*.f64 x x) eps)))))))
(/.f64 (-.f64 (*.f64 (*.f64 x x) x) (*.f64 (sqrt.f64 (-.f64 (*.f64 x x) eps)) (-.f64 (*.f64 x x) eps))) (fma.f64 x x (+.f64 (-.f64 (*.f64 x x) eps) (*.f64 x (sqrt.f64 (-.f64 (*.f64 x x) eps))))))
(/.f64 (neg.f64 (-.f64 (*.f64 x x) (-.f64 (*.f64 x x) eps))) (neg.f64 (+.f64 (sqrt.f64 (-.f64 (*.f64 x x) eps)) x)))
(/.f64 (-.f64 (*.f64 x x) (-.f64 (*.f64 x x) eps)) (+.f64 (sqrt.f64 (-.f64 (*.f64 x x) eps)) x))
(-.f64 (/.f64 (*.f64 x x) (+.f64 (sqrt.f64 (-.f64 (*.f64 x x) eps)) x)) (/.f64 (-.f64 (*.f64 x x) eps) (+.f64 (sqrt.f64 (-.f64 (*.f64 x x) eps)) x)))
(-.f64 x (sqrt.f64 (-.f64 (*.f64 x x) eps)))
(/.f64 (neg.f64 (-.f64 (*.f64 (*.f64 x x) (*.f64 x x)) (*.f64 (-.f64 (*.f64 x x) eps) (-.f64 (*.f64 x x) eps)))) (neg.f64 (fma.f64 x x (-.f64 (*.f64 x x) eps))))
(/.f64 (neg.f64 (-.f64 (*.f64 (*.f64 (*.f64 x x) (*.f64 x x)) (*.f64 x x)) (pow.f64 (-.f64 (*.f64 x x) eps) #s(literal 3 binary64)))) (neg.f64 (fma.f64 (*.f64 x x) (*.f64 x x) (fma.f64 (-.f64 (*.f64 x x) eps) (-.f64 (*.f64 x x) eps) (*.f64 (*.f64 x x) (-.f64 (*.f64 x x) eps))))))
(/.f64 (-.f64 (*.f64 (*.f64 x x) (*.f64 x x)) (*.f64 (-.f64 (*.f64 x x) eps) (-.f64 (*.f64 x x) eps))) (fma.f64 x x (-.f64 (*.f64 x x) eps)))
(/.f64 (-.f64 (*.f64 (*.f64 (*.f64 x x) (*.f64 x x)) (*.f64 x x)) (pow.f64 (-.f64 (*.f64 x x) eps) #s(literal 3 binary64))) (fma.f64 (*.f64 x x) (*.f64 x x) (fma.f64 (-.f64 (*.f64 x x) eps) (-.f64 (*.f64 x x) eps) (*.f64 (*.f64 x x) (-.f64 (*.f64 x x) eps)))))
(-.f64 (*.f64 x x) (-.f64 (*.f64 x x) eps))
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#s(approx (sqrt (- (* x x) eps)) (*.f64 (neg.f64 eps) (+.f64 (fma.f64 (/.f64 (*.f64 (*.f64 x x) (*.f64 x x)) (*.f64 (/.f64 #s(literal 1 binary64) (*.f64 (sqrt.f64 (neg.f64 eps)) (neg.f64 eps))) (*.f64 (*.f64 eps eps) (*.f64 eps eps)))) #s(literal -1/8 binary64) (/.f64 (*.f64 #s(literal 1/2 binary64) (*.f64 x x)) (*.f64 (*.f64 eps eps) (sqrt.f64 (/.f64 #s(literal -1 binary64) eps))))) (sqrt.f64 (/.f64 #s(literal -1 binary64) eps)))))
#s(approx (sqrt (- (* x x) eps)) (*.f64 (neg.f64 eps) (+.f64 (fma.f64 (/.f64 (*.f64 (*.f64 x x) (*.f64 x x)) (*.f64 (/.f64 #s(literal 1 binary64) (*.f64 (sqrt.f64 (neg.f64 eps)) (neg.f64 eps))) (*.f64 (*.f64 eps eps) (*.f64 eps eps)))) #s(literal -1/8 binary64) (fma.f64 (/.f64 (exp.f64 (-.f64 (*.f64 (log.f64 x) #s(literal 6 binary64)) (*.f64 (log.f64 eps) #s(literal 6 binary64)))) (pow.f64 (/.f64 #s(literal -1 binary64) eps) #s(literal 5/2 binary64))) #s(literal 1/16 binary64) (/.f64 (*.f64 #s(literal 1/2 binary64) (*.f64 x x)) (*.f64 (*.f64 eps eps) (sqrt.f64 (/.f64 #s(literal -1 binary64) eps)))))) (sqrt.f64 (/.f64 #s(literal -1 binary64) eps)))))
#s(approx (- x (sqrt (- (* x x) eps))) (*.f64 (-.f64 (/.f64 (neg.f64 x) eps) (sqrt.f64 (/.f64 #s(literal -1 binary64) eps))) (neg.f64 eps)))
#s(approx (- x (sqrt (- (* x x) eps))) (*.f64 (neg.f64 eps) (-.f64 (neg.f64 (/.f64 (fma.f64 (/.f64 (*.f64 x x) (*.f64 (sqrt.f64 (/.f64 #s(literal -1 binary64) eps)) eps)) #s(literal 1/2 binary64) x) eps)) (sqrt.f64 (/.f64 #s(literal -1 binary64) eps)))))
#s(approx (- x (sqrt (- (* x x) eps))) (*.f64 (neg.f64 eps) (-.f64 (neg.f64 (/.f64 (+.f64 (neg.f64 (/.f64 (fma.f64 (/.f64 (*.f64 (*.f64 x x) (*.f64 x x)) (*.f64 (/.f64 #s(literal 1 binary64) (*.f64 (sqrt.f64 (neg.f64 eps)) (neg.f64 eps))) (*.f64 eps eps))) #s(literal 1/8 binary64) (*.f64 #s(literal -1/2 binary64) (/.f64 (*.f64 x x) (sqrt.f64 (/.f64 #s(literal -1 binary64) eps))))) eps)) x) eps)) (sqrt.f64 (/.f64 #s(literal -1 binary64) eps)))))
#s(approx (* (neg eps) (- (/ (neg x) eps) (sqrt (/ -1 eps)))) (*.f64 (neg.f64 eps) (+.f64 (/.f64 (neg.f64 x) eps) (neg.f64 (sqrt.f64 (/.f64 #s(literal -1 binary64) eps))))))

eval42.0ms (1.4%)

Memory
18.2MiB live, 62.7MiB allocated; 5ms collecting garbage
Compiler

Compiled 4 944 to 1 883 computations (61.9% saved)

prune14.0ms (0.5%)

Memory
-23.6MiB live, 22.7MiB allocated; 3ms collecting garbage
Pruning

15 alts after pruning (7 fresh and 8 done)

PrunedKeptTotal
New3837390
Fresh202
Picked325
Done066
Total38815403
Accuracy
100.0%
Counts
403 → 15
Alt Table
Click to see full alt table
StatusAccuracyProgram
▶99.5%
(/.f64 #s(approx (- (* x x) (- (* x x) eps)) eps) (+.f64 x (sqrt.f64 (-.f64 (*.f64 x x) eps))))
✓61.5%
(-.f64 x (sqrt.f64 (-.f64 (*.f64 x x) eps)))
✓61.5%
(-.f64 x (sqrt.f64 #s(approx (- (* x x) eps) (fma.f64 x x (neg.f64 eps)))))
✓61.5%
(-.f64 x (sqrt.f64 #s(approx (- (* x x) eps) (*.f64 (-.f64 (/.f64 (*.f64 x x) eps) #s(literal 1 binary64)) eps))))
✓57.1%
(-.f64 x (sqrt.f64 #s(approx (- (* x x) eps) (neg.f64 eps))))
▶58.7%
(-.f64 x (sqrt.f64 #s(approx (- (* x x) eps) (fabs.f64 eps))))
✓4.2%
(-.f64 x #s(approx (sqrt (- (* x x) eps)) (fabs.f64 x)))
28.2%
#s(approx (- x (sqrt (- (* x x) eps))) (/.f64 (-.f64 (fma.f64 #s(literal 1/2 binary64) eps (neg.f64 (/.f64 (*.f64 (*.f64 (*.f64 eps eps) (*.f64 eps eps)) #s(literal -5/128 binary64)) (*.f64 (*.f64 (*.f64 x x) (*.f64 x x)) (*.f64 x x))))) (fma.f64 #s(literal -1/16 binary64) (/.f64 (*.f64 (*.f64 eps eps) eps) (*.f64 (*.f64 x x) (*.f64 x x))) (/.f64 (*.f64 #s(literal -1/8 binary64) (*.f64 eps eps)) (*.f64 x x)))) x))
42.3%
#s(approx (- x (sqrt (- (* x x) eps))) (/.f64 #s(approx (+ (* (/ (* eps eps) (* x x)) 1/8) (* 1/2 eps)) (*.f64 (fma.f64 (/.f64 eps (*.f64 x x)) #s(literal 1/8 binary64) #s(literal 1/2 binary64)) eps)) x))
▶56.5%
#s(approx (- x (sqrt (- (* x x) eps))) (/.f64 eps (sqrt.f64 (neg.f64 eps))))
✓3.7%
#s(approx (- x (sqrt (- (* x x) eps))) (+.f64 x x))
✓44.7%
#s(approx (- x (sqrt (- (* x x) eps))) (*.f64 (/.f64 eps x) #s(literal 1/2 binary64)))
▶1.7%
#s(approx (- x (sqrt (- (* x x) eps))) (sqrt.f64 (neg.f64 eps)))
✓56.9%
#s(approx (- x (sqrt (- (* x x) eps))) (neg.f64 (sqrt.f64 (neg.f64 eps))))
▶56.9%
#s(approx (- x (sqrt (- (* x x) eps))) #s(approx (* (neg eps) (- (/ (neg x) eps) (sqrt (/ -1 eps)))) (fma.f64 (sqrt.f64 (/.f64 #s(literal -1 binary64) eps)) eps x)))
Compiler

Compiled 307 to 285 computations (7.2% saved)

series13.0ms (0.5%)

Memory
19.3MiB live, 19.3MiB allocated; 0ms collecting garbage
Counts
23 → 106
Calls
Call 1
Inputs
(/.f64 #s(approx (- (* x x) (- (* x x) eps)) eps) (+.f64 x (sqrt.f64 (-.f64 (*.f64 x x) eps))))
#s(approx (- (* x x) (- (* x x) eps)) eps)
eps
(+.f64 x (sqrt.f64 (-.f64 (*.f64 x x) eps)))
x
(sqrt.f64 (-.f64 (*.f64 x x) eps))
(-.f64 (*.f64 x x) eps)
(*.f64 x x)
#s(approx (- x (sqrt (- (* x x) eps))) (sqrt.f64 (neg.f64 eps)))
(sqrt.f64 (neg.f64 eps))
(neg.f64 eps)
(-.f64 x (sqrt.f64 #s(approx (- (* x x) eps) (fabs.f64 eps))))
(sqrt.f64 #s(approx (- (* x x) eps) (fabs.f64 eps)))
#s(approx (- (* x x) eps) (fabs.f64 eps))
(fabs.f64 eps)
#s(approx (- x (sqrt (- (* x x) eps))) (/.f64 eps (sqrt.f64 (neg.f64 eps))))
(/.f64 eps (sqrt.f64 (neg.f64 eps)))
#s(approx (- x (sqrt (- (* x x) eps))) #s(approx (* (neg eps) (- (/ (neg x) eps) (sqrt (/ -1 eps)))) (fma.f64 (sqrt.f64 (/.f64 #s(literal -1 binary64) eps)) eps x)))
#s(approx (* (neg eps) (- (/ (neg x) eps) (sqrt (/ -1 eps)))) (fma.f64 (sqrt.f64 (/.f64 #s(literal -1 binary64) eps)) eps x))
(fma.f64 (sqrt.f64 (/.f64 #s(literal -1 binary64) eps)) eps x)
(sqrt.f64 (/.f64 #s(literal -1 binary64) eps))
(/.f64 #s(literal -1 binary64) eps)
#s(literal -1 binary64)
Outputs
#s(approx (/ (- (* x x) (- (* x x) eps)) (+ x (sqrt (- (* x x) eps)))) #s(hole binary64 (/ eps (sqrt (neg eps)))))
#s(approx (/ (- (* x x) (- (* x x) eps)) (+ x (sqrt (- (* x x) eps)))) #s(hole binary64 (+ (* -1 (/ (* eps x) (pow (sqrt (neg eps)) 2))) (/ eps (sqrt (neg eps))))))
#s(approx (/ (- (* x x) (- (* x x) eps)) (+ x (sqrt (- (* x x) eps)))) #s(hole binary64 (+ (* x (- (* -1 (* x (+ (* -1 (/ eps (pow (sqrt (neg eps)) 3))) (* 1/2 (/ eps (pow (sqrt (neg eps)) 3)))))) (/ eps (pow (sqrt (neg eps)) 2)))) (/ eps (sqrt (neg eps))))))
#s(approx (/ (- (* x x) (- (* x x) eps)) (+ x (sqrt (- (* x x) eps)))) #s(hole binary64 (+ (* x (- (* x (- (* -1 (* x (+ (* -1 (/ (+ (* -1 (/ eps (pow (sqrt (neg eps)) 3))) (* 1/2 (/ eps (pow (sqrt (neg eps)) 3)))) (sqrt (neg eps)))) (* -1/2 (/ eps (pow (sqrt (neg eps)) 4)))))) (+ (* -1 (/ eps (pow (sqrt (neg eps)) 3))) (* 1/2 (/ eps (pow (sqrt (neg eps)) 3)))))) (/ eps (pow (sqrt (neg eps)) 2)))) (/ eps (sqrt (neg eps))))))
#s(approx (- (* x x) (- (* x x) eps)) #s(hole binary64 eps))
#s(approx (+ x (sqrt (- (* x x) eps))) #s(hole binary64 (sqrt (neg eps))))
#s(approx (+ x (sqrt (- (* x x) eps))) #s(hole binary64 (+ x (sqrt (neg eps)))))
#s(approx (+ x (sqrt (- (* x x) eps))) #s(hole binary64 (+ (sqrt (neg eps)) (* x (+ 1 (* 1/2 (/ x (sqrt (neg eps)))))))))
#s(approx (+ x (sqrt (- (* x x) eps))) #s(hole binary64 (+ (sqrt (neg eps)) (* x (+ 1 (* x (+ (* -1/8 (/ (pow x 2) (pow (sqrt (neg eps)) 3))) (* 1/2 (/ 1 (sqrt (neg eps)))))))))))
#s(approx x #s(hole binary64 x))
#s(approx (sqrt (- (* x x) eps)) #s(hole binary64 (+ (sqrt (neg eps)) (* 1/2 (/ (pow x 2) (sqrt (neg eps)))))))
#s(approx (sqrt (- (* x x) eps)) #s(hole binary64 (+ (sqrt (neg eps)) (* (pow x 2) (+ (* -1/8 (/ (pow x 2) (pow (sqrt (neg eps)) 3))) (* 1/2 (/ 1 (sqrt (neg eps)))))))))
#s(approx (sqrt (- (* x x) eps)) #s(hole binary64 (+ (sqrt (neg eps)) (* (pow x 2) (+ (* (pow x 2) (- (* 1/16 (/ (pow x 2) (pow (sqrt (neg eps)) 5))) (* 1/8 (/ 1 (pow (sqrt (neg eps)) 3))))) (* 1/2 (/ 1 (sqrt (neg eps)))))))))
#s(approx (- (* x x) eps) #s(hole binary64 (* -1 eps)))
#s(approx (- (* x x) eps) #s(hole binary64 (- (pow x 2) eps)))
#s(approx (* x x) #s(hole binary64 (pow x 2)))
#s(approx (- x (sqrt (- (* x x) eps))) #s(hole binary64 (* -1 (sqrt (neg eps)))))
#s(approx (- x (sqrt (- (* x x) eps))) #s(hole binary64 (- x (sqrt (neg eps)))))
#s(approx (- x (sqrt (- (* x x) eps))) #s(hole binary64 (- (* x (+ 1 (* -1/2 (/ x (sqrt (neg eps)))))) (sqrt (neg eps)))))
#s(approx (- x (sqrt (- (* x x) eps))) #s(hole binary64 (- (* x (+ 1 (* x (- (* 1/8 (/ (pow x 2) (pow (sqrt (neg eps)) 3))) (* 1/2 (/ 1 (sqrt (neg eps)))))))) (sqrt (neg eps)))))
#s(approx (* (neg eps) (- (/ (neg x) eps) (sqrt (/ -1 eps)))) #s(hole binary64 (* eps (sqrt (/ -1 eps)))))
#s(approx (* (neg eps) (- (/ (neg x) eps) (sqrt (/ -1 eps)))) #s(hole binary64 (+ x (* eps (sqrt (/ -1 eps))))))
#s(approx (/ (- (* x x) (- (* x x) eps)) (+ x (sqrt (- (* x x) eps)))) #s(hole binary64 (* 1/2 (/ eps x))))
#s(approx (/ (- (* x x) (- (* x x) eps)) (+ x (sqrt (- (* x x) eps)))) #s(hole binary64 (/ (+ (* 1/8 (/ (pow eps 2) (pow x 2))) (* 1/2 eps)) x)))
#s(approx (/ (- (* x x) (- (* x x) eps)) (+ x (sqrt (- (* x x) eps)))) #s(hole binary64 (/ (- (+ (* 1/16 (/ (pow eps 3) (pow x 4))) (* 1/2 eps)) (* -1/8 (/ (pow eps 2) (pow x 2)))) x)))
#s(approx (/ (- (* x x) (- (* x x) eps)) (+ x (sqrt (- (* x x) eps)))) #s(hole binary64 (/ (- (+ (* -1 (/ (+ (* -1/32 (pow eps 4)) (* -1/128 (pow eps 4))) (pow x 6))) (* 1/2 eps)) (+ (* -1/8 (/ (pow eps 2) (pow x 2))) (* -1/16 (/ (pow eps 3) (pow x 4))))) x)))
#s(approx (+ x (sqrt (- (* x x) eps))) #s(hole binary64 (* 2 x)))
#s(approx (+ x (sqrt (- (* x x) eps))) #s(hole binary64 (* x (+ 2 (* -1/2 (/ eps (pow x 2)))))))
#s(approx (+ x (sqrt (- (* x x) eps))) #s(hole binary64 (* x (+ 2 (+ (* -1/2 (/ eps (pow x 2))) (* -1/8 (/ (pow eps 2) (pow x 4))))))))
#s(approx (+ x (sqrt (- (* x x) eps))) #s(hole binary64 (* x (+ 2 (+ (* -1/2 (/ eps (pow x 2))) (+ (* -1/8 (/ (pow eps 2) (pow x 4))) (* -1/16 (/ (pow eps 3) (pow x 6)))))))))
#s(approx (sqrt (- (* x x) eps)) #s(hole binary64 (* x (+ 1 (* -1/2 (/ eps (pow x 2)))))))
#s(approx (sqrt (- (* x x) eps)) #s(hole binary64 (* x (+ 1 (+ (* -1/2 (/ eps (pow x 2))) (* -1/8 (/ (pow eps 2) (pow x 4))))))))
#s(approx (sqrt (- (* x x) eps)) #s(hole binary64 (* x (+ 1 (+ (* -1/2 (/ eps (pow x 2))) (+ (* -1/8 (/ (pow eps 2) (pow x 4))) (* -1/16 (/ (pow eps 3) (pow x 6)))))))))
#s(approx (- (* x x) eps) #s(hole binary64 (* (pow x 2) (+ 1 (* -1 (/ eps (pow x 2)))))))
#s(approx (- x (sqrt (- (* x x) eps))) #s(hole binary64 (/ (- (* 1/8 (/ (pow eps 2) (pow x 2))) (* -1/2 eps)) x)))
#s(approx (- x (sqrt (- (* x x) eps))) #s(hole binary64 (/ (- (* 1/16 (/ (pow eps 3) (pow x 4))) (+ (* -1/2 eps) (* -1/8 (/ (pow eps 2) (pow x 2))))) x)))
#s(approx (- x (sqrt (- (* x x) eps))) #s(hole binary64 (/ (- (* 1/2 (/ (+ (* 1/64 (pow eps 4)) (* 1/16 (pow eps 4))) (pow x 6))) (+ (* -1/2 eps) (+ (* -1/8 (/ (pow eps 2) (pow x 2))) (* -1/16 (/ (pow eps 3) (pow x 4)))))) x)))
#s(approx (* (neg eps) (- (/ (neg x) eps) (sqrt (/ -1 eps)))) #s(hole binary64 (* x (+ 1 (/ (* eps (sqrt (/ -1 eps))) x)))))
#s(approx (/ (- (* x x) (- (* x x) eps)) (+ x (sqrt (- (* x x) eps)))) #s(hole binary64 (* -1 (* x (- (* 1/2 (/ eps (pow x 2))) 2)))))
#s(approx (/ (- (* x x) (- (* x x) eps)) (+ x (sqrt (- (* x x) eps)))) #s(hole binary64 (* -1 (* x (- (* -1 (/ (+ (* -1/4 (pow eps 2)) (* 1/8 (pow eps 2))) (pow x 4))) (+ 2 (* -1/2 (/ eps (pow x 2)))))))))
#s(approx (/ (- (* x x) (- (* x x) eps)) (+ x (sqrt (- (* x x) eps)))) #s(hole binary64 (* -1 (* x (- (* -1 (/ (+ (* -2 (/ (+ (* 1/64 (pow eps 4)) (* 1/16 (pow eps 4))) eps)) (+ (* -1/4 (* eps (+ (* -1/4 (pow eps 2)) (* 1/8 (pow eps 2))))) (* 1/16 (pow eps 3)))) (pow x 6))) (+ 2 (+ (* -1/2 (/ eps (pow x 2))) (+ (* -1/4 (/ (pow eps 2) (pow x 4))) (* 1/8 (/ (pow eps 2) (pow x 4)))))))))))
#s(approx (+ x (sqrt (- (* x x) eps))) #s(hole binary64 (* -1 (/ (+ (* -1/2 eps) (* -1/8 (/ (pow eps 2) (pow x 2)))) x))))
#s(approx (+ x (sqrt (- (* x x) eps))) #s(hole binary64 (* -1 (/ (+ (* -1/2 eps) (+ (* -1/8 (/ (pow eps 2) (pow x 2))) (* -1/16 (/ (pow eps 3) (pow x 4))))) x))))
#s(approx (+ x (sqrt (- (* x x) eps))) #s(hole binary64 (* -1 (/ (+ (* -1/2 eps) (+ (* -1/2 (/ (+ (* 1/64 (pow eps 4)) (* 1/16 (pow eps 4))) (pow x 6))) (+ (* -1/8 (/ (pow eps 2) (pow x 2))) (* -1/16 (/ (pow eps 3) (pow x 4)))))) x))))
#s(approx (sqrt (- (* x x) eps)) #s(hole binary64 (* -1 x)))
#s(approx (sqrt (- (* x x) eps)) #s(hole binary64 (* -1 (* x (+ 1 (* -1/2 (/ eps (pow x 2))))))))
#s(approx (sqrt (- (* x x) eps)) #s(hole binary64 (* -1 (* x (+ 1 (+ (* -1/2 (/ eps (pow x 2))) (* -1/8 (/ (pow eps 2) (pow x 4)))))))))
#s(approx (sqrt (- (* x x) eps)) #s(hole binary64 (* -1 (* x (+ 1 (+ (* -1/2 (/ eps (pow x 2))) (+ (* -1/8 (/ (pow eps 2) (pow x 4))) (* -1/16 (/ (pow eps 3) (pow x 6))))))))))
#s(approx (- x (sqrt (- (* x x) eps))) #s(hole binary64 (* -1 (* x (- (* 1/8 (/ (pow eps 2) (pow x 4))) (+ 2 (* -1/2 (/ eps (pow x 2)))))))))
#s(approx (- x (sqrt (- (* x x) eps))) #s(hole binary64 (* -1 (* x (- (* 1/16 (/ (pow eps 3) (pow x 6))) (+ 2 (+ (* -1/2 (/ eps (pow x 2))) (* -1/8 (/ (pow eps 2) (pow x 4))))))))))
#s(approx (* (neg eps) (- (/ (neg x) eps) (sqrt (/ -1 eps)))) #s(hole binary64 (* -1 (* x (- (* -1 (/ (* eps (sqrt (/ -1 eps))) x)) 1)))))
#s(approx (/ (- (* x x) (- (* x x) eps)) (+ x (sqrt (- (* x x) eps)))) #s(hole binary64 (/ eps (+ x (sqrt (pow x 2))))))
#s(approx (/ (- (* x x) (- (* x x) eps)) (+ x (sqrt (- (* x x) eps)))) #s(hole binary64 (* eps (+ (* 1/2 (/ eps (* (sqrt (pow x 2)) (pow (+ x (sqrt (pow x 2))) 2)))) (/ 1 (+ x (sqrt (pow x 2))))))))
#s(approx (/ (- (* x x) (- (* x x) eps)) (+ x (sqrt (- (* x x) eps)))) #s(hole binary64 (* eps (+ (* eps (+ (* eps (+ (* 1/4 (/ 1 (* (pow (sqrt (pow x 2)) 2) (pow (+ x (sqrt (pow x 2))) 3)))) (* 1/8 (/ 1 (* (pow (sqrt (pow x 2)) 3) (pow (+ x (sqrt (pow x 2))) 2)))))) (* 1/2 (/ 1 (* (sqrt (pow x 2)) (pow (+ x (sqrt (pow x 2))) 2)))))) (/ 1 (+ x (sqrt (pow x 2))))))))
#s(approx (/ (- (* x x) (- (* x x) eps)) (+ x (sqrt (- (* x x) eps)))) #s(hole binary64 (* eps (+ (* eps (+ (* eps (+ (* 1/8 (/ 1 (* (pow (sqrt (pow x 2)) 3) (pow (+ x (sqrt (pow x 2))) 2)))) (+ (* 1/4 (/ 1 (* (pow (sqrt (pow x 2)) 2) (pow (+ x (sqrt (pow x 2))) 3)))) (* eps (- (+ (* 1/16 (/ 1 (* (pow (sqrt (pow x 2)) 4) (pow (+ x (sqrt (pow x 2))) 3)))) (* 1/16 (/ 1 (* (pow (sqrt (pow x 2)) 5) (pow (+ x (sqrt (pow x 2))) 2))))) (* -1/2 (/ (+ (* 1/4 (/ 1 (* (pow (sqrt (pow x 2)) 2) (pow (+ x (sqrt (pow x 2))) 3)))) (* 1/8 (/ 1 (* (pow (sqrt (pow x 2)) 3) (pow (+ x (sqrt (pow x 2))) 2))))) (* (sqrt (pow x 2)) (+ x (sqrt (pow x 2))))))))))) (* 1/2 (/ 1 (* (sqrt (pow x 2)) (pow (+ x (sqrt (pow x 2))) 2)))))) (/ 1 (+ x (sqrt (pow x 2))))))))
#s(approx (+ x (sqrt (- (* x x) eps))) #s(hole binary64 (+ x (sqrt (pow x 2)))))
#s(approx (+ x (sqrt (- (* x x) eps))) #s(hole binary64 (+ x (+ (sqrt (pow x 2)) (* -1/2 (/ eps (sqrt (pow x 2))))))))
#s(approx (+ x (sqrt (- (* x x) eps))) #s(hole binary64 (+ x (+ (sqrt (pow x 2)) (* eps (- (* -1/8 (/ eps (pow (sqrt (pow x 2)) 3))) (* 1/2 (/ 1 (sqrt (pow x 2))))))))))
#s(approx (+ x (sqrt (- (* x x) eps))) #s(hole binary64 (+ x (+ (sqrt (pow x 2)) (* eps (- (* eps (- (* -1/16 (/ eps (pow (sqrt (pow x 2)) 5))) (* 1/8 (/ 1 (pow (sqrt (pow x 2)) 3))))) (* 1/2 (/ 1 (sqrt (pow x 2))))))))))
#s(approx (sqrt (- (* x x) eps)) #s(hole binary64 (sqrt (pow x 2))))
#s(approx (sqrt (- (* x x) eps)) #s(hole binary64 (+ (sqrt (pow x 2)) (* -1/2 (/ eps (sqrt (pow x 2)))))))
#s(approx (sqrt (- (* x x) eps)) #s(hole binary64 (+ (sqrt (pow x 2)) (* eps (- (* -1/8 (/ eps (pow (sqrt (pow x 2)) 3))) (* 1/2 (/ 1 (sqrt (pow x 2)))))))))
#s(approx (sqrt (- (* x x) eps)) #s(hole binary64 (+ (sqrt (pow x 2)) (* eps (- (* eps (- (* -1/16 (/ eps (pow (sqrt (pow x 2)) 5))) (* 1/8 (/ 1 (pow (sqrt (pow x 2)) 3))))) (* 1/2 (/ 1 (sqrt (pow x 2)))))))))
#s(approx (- (* x x) eps) #s(hole binary64 (+ (* -1 eps) (pow x 2))))
#s(approx (- x (sqrt (- (* x x) eps))) #s(hole binary64 (- x (sqrt (pow x 2)))))
#s(approx (- x (sqrt (- (* x x) eps))) #s(hole binary64 (- (+ x (* 1/2 (/ eps (sqrt (pow x 2))))) (sqrt (pow x 2)))))
#s(approx (- x (sqrt (- (* x x) eps))) #s(hole binary64 (- (+ x (* eps (+ (* 1/8 (/ eps (pow (sqrt (pow x 2)) 3))) (* 1/2 (/ 1 (sqrt (pow x 2))))))) (sqrt (pow x 2)))))
#s(approx (- x (sqrt (- (* x x) eps))) #s(hole binary64 (- (+ x (* eps (+ (* eps (+ (* 1/16 (/ eps (pow (sqrt (pow x 2)) 5))) (* 1/8 (/ 1 (pow (sqrt (pow x 2)) 3))))) (* 1/2 (/ 1 (sqrt (pow x 2))))))) (sqrt (pow x 2)))))
#s(approx (sqrt (neg eps)) #s(hole binary64 (sqrt (* -1 eps))))
#s(approx (fabs eps) #s(hole binary64 (fabs eps)))
#s(approx (/ eps (sqrt (neg eps))) #s(hole binary64 (/ eps (sqrt (* -1 eps)))))
#s(approx (* (neg eps) (- (/ (neg x) eps) (sqrt (/ -1 eps)))) #s(hole binary64 (* -1 (- (* -1 x) (sqrt (* -1 eps))))))
#s(approx (+ (* (sqrt (/ -1 eps)) eps) x) #s(hole binary64 (+ x (sqrt (* -1 eps)))))
#s(approx (sqrt (/ -1 eps)) #s(hole binary64 (/ (sqrt (* -1 eps)) eps)))
#s(approx (/ -1 eps) #s(hole binary64 (/ -1 eps)))
#s(approx (/ (- (* x x) (- (* x x) eps)) (+ x (sqrt (- (* x x) eps)))) #s(hole binary64 (/ 1 (sqrt (/ -1 eps)))))
#s(approx (/ (- (* x x) (- (* x x) eps)) (+ x (sqrt (- (* x x) eps)))) #s(hole binary64 (+ (* -1 (/ x (* eps (pow (sqrt (/ -1 eps)) 2)))) (/ 1 (sqrt (/ -1 eps))))))
#s(approx (/ (- (* x x) (- (* x x) eps)) (+ x (sqrt (- (* x x) eps)))) #s(hole binary64 (- (+ (* -1 (/ (+ (* -1 (/ (pow x 2) (pow (sqrt (/ -1 eps)) 3))) (* 1/2 (/ (pow x 2) (pow (sqrt (/ -1 eps)) 3)))) (pow eps 2))) (/ 1 (sqrt (/ -1 eps)))) (/ x (* eps (pow (sqrt (/ -1 eps)) 2))))))
#s(approx (/ (- (* x x) (- (* x x) eps)) (+ x (sqrt (- (* x x) eps)))) #s(hole binary64 (- (+ (* -1 (/ (+ (* -1 (/ (* x (+ (* -1 (/ (pow x 2) (pow (sqrt (/ -1 eps)) 3))) (* 1/2 (/ (pow x 2) (pow (sqrt (/ -1 eps)) 3))))) (sqrt (/ -1 eps)))) (* -1/2 (/ (pow x 3) (pow (sqrt (/ -1 eps)) 4)))) (pow eps 3))) (/ 1 (sqrt (/ -1 eps)))) (+ (* -1 (/ (pow x 2) (* (pow eps 2) (pow (sqrt (/ -1 eps)) 3)))) (+ (* 1/2 (/ (pow x 2) (* (pow eps 2) (pow (sqrt (/ -1 eps)) 3)))) (/ x (* eps (pow (sqrt (/ -1 eps)) 2))))))))
#s(approx (+ x (sqrt (- (* x x) eps))) #s(hole binary64 (* eps (+ (sqrt (/ -1 eps)) (/ x eps)))))
#s(approx (+ x (sqrt (- (* x x) eps))) #s(hole binary64 (* eps (+ (sqrt (/ -1 eps)) (+ (* 1/2 (/ (pow x 2) (* (pow eps 2) (sqrt (/ -1 eps))))) (/ x eps))))))
#s(approx (+ x (sqrt (- (* x x) eps))) #s(hole binary64 (* eps (+ (sqrt (/ -1 eps)) (+ (* -1/8 (/ (pow x 4) (* (pow eps 4) (pow (sqrt (/ -1 eps)) 3)))) (+ (* 1/2 (/ (pow x 2) (* (pow eps 2) (sqrt (/ -1 eps))))) (/ x eps)))))))
#s(approx (sqrt (- (* x x) eps)) #s(hole binary64 (* eps (+ (sqrt (/ -1 eps)) (* 1/2 (/ (pow x 2) (* (pow eps 2) (sqrt (/ -1 eps)))))))))
#s(approx (sqrt (- (* x x) eps)) #s(hole binary64 (* eps (+ (sqrt (/ -1 eps)) (+ (* -1/8 (/ (pow x 4) (* (pow eps 4) (pow (sqrt (/ -1 eps)) 3)))) (* 1/2 (/ (pow x 2) (* (pow eps 2) (sqrt (/ -1 eps))))))))))
#s(approx (sqrt (- (* x x) eps)) #s(hole binary64 (* eps (+ (sqrt (/ -1 eps)) (+ (* -1/8 (/ (pow x 4) (* (pow eps 4) (pow (sqrt (/ -1 eps)) 3)))) (+ (* 1/16 (/ (pow x 6) (* (pow eps 6) (pow (sqrt (/ -1 eps)) 5)))) (* 1/2 (/ (pow x 2) (* (pow eps 2) (sqrt (/ -1 eps)))))))))))
#s(approx (- (* x x) eps) #s(hole binary64 (* eps (- (/ (pow x 2) eps) 1))))
#s(approx (- x (sqrt (- (* x x) eps))) #s(hole binary64 (* -1 (* eps (sqrt (/ -1 eps))))))
#s(approx (- x (sqrt (- (* x x) eps))) #s(hole binary64 (* eps (- (/ x eps) (sqrt (/ -1 eps))))))
#s(approx (- x (sqrt (- (* x x) eps))) #s(hole binary64 (* eps (- (+ (* -1/2 (/ (pow x 2) (* (pow eps 2) (sqrt (/ -1 eps))))) (/ x eps)) (sqrt (/ -1 eps))))))
#s(approx (- x (sqrt (- (* x x) eps))) #s(hole binary64 (* eps (- (+ (* 1/8 (/ (pow x 4) (* (pow eps 4) (pow (sqrt (/ -1 eps)) 3)))) (/ x eps)) (+ (sqrt (/ -1 eps)) (* 1/2 (/ (pow x 2) (* (pow eps 2) (sqrt (/ -1 eps))))))))))
#s(approx (sqrt (/ -1 eps)) #s(hole binary64 (sqrt (/ -1 eps))))
#s(approx (/ (- (* x x) (- (* x x) eps)) (+ x (sqrt (- (* x x) eps)))) #s(hole binary64 (/ -1 (sqrt (/ -1 eps)))))
#s(approx (/ (- (* x x) (- (* x x) eps)) (+ x (sqrt (- (* x x) eps)))) #s(hole binary64 (- (* -1 (/ x (* eps (pow (sqrt (/ -1 eps)) 2)))) (/ 1 (sqrt (/ -1 eps))))))
#s(approx (/ (- (* x x) (- (* x x) eps)) (+ x (sqrt (- (* x x) eps)))) #s(hole binary64 (- (* -1 (/ (- (+ (* -1/2 (/ (pow x 2) (* eps (pow (sqrt (/ -1 eps)) 3)))) (/ (pow x 2) (* eps (pow (sqrt (/ -1 eps)) 3)))) (* -1 (/ x (pow (sqrt (/ -1 eps)) 2)))) eps)) (/ 1 (sqrt (/ -1 eps))))))
#s(approx (/ (- (* x x) (- (* x x) eps)) (+ x (sqrt (- (* x x) eps)))) #s(hole binary64 (- (* -1 (/ (- (* -1 (/ (- (+ (* -1 (/ (* x (+ (* -1/2 (/ (pow x 2) (pow (sqrt (/ -1 eps)) 3))) (/ (pow x 2) (pow (sqrt (/ -1 eps)) 3)))) (* eps (sqrt (/ -1 eps))))) (* 1/2 (/ (pow x 3) (* eps (pow (sqrt (/ -1 eps)) 4))))) (+ (* -1/2 (/ (pow x 2) (pow (sqrt (/ -1 eps)) 3))) (/ (pow x 2) (pow (sqrt (/ -1 eps)) 3)))) eps)) (* -1 (/ x (pow (sqrt (/ -1 eps)) 2)))) eps)) (/ 1 (sqrt (/ -1 eps))))))
#s(approx (+ x (sqrt (- (* x x) eps))) #s(hole binary64 (* -1 (* eps (+ (sqrt (/ -1 eps)) (* -1 (/ x eps)))))))
#s(approx (+ x (sqrt (- (* x x) eps))) #s(hole binary64 (* -1 (* eps (+ (sqrt (/ -1 eps)) (* -1 (/ (+ x (* -1/2 (/ (pow x 2) (* eps (sqrt (/ -1 eps)))))) eps)))))))
#s(approx (+ x (sqrt (- (* x x) eps))) #s(hole binary64 (* -1 (* eps (+ (sqrt (/ -1 eps)) (* -1 (/ (+ x (* -1 (/ (+ (* -1/8 (/ (pow x 4) (* (pow eps 2) (pow (sqrt (/ -1 eps)) 3)))) (* 1/2 (/ (pow x 2) (sqrt (/ -1 eps))))) eps))) eps)))))))
#s(approx (sqrt (- (* x x) eps)) #s(hole binary64 (* -1 (* eps (+ (sqrt (/ -1 eps)) (* 1/2 (/ (pow x 2) (* (pow eps 2) (sqrt (/ -1 eps))))))))))
#s(approx (sqrt (- (* x x) eps)) #s(hole binary64 (* -1 (* eps (+ (sqrt (/ -1 eps)) (+ (* -1/8 (/ (pow x 4) (* (pow eps 4) (pow (sqrt (/ -1 eps)) 3)))) (* 1/2 (/ (pow x 2) (* (pow eps 2) (sqrt (/ -1 eps)))))))))))
#s(approx (sqrt (- (* x x) eps)) #s(hole binary64 (* -1 (* eps (+ (sqrt (/ -1 eps)) (+ (* -1/8 (/ (pow x 4) (* (pow eps 4) (pow (sqrt (/ -1 eps)) 3)))) (+ (* 1/16 (/ (pow x 6) (* (pow eps 6) (pow (sqrt (/ -1 eps)) 5)))) (* 1/2 (/ (pow x 2) (* (pow eps 2) (sqrt (/ -1 eps))))))))))))
#s(approx (- (* x x) eps) #s(hole binary64 (* -1 (* eps (+ 1 (* -1 (/ (pow x 2) eps)))))))
#s(approx (- x (sqrt (- (* x x) eps))) #s(hole binary64 (* -1 (* eps (- (* -1 (/ x eps)) (sqrt (/ -1 eps)))))))
#s(approx (- x (sqrt (- (* x x) eps))) #s(hole binary64 (* -1 (* eps (- (* -1 (/ (+ x (* 1/2 (/ (pow x 2) (* eps (sqrt (/ -1 eps)))))) eps)) (sqrt (/ -1 eps)))))))
#s(approx (- x (sqrt (- (* x x) eps))) #s(hole binary64 (* -1 (* eps (- (* -1 (/ (+ x (* -1 (/ (- (* 1/8 (/ (pow x 4) (* (pow eps 2) (pow (sqrt (/ -1 eps)) 3)))) (* 1/2 (/ (pow x 2) (sqrt (/ -1 eps))))) eps))) eps)) (sqrt (/ -1 eps)))))))
#s(approx (* (neg eps) (- (/ (neg x) eps) (sqrt (/ -1 eps)))) #s(hole binary64 (* -1 (* eps (+ (* -1 (sqrt (/ -1 eps))) (* -1 (/ x eps)))))))
Calls

6 calls:

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

rewrite172.0ms (5.9%)

Memory
-6.3MiB live, 177.9MiB allocated; 27ms collecting garbage
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
06173873
06383563
136353168
083603078
Stop Event
1×iter-limit
1×node-limit
1×iter-limit
Counts
129 → 309
Calls
Call 1
Inputs
(/.f64 #s(approx (- (* x x) (- (* x x) eps)) eps) (+.f64 x (sqrt.f64 (-.f64 (*.f64 x x) eps))))
#s(approx (- (* x x) (- (* x x) eps)) eps)
eps
(+.f64 x (sqrt.f64 (-.f64 (*.f64 x x) eps)))
x
(sqrt.f64 (-.f64 (*.f64 x x) eps))
(-.f64 (*.f64 x x) eps)
(*.f64 x x)
#s(approx (- x (sqrt (- (* x x) eps))) (sqrt.f64 (neg.f64 eps)))
(sqrt.f64 (neg.f64 eps))
(neg.f64 eps)
(-.f64 x (sqrt.f64 #s(approx (- (* x x) eps) (fabs.f64 eps))))
(sqrt.f64 #s(approx (- (* x x) eps) (fabs.f64 eps)))
#s(approx (- (* x x) eps) (fabs.f64 eps))
(fabs.f64 eps)
#s(approx (- x (sqrt (- (* x x) eps))) (/.f64 eps (sqrt.f64 (neg.f64 eps))))
(/.f64 eps (sqrt.f64 (neg.f64 eps)))
#s(approx (- x (sqrt (- (* x x) eps))) #s(approx (* (neg eps) (- (/ (neg x) eps) (sqrt (/ -1 eps)))) (fma.f64 (sqrt.f64 (/.f64 #s(literal -1 binary64) eps)) eps x)))
#s(approx (* (neg eps) (- (/ (neg x) eps) (sqrt (/ -1 eps)))) (fma.f64 (sqrt.f64 (/.f64 #s(literal -1 binary64) eps)) eps x))
(fma.f64 (sqrt.f64 (/.f64 #s(literal -1 binary64) eps)) eps x)
(sqrt.f64 (/.f64 #s(literal -1 binary64) eps))
(/.f64 #s(literal -1 binary64) eps)
#s(literal -1 binary64)
#s(approx (/ (- (* x x) (- (* x x) eps)) (+ x (sqrt (- (* x x) eps)))) #s(hole binary64 (/ eps (sqrt (neg eps)))))
#s(approx (/ (- (* x x) (- (* x x) eps)) (+ x (sqrt (- (* x x) eps)))) #s(hole binary64 (+ (* -1 (/ (* eps x) (pow (sqrt (neg eps)) 2))) (/ eps (sqrt (neg eps))))))
#s(approx (/ (- (* x x) (- (* x x) eps)) (+ x (sqrt (- (* x x) eps)))) #s(hole binary64 (+ (* x (- (* -1 (* x (+ (* -1 (/ eps (pow (sqrt (neg eps)) 3))) (* 1/2 (/ eps (pow (sqrt (neg eps)) 3)))))) (/ eps (pow (sqrt (neg eps)) 2)))) (/ eps (sqrt (neg eps))))))
#s(approx (/ (- (* x x) (- (* x x) eps)) (+ x (sqrt (- (* x x) eps)))) #s(hole binary64 (+ (* x (- (* x (- (* -1 (* x (+ (* -1 (/ (+ (* -1 (/ eps (pow (sqrt (neg eps)) 3))) (* 1/2 (/ eps (pow (sqrt (neg eps)) 3)))) (sqrt (neg eps)))) (* -1/2 (/ eps (pow (sqrt (neg eps)) 4)))))) (+ (* -1 (/ eps (pow (sqrt (neg eps)) 3))) (* 1/2 (/ eps (pow (sqrt (neg eps)) 3)))))) (/ eps (pow (sqrt (neg eps)) 2)))) (/ eps (sqrt (neg eps))))))
#s(approx (- (* x x) (- (* x x) eps)) #s(hole binary64 eps))
#s(approx (+ x (sqrt (- (* x x) eps))) #s(hole binary64 (sqrt (neg eps))))
#s(approx (+ x (sqrt (- (* x x) eps))) #s(hole binary64 (+ x (sqrt (neg eps)))))
#s(approx (+ x (sqrt (- (* x x) eps))) #s(hole binary64 (+ (sqrt (neg eps)) (* x (+ 1 (* 1/2 (/ x (sqrt (neg eps)))))))))
#s(approx (+ x (sqrt (- (* x x) eps))) #s(hole binary64 (+ (sqrt (neg eps)) (* x (+ 1 (* x (+ (* -1/8 (/ (pow x 2) (pow (sqrt (neg eps)) 3))) (* 1/2 (/ 1 (sqrt (neg eps)))))))))))
#s(approx x #s(hole binary64 x))
#s(approx (sqrt (- (* x x) eps)) #s(hole binary64 (+ (sqrt (neg eps)) (* 1/2 (/ (pow x 2) (sqrt (neg eps)))))))
#s(approx (sqrt (- (* x x) eps)) #s(hole binary64 (+ (sqrt (neg eps)) (* (pow x 2) (+ (* -1/8 (/ (pow x 2) (pow (sqrt (neg eps)) 3))) (* 1/2 (/ 1 (sqrt (neg eps)))))))))
#s(approx (sqrt (- (* x x) eps)) #s(hole binary64 (+ (sqrt (neg eps)) (* (pow x 2) (+ (* (pow x 2) (- (* 1/16 (/ (pow x 2) (pow (sqrt (neg eps)) 5))) (* 1/8 (/ 1 (pow (sqrt (neg eps)) 3))))) (* 1/2 (/ 1 (sqrt (neg eps)))))))))
#s(approx (- (* x x) eps) #s(hole binary64 (* -1 eps)))
#s(approx (- (* x x) eps) #s(hole binary64 (- (pow x 2) eps)))
#s(approx (* x x) #s(hole binary64 (pow x 2)))
#s(approx (- x (sqrt (- (* x x) eps))) #s(hole binary64 (* -1 (sqrt (neg eps)))))
#s(approx (- x (sqrt (- (* x x) eps))) #s(hole binary64 (- x (sqrt (neg eps)))))
#s(approx (- x (sqrt (- (* x x) eps))) #s(hole binary64 (- (* x (+ 1 (* -1/2 (/ x (sqrt (neg eps)))))) (sqrt (neg eps)))))
#s(approx (- x (sqrt (- (* x x) eps))) #s(hole binary64 (- (* x (+ 1 (* x (- (* 1/8 (/ (pow x 2) (pow (sqrt (neg eps)) 3))) (* 1/2 (/ 1 (sqrt (neg eps)))))))) (sqrt (neg eps)))))
#s(approx (* (neg eps) (- (/ (neg x) eps) (sqrt (/ -1 eps)))) #s(hole binary64 (* eps (sqrt (/ -1 eps)))))
#s(approx (* (neg eps) (- (/ (neg x) eps) (sqrt (/ -1 eps)))) #s(hole binary64 (+ x (* eps (sqrt (/ -1 eps))))))
#s(approx (/ (- (* x x) (- (* x x) eps)) (+ x (sqrt (- (* x x) eps)))) #s(hole binary64 (* 1/2 (/ eps x))))
#s(approx (/ (- (* x x) (- (* x x) eps)) (+ x (sqrt (- (* x x) eps)))) #s(hole binary64 (/ (+ (* 1/8 (/ (pow eps 2) (pow x 2))) (* 1/2 eps)) x)))
#s(approx (/ (- (* x x) (- (* x x) eps)) (+ x (sqrt (- (* x x) eps)))) #s(hole binary64 (/ (- (+ (* 1/16 (/ (pow eps 3) (pow x 4))) (* 1/2 eps)) (* -1/8 (/ (pow eps 2) (pow x 2)))) x)))
#s(approx (/ (- (* x x) (- (* x x) eps)) (+ x (sqrt (- (* x x) eps)))) #s(hole binary64 (/ (- (+ (* -1 (/ (+ (* -1/32 (pow eps 4)) (* -1/128 (pow eps 4))) (pow x 6))) (* 1/2 eps)) (+ (* -1/8 (/ (pow eps 2) (pow x 2))) (* -1/16 (/ (pow eps 3) (pow x 4))))) x)))
#s(approx (+ x (sqrt (- (* x x) eps))) #s(hole binary64 (* 2 x)))
#s(approx (+ x (sqrt (- (* x x) eps))) #s(hole binary64 (* x (+ 2 (* -1/2 (/ eps (pow x 2)))))))
#s(approx (+ x (sqrt (- (* x x) eps))) #s(hole binary64 (* x (+ 2 (+ (* -1/2 (/ eps (pow x 2))) (* -1/8 (/ (pow eps 2) (pow x 4))))))))
#s(approx (+ x (sqrt (- (* x x) eps))) #s(hole binary64 (* x (+ 2 (+ (* -1/2 (/ eps (pow x 2))) (+ (* -1/8 (/ (pow eps 2) (pow x 4))) (* -1/16 (/ (pow eps 3) (pow x 6)))))))))
#s(approx (sqrt (- (* x x) eps)) #s(hole binary64 (* x (+ 1 (* -1/2 (/ eps (pow x 2)))))))
#s(approx (sqrt (- (* x x) eps)) #s(hole binary64 (* x (+ 1 (+ (* -1/2 (/ eps (pow x 2))) (* -1/8 (/ (pow eps 2) (pow x 4))))))))
#s(approx (sqrt (- (* x x) eps)) #s(hole binary64 (* x (+ 1 (+ (* -1/2 (/ eps (pow x 2))) (+ (* -1/8 (/ (pow eps 2) (pow x 4))) (* -1/16 (/ (pow eps 3) (pow x 6)))))))))
#s(approx (- (* x x) eps) #s(hole binary64 (* (pow x 2) (+ 1 (* -1 (/ eps (pow x 2)))))))
#s(approx (- x (sqrt (- (* x x) eps))) #s(hole binary64 (/ (- (* 1/8 (/ (pow eps 2) (pow x 2))) (* -1/2 eps)) x)))
#s(approx (- x (sqrt (- (* x x) eps))) #s(hole binary64 (/ (- (* 1/16 (/ (pow eps 3) (pow x 4))) (+ (* -1/2 eps) (* -1/8 (/ (pow eps 2) (pow x 2))))) x)))
#s(approx (- x (sqrt (- (* x x) eps))) #s(hole binary64 (/ (- (* 1/2 (/ (+ (* 1/64 (pow eps 4)) (* 1/16 (pow eps 4))) (pow x 6))) (+ (* -1/2 eps) (+ (* -1/8 (/ (pow eps 2) (pow x 2))) (* -1/16 (/ (pow eps 3) (pow x 4)))))) x)))
#s(approx (* (neg eps) (- (/ (neg x) eps) (sqrt (/ -1 eps)))) #s(hole binary64 (* x (+ 1 (/ (* eps (sqrt (/ -1 eps))) x)))))
#s(approx (/ (- (* x x) (- (* x x) eps)) (+ x (sqrt (- (* x x) eps)))) #s(hole binary64 (* -1 (* x (- (* 1/2 (/ eps (pow x 2))) 2)))))
#s(approx (/ (- (* x x) (- (* x x) eps)) (+ x (sqrt (- (* x x) eps)))) #s(hole binary64 (* -1 (* x (- (* -1 (/ (+ (* -1/4 (pow eps 2)) (* 1/8 (pow eps 2))) (pow x 4))) (+ 2 (* -1/2 (/ eps (pow x 2)))))))))
#s(approx (/ (- (* x x) (- (* x x) eps)) (+ x (sqrt (- (* x x) eps)))) #s(hole binary64 (* -1 (* x (- (* -1 (/ (+ (* -2 (/ (+ (* 1/64 (pow eps 4)) (* 1/16 (pow eps 4))) eps)) (+ (* -1/4 (* eps (+ (* -1/4 (pow eps 2)) (* 1/8 (pow eps 2))))) (* 1/16 (pow eps 3)))) (pow x 6))) (+ 2 (+ (* -1/2 (/ eps (pow x 2))) (+ (* -1/4 (/ (pow eps 2) (pow x 4))) (* 1/8 (/ (pow eps 2) (pow x 4)))))))))))
#s(approx (+ x (sqrt (- (* x x) eps))) #s(hole binary64 (* -1 (/ (+ (* -1/2 eps) (* -1/8 (/ (pow eps 2) (pow x 2)))) x))))
#s(approx (+ x (sqrt (- (* x x) eps))) #s(hole binary64 (* -1 (/ (+ (* -1/2 eps) (+ (* -1/8 (/ (pow eps 2) (pow x 2))) (* -1/16 (/ (pow eps 3) (pow x 4))))) x))))
#s(approx (+ x (sqrt (- (* x x) eps))) #s(hole binary64 (* -1 (/ (+ (* -1/2 eps) (+ (* -1/2 (/ (+ (* 1/64 (pow eps 4)) (* 1/16 (pow eps 4))) (pow x 6))) (+ (* -1/8 (/ (pow eps 2) (pow x 2))) (* -1/16 (/ (pow eps 3) (pow x 4)))))) x))))
#s(approx (sqrt (- (* x x) eps)) #s(hole binary64 (* -1 x)))
#s(approx (sqrt (- (* x x) eps)) #s(hole binary64 (* -1 (* x (+ 1 (* -1/2 (/ eps (pow x 2))))))))
#s(approx (sqrt (- (* x x) eps)) #s(hole binary64 (* -1 (* x (+ 1 (+ (* -1/2 (/ eps (pow x 2))) (* -1/8 (/ (pow eps 2) (pow x 4)))))))))
#s(approx (sqrt (- (* x x) eps)) #s(hole binary64 (* -1 (* x (+ 1 (+ (* -1/2 (/ eps (pow x 2))) (+ (* -1/8 (/ (pow eps 2) (pow x 4))) (* -1/16 (/ (pow eps 3) (pow x 6))))))))))
#s(approx (- x (sqrt (- (* x x) eps))) #s(hole binary64 (* -1 (* x (- (* 1/8 (/ (pow eps 2) (pow x 4))) (+ 2 (* -1/2 (/ eps (pow x 2)))))))))
#s(approx (- x (sqrt (- (* x x) eps))) #s(hole binary64 (* -1 (* x (- (* 1/16 (/ (pow eps 3) (pow x 6))) (+ 2 (+ (* -1/2 (/ eps (pow x 2))) (* -1/8 (/ (pow eps 2) (pow x 4))))))))))
#s(approx (* (neg eps) (- (/ (neg x) eps) (sqrt (/ -1 eps)))) #s(hole binary64 (* -1 (* x (- (* -1 (/ (* eps (sqrt (/ -1 eps))) x)) 1)))))
#s(approx (/ (- (* x x) (- (* x x) eps)) (+ x (sqrt (- (* x x) eps)))) #s(hole binary64 (/ eps (+ x (sqrt (pow x 2))))))
#s(approx (/ (- (* x x) (- (* x x) eps)) (+ x (sqrt (- (* x x) eps)))) #s(hole binary64 (* eps (+ (* 1/2 (/ eps (* (sqrt (pow x 2)) (pow (+ x (sqrt (pow x 2))) 2)))) (/ 1 (+ x (sqrt (pow x 2))))))))
#s(approx (/ (- (* x x) (- (* x x) eps)) (+ x (sqrt (- (* x x) eps)))) #s(hole binary64 (* eps (+ (* eps (+ (* eps (+ (* 1/4 (/ 1 (* (pow (sqrt (pow x 2)) 2) (pow (+ x (sqrt (pow x 2))) 3)))) (* 1/8 (/ 1 (* (pow (sqrt (pow x 2)) 3) (pow (+ x (sqrt (pow x 2))) 2)))))) (* 1/2 (/ 1 (* (sqrt (pow x 2)) (pow (+ x (sqrt (pow x 2))) 2)))))) (/ 1 (+ x (sqrt (pow x 2))))))))
#s(approx (/ (- (* x x) (- (* x x) eps)) (+ x (sqrt (- (* x x) eps)))) #s(hole binary64 (* eps (+ (* eps (+ (* eps (+ (* 1/8 (/ 1 (* (pow (sqrt (pow x 2)) 3) (pow (+ x (sqrt (pow x 2))) 2)))) (+ (* 1/4 (/ 1 (* (pow (sqrt (pow x 2)) 2) (pow (+ x (sqrt (pow x 2))) 3)))) (* eps (- (+ (* 1/16 (/ 1 (* (pow (sqrt (pow x 2)) 4) (pow (+ x (sqrt (pow x 2))) 3)))) (* 1/16 (/ 1 (* (pow (sqrt (pow x 2)) 5) (pow (+ x (sqrt (pow x 2))) 2))))) (* -1/2 (/ (+ (* 1/4 (/ 1 (* (pow (sqrt (pow x 2)) 2) (pow (+ x (sqrt (pow x 2))) 3)))) (* 1/8 (/ 1 (* (pow (sqrt (pow x 2)) 3) (pow (+ x (sqrt (pow x 2))) 2))))) (* (sqrt (pow x 2)) (+ x (sqrt (pow x 2))))))))))) (* 1/2 (/ 1 (* (sqrt (pow x 2)) (pow (+ x (sqrt (pow x 2))) 2)))))) (/ 1 (+ x (sqrt (pow x 2))))))))
#s(approx (+ x (sqrt (- (* x x) eps))) #s(hole binary64 (+ x (sqrt (pow x 2)))))
#s(approx (+ x (sqrt (- (* x x) eps))) #s(hole binary64 (+ x (+ (sqrt (pow x 2)) (* -1/2 (/ eps (sqrt (pow x 2))))))))
#s(approx (+ x (sqrt (- (* x x) eps))) #s(hole binary64 (+ x (+ (sqrt (pow x 2)) (* eps (- (* -1/8 (/ eps (pow (sqrt (pow x 2)) 3))) (* 1/2 (/ 1 (sqrt (pow x 2))))))))))
#s(approx (+ x (sqrt (- (* x x) eps))) #s(hole binary64 (+ x (+ (sqrt (pow x 2)) (* eps (- (* eps (- (* -1/16 (/ eps (pow (sqrt (pow x 2)) 5))) (* 1/8 (/ 1 (pow (sqrt (pow x 2)) 3))))) (* 1/2 (/ 1 (sqrt (pow x 2))))))))))
#s(approx (sqrt (- (* x x) eps)) #s(hole binary64 (sqrt (pow x 2))))
#s(approx (sqrt (- (* x x) eps)) #s(hole binary64 (+ (sqrt (pow x 2)) (* -1/2 (/ eps (sqrt (pow x 2)))))))
#s(approx (sqrt (- (* x x) eps)) #s(hole binary64 (+ (sqrt (pow x 2)) (* eps (- (* -1/8 (/ eps (pow (sqrt (pow x 2)) 3))) (* 1/2 (/ 1 (sqrt (pow x 2)))))))))
#s(approx (sqrt (- (* x x) eps)) #s(hole binary64 (+ (sqrt (pow x 2)) (* eps (- (* eps (- (* -1/16 (/ eps (pow (sqrt (pow x 2)) 5))) (* 1/8 (/ 1 (pow (sqrt (pow x 2)) 3))))) (* 1/2 (/ 1 (sqrt (pow x 2)))))))))
#s(approx (- (* x x) eps) #s(hole binary64 (+ (* -1 eps) (pow x 2))))
#s(approx (- x (sqrt (- (* x x) eps))) #s(hole binary64 (- x (sqrt (pow x 2)))))
#s(approx (- x (sqrt (- (* x x) eps))) #s(hole binary64 (- (+ x (* 1/2 (/ eps (sqrt (pow x 2))))) (sqrt (pow x 2)))))
#s(approx (- x (sqrt (- (* x x) eps))) #s(hole binary64 (- (+ x (* eps (+ (* 1/8 (/ eps (pow (sqrt (pow x 2)) 3))) (* 1/2 (/ 1 (sqrt (pow x 2))))))) (sqrt (pow x 2)))))
#s(approx (- x (sqrt (- (* x x) eps))) #s(hole binary64 (- (+ x (* eps (+ (* eps (+ (* 1/16 (/ eps (pow (sqrt (pow x 2)) 5))) (* 1/8 (/ 1 (pow (sqrt (pow x 2)) 3))))) (* 1/2 (/ 1 (sqrt (pow x 2))))))) (sqrt (pow x 2)))))
#s(approx (sqrt (neg eps)) #s(hole binary64 (sqrt (* -1 eps))))
#s(approx (fabs eps) #s(hole binary64 (fabs eps)))
#s(approx (/ eps (sqrt (neg eps))) #s(hole binary64 (/ eps (sqrt (* -1 eps)))))
#s(approx (* (neg eps) (- (/ (neg x) eps) (sqrt (/ -1 eps)))) #s(hole binary64 (* -1 (- (* -1 x) (sqrt (* -1 eps))))))
#s(approx (+ (* (sqrt (/ -1 eps)) eps) x) #s(hole binary64 (+ x (sqrt (* -1 eps)))))
#s(approx (sqrt (/ -1 eps)) #s(hole binary64 (/ (sqrt (* -1 eps)) eps)))
#s(approx (/ -1 eps) #s(hole binary64 (/ -1 eps)))
#s(approx (/ (- (* x x) (- (* x x) eps)) (+ x (sqrt (- (* x x) eps)))) #s(hole binary64 (/ 1 (sqrt (/ -1 eps)))))
#s(approx (/ (- (* x x) (- (* x x) eps)) (+ x (sqrt (- (* x x) eps)))) #s(hole binary64 (+ (* -1 (/ x (* eps (pow (sqrt (/ -1 eps)) 2)))) (/ 1 (sqrt (/ -1 eps))))))
#s(approx (/ (- (* x x) (- (* x x) eps)) (+ x (sqrt (- (* x x) eps)))) #s(hole binary64 (- (+ (* -1 (/ (+ (* -1 (/ (pow x 2) (pow (sqrt (/ -1 eps)) 3))) (* 1/2 (/ (pow x 2) (pow (sqrt (/ -1 eps)) 3)))) (pow eps 2))) (/ 1 (sqrt (/ -1 eps)))) (/ x (* eps (pow (sqrt (/ -1 eps)) 2))))))
#s(approx (/ (- (* x x) (- (* x x) eps)) (+ x (sqrt (- (* x x) eps)))) #s(hole binary64 (- (+ (* -1 (/ (+ (* -1 (/ (* x (+ (* -1 (/ (pow x 2) (pow (sqrt (/ -1 eps)) 3))) (* 1/2 (/ (pow x 2) (pow (sqrt (/ -1 eps)) 3))))) (sqrt (/ -1 eps)))) (* -1/2 (/ (pow x 3) (pow (sqrt (/ -1 eps)) 4)))) (pow eps 3))) (/ 1 (sqrt (/ -1 eps)))) (+ (* -1 (/ (pow x 2) (* (pow eps 2) (pow (sqrt (/ -1 eps)) 3)))) (+ (* 1/2 (/ (pow x 2) (* (pow eps 2) (pow (sqrt (/ -1 eps)) 3)))) (/ x (* eps (pow (sqrt (/ -1 eps)) 2))))))))
#s(approx (+ x (sqrt (- (* x x) eps))) #s(hole binary64 (* eps (+ (sqrt (/ -1 eps)) (/ x eps)))))
#s(approx (+ x (sqrt (- (* x x) eps))) #s(hole binary64 (* eps (+ (sqrt (/ -1 eps)) (+ (* 1/2 (/ (pow x 2) (* (pow eps 2) (sqrt (/ -1 eps))))) (/ x eps))))))
#s(approx (+ x (sqrt (- (* x x) eps))) #s(hole binary64 (* eps (+ (sqrt (/ -1 eps)) (+ (* -1/8 (/ (pow x 4) (* (pow eps 4) (pow (sqrt (/ -1 eps)) 3)))) (+ (* 1/2 (/ (pow x 2) (* (pow eps 2) (sqrt (/ -1 eps))))) (/ x eps)))))))
#s(approx (sqrt (- (* x x) eps)) #s(hole binary64 (* eps (+ (sqrt (/ -1 eps)) (* 1/2 (/ (pow x 2) (* (pow eps 2) (sqrt (/ -1 eps)))))))))
#s(approx (sqrt (- (* x x) eps)) #s(hole binary64 (* eps (+ (sqrt (/ -1 eps)) (+ (* -1/8 (/ (pow x 4) (* (pow eps 4) (pow (sqrt (/ -1 eps)) 3)))) (* 1/2 (/ (pow x 2) (* (pow eps 2) (sqrt (/ -1 eps))))))))))
#s(approx (sqrt (- (* x x) eps)) #s(hole binary64 (* eps (+ (sqrt (/ -1 eps)) (+ (* -1/8 (/ (pow x 4) (* (pow eps 4) (pow (sqrt (/ -1 eps)) 3)))) (+ (* 1/16 (/ (pow x 6) (* (pow eps 6) (pow (sqrt (/ -1 eps)) 5)))) (* 1/2 (/ (pow x 2) (* (pow eps 2) (sqrt (/ -1 eps)))))))))))
#s(approx (- (* x x) eps) #s(hole binary64 (* eps (- (/ (pow x 2) eps) 1))))
#s(approx (- x (sqrt (- (* x x) eps))) #s(hole binary64 (* -1 (* eps (sqrt (/ -1 eps))))))
#s(approx (- x (sqrt (- (* x x) eps))) #s(hole binary64 (* eps (- (/ x eps) (sqrt (/ -1 eps))))))
#s(approx (- x (sqrt (- (* x x) eps))) #s(hole binary64 (* eps (- (+ (* -1/2 (/ (pow x 2) (* (pow eps 2) (sqrt (/ -1 eps))))) (/ x eps)) (sqrt (/ -1 eps))))))
#s(approx (- x (sqrt (- (* x x) eps))) #s(hole binary64 (* eps (- (+ (* 1/8 (/ (pow x 4) (* (pow eps 4) (pow (sqrt (/ -1 eps)) 3)))) (/ x eps)) (+ (sqrt (/ -1 eps)) (* 1/2 (/ (pow x 2) (* (pow eps 2) (sqrt (/ -1 eps))))))))))
#s(approx (sqrt (/ -1 eps)) #s(hole binary64 (sqrt (/ -1 eps))))
#s(approx (/ (- (* x x) (- (* x x) eps)) (+ x (sqrt (- (* x x) eps)))) #s(hole binary64 (/ -1 (sqrt (/ -1 eps)))))
#s(approx (/ (- (* x x) (- (* x x) eps)) (+ x (sqrt (- (* x x) eps)))) #s(hole binary64 (- (* -1 (/ x (* eps (pow (sqrt (/ -1 eps)) 2)))) (/ 1 (sqrt (/ -1 eps))))))
#s(approx (/ (- (* x x) (- (* x x) eps)) (+ x (sqrt (- (* x x) eps)))) #s(hole binary64 (- (* -1 (/ (- (+ (* -1/2 (/ (pow x 2) (* eps (pow (sqrt (/ -1 eps)) 3)))) (/ (pow x 2) (* eps (pow (sqrt (/ -1 eps)) 3)))) (* -1 (/ x (pow (sqrt (/ -1 eps)) 2)))) eps)) (/ 1 (sqrt (/ -1 eps))))))
#s(approx (/ (- (* x x) (- (* x x) eps)) (+ x (sqrt (- (* x x) eps)))) #s(hole binary64 (- (* -1 (/ (- (* -1 (/ (- (+ (* -1 (/ (* x (+ (* -1/2 (/ (pow x 2) (pow (sqrt (/ -1 eps)) 3))) (/ (pow x 2) (pow (sqrt (/ -1 eps)) 3)))) (* eps (sqrt (/ -1 eps))))) (* 1/2 (/ (pow x 3) (* eps (pow (sqrt (/ -1 eps)) 4))))) (+ (* -1/2 (/ (pow x 2) (pow (sqrt (/ -1 eps)) 3))) (/ (pow x 2) (pow (sqrt (/ -1 eps)) 3)))) eps)) (* -1 (/ x (pow (sqrt (/ -1 eps)) 2)))) eps)) (/ 1 (sqrt (/ -1 eps))))))
#s(approx (+ x (sqrt (- (* x x) eps))) #s(hole binary64 (* -1 (* eps (+ (sqrt (/ -1 eps)) (* -1 (/ x eps)))))))
#s(approx (+ x (sqrt (- (* x x) eps))) #s(hole binary64 (* -1 (* eps (+ (sqrt (/ -1 eps)) (* -1 (/ (+ x (* -1/2 (/ (pow x 2) (* eps (sqrt (/ -1 eps)))))) eps)))))))
#s(approx (+ x (sqrt (- (* x x) eps))) #s(hole binary64 (* -1 (* eps (+ (sqrt (/ -1 eps)) (* -1 (/ (+ x (* -1 (/ (+ (* -1/8 (/ (pow x 4) (* (pow eps 2) (pow (sqrt (/ -1 eps)) 3)))) (* 1/2 (/ (pow x 2) (sqrt (/ -1 eps))))) eps))) eps)))))))
#s(approx (sqrt (- (* x x) eps)) #s(hole binary64 (* -1 (* eps (+ (sqrt (/ -1 eps)) (* 1/2 (/ (pow x 2) (* (pow eps 2) (sqrt (/ -1 eps))))))))))
#s(approx (sqrt (- (* x x) eps)) #s(hole binary64 (* -1 (* eps (+ (sqrt (/ -1 eps)) (+ (* -1/8 (/ (pow x 4) (* (pow eps 4) (pow (sqrt (/ -1 eps)) 3)))) (* 1/2 (/ (pow x 2) (* (pow eps 2) (sqrt (/ -1 eps)))))))))))
#s(approx (sqrt (- (* x x) eps)) #s(hole binary64 (* -1 (* eps (+ (sqrt (/ -1 eps)) (+ (* -1/8 (/ (pow x 4) (* (pow eps 4) (pow (sqrt (/ -1 eps)) 3)))) (+ (* 1/16 (/ (pow x 6) (* (pow eps 6) (pow (sqrt (/ -1 eps)) 5)))) (* 1/2 (/ (pow x 2) (* (pow eps 2) (sqrt (/ -1 eps))))))))))))
#s(approx (- (* x x) eps) #s(hole binary64 (* -1 (* eps (+ 1 (* -1 (/ (pow x 2) eps)))))))
#s(approx (- x (sqrt (- (* x x) eps))) #s(hole binary64 (* -1 (* eps (- (* -1 (/ x eps)) (sqrt (/ -1 eps)))))))
#s(approx (- x (sqrt (- (* x x) eps))) #s(hole binary64 (* -1 (* eps (- (* -1 (/ (+ x (* 1/2 (/ (pow x 2) (* eps (sqrt (/ -1 eps)))))) eps)) (sqrt (/ -1 eps)))))))
#s(approx (- x (sqrt (- (* x x) eps))) #s(hole binary64 (* -1 (* eps (- (* -1 (/ (+ x (* -1 (/ (- (* 1/8 (/ (pow x 4) (* (pow eps 2) (pow (sqrt (/ -1 eps)) 3)))) (* 1/2 (/ (pow x 2) (sqrt (/ -1 eps))))) eps))) eps)) (sqrt (/ -1 eps)))))))
#s(approx (* (neg eps) (- (/ (neg x) eps) (sqrt (/ -1 eps)))) #s(hole binary64 (* -1 (* eps (+ (* -1 (sqrt (/ -1 eps))) (* -1 (/ x eps)))))))
Outputs
(/.f64 (neg.f64 (neg.f64 #s(approx (- (* x x) (- (* x x) eps)) eps))) (neg.f64 (neg.f64 (+.f64 (sqrt.f64 (-.f64 (*.f64 x x) eps)) x))))
(/.f64 (neg.f64 #s(approx (- (* x x) (- (* x x) eps)) eps)) (neg.f64 (+.f64 (sqrt.f64 (-.f64 (*.f64 x x) eps)) x)))
(/.f64 #s(approx (- (* x x) (- (* x x) eps)) eps) (+.f64 (sqrt.f64 (-.f64 (*.f64 x x) eps)) x))
#s(approx (- (* x x) (- (* x x) eps)) eps)
eps
(/.f64 (neg.f64 (fma.f64 (*.f64 x x) x (*.f64 (sqrt.f64 (-.f64 (*.f64 x x) eps)) (-.f64 (*.f64 x x) eps)))) (neg.f64 (fma.f64 x x (-.f64 (-.f64 (*.f64 x x) eps) (*.f64 x (sqrt.f64 (-.f64 (*.f64 x x) eps)))))))
(/.f64 (fma.f64 (*.f64 x x) x (*.f64 (sqrt.f64 (-.f64 (*.f64 x x) eps)) (-.f64 (*.f64 x x) eps))) (fma.f64 x x (-.f64 (-.f64 (*.f64 x x) eps) (*.f64 x (sqrt.f64 (-.f64 (*.f64 x x) eps))))))
(/.f64 (neg.f64 (-.f64 (*.f64 x x) (-.f64 (*.f64 x x) eps))) (neg.f64 (-.f64 x (sqrt.f64 (-.f64 (*.f64 x x) eps)))))
(/.f64 (-.f64 (*.f64 x x) (-.f64 (*.f64 x x) eps)) (-.f64 x (sqrt.f64 (-.f64 (*.f64 x x) eps))))
(fma.f64 (pow.f64 (-.f64 (*.f64 x x) eps) #s(literal -1/2 binary64)) (-.f64 (*.f64 x x) eps) x)
(+.f64 (sqrt.f64 (-.f64 (*.f64 x x) eps)) x)
(+.f64 x (sqrt.f64 (-.f64 (*.f64 x x) eps)))
x
(*.f64 (pow.f64 (-.f64 (*.f64 x x) eps) #s(literal -1/2 binary64)) (-.f64 (*.f64 x x) eps))
(pow.f64 (-.f64 (*.f64 x x) eps) #s(literal 1/2 binary64))
(/.f64 (sqrt.f64 (-.f64 (*.f64 (*.f64 x x) (*.f64 x x)) (*.f64 eps eps))) (sqrt.f64 (fma.f64 x x eps)))
(/.f64 (sqrt.f64 (-.f64 (*.f64 (*.f64 (*.f64 x x) x) (*.f64 (*.f64 x x) x)) (*.f64 (*.f64 eps eps) eps))) (sqrt.f64 (fma.f64 (*.f64 x x) (*.f64 x x) (fma.f64 eps eps (*.f64 (*.f64 x x) eps)))))
(/.f64 #s(literal 1 binary64) (pow.f64 (-.f64 (*.f64 x x) eps) #s(literal -1/2 binary64)))
(sqrt.f64 (-.f64 (*.f64 x x) eps))
(exp.f64 (*.f64 (log.f64 (-.f64 (*.f64 x x) eps)) #s(literal 1/2 binary64)))
(*.f64 (fabs.f64 (sqrt.f64 (-.f64 (*.f64 x x) eps))) (fabs.f64 (sqrt.f64 (-.f64 (*.f64 x x) eps))))
(*.f64 (neg.f64 (sqrt.f64 (-.f64 (*.f64 x x) eps))) (neg.f64 (sqrt.f64 (-.f64 (*.f64 x x) eps))))
(*.f64 (sqrt.f64 (-.f64 (*.f64 x x) eps)) (sqrt.f64 (-.f64 (*.f64 x x) eps)))
(pow.f64 (*.f64 (-.f64 (*.f64 x x) eps) (-.f64 (*.f64 x x) eps)) #s(literal 1/2 binary64))
(pow.f64 (sqrt.f64 (-.f64 (*.f64 x x) eps)) #s(literal 2 binary64))
(pow.f64 (-.f64 (*.f64 x x) eps) #s(literal 1 binary64))
(/.f64 (neg.f64 (-.f64 (*.f64 (*.f64 x x) (*.f64 x x)) (*.f64 eps eps))) (neg.f64 (fma.f64 x x eps)))
(/.f64 (neg.f64 (-.f64 (*.f64 (*.f64 (*.f64 x x) x) (*.f64 (*.f64 x x) x)) (*.f64 (*.f64 eps eps) eps))) (neg.f64 (fma.f64 (*.f64 x x) (*.f64 x x) (fma.f64 eps eps (*.f64 (*.f64 x x) eps)))))
(/.f64 (-.f64 (*.f64 (*.f64 x x) (*.f64 x x)) (*.f64 eps eps)) (fma.f64 x x eps))
(/.f64 (-.f64 (*.f64 (*.f64 (*.f64 x x) x) (*.f64 (*.f64 x x) x)) (*.f64 (*.f64 eps eps) eps)) (fma.f64 (*.f64 x x) (*.f64 x x) (fma.f64 eps eps (*.f64 (*.f64 x x) eps))))
(sqrt.f64 (*.f64 (-.f64 (*.f64 x x) eps) (-.f64 (*.f64 x x) eps)))
(-.f64 (*.f64 x x) eps)
(*.f64 (exp.f64 (log.f64 x)) (exp.f64 (log.f64 x)))
(*.f64 (exp.f64 (log.f64 (fabs.f64 x))) (exp.f64 (log.f64 (fabs.f64 x))))
(*.f64 (pow.f64 (neg.f64 x) #s(literal 1 binary64)) (pow.f64 (neg.f64 x) #s(literal 1 binary64)))
(*.f64 (neg.f64 (neg.f64 x)) (neg.f64 (neg.f64 x)))
(*.f64 (neg.f64 (fabs.f64 x)) (neg.f64 (fabs.f64 x)))
(*.f64 (fabs.f64 x) (fabs.f64 x))
(*.f64 (neg.f64 x) (neg.f64 x))
(*.f64 x x)
(pow.f64 (exp.f64 (log.f64 x)) #s(literal 2 binary64))
(pow.f64 (exp.f64 (log.f64 (fabs.f64 x))) #s(literal 2 binary64))
(pow.f64 (fabs.f64 x) #s(literal 2 binary64))
(pow.f64 (*.f64 (*.f64 x x) (*.f64 x x)) #s(literal 1/2 binary64))
(pow.f64 (*.f64 x x) #s(literal 1 binary64))
(pow.f64 (neg.f64 x) #s(literal 2 binary64))
(pow.f64 x #s(literal 2 binary64))
(/.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (*.f64 x x)))
(sqrt.f64 (*.f64 (*.f64 x x) (*.f64 x x)))
(fabs.f64 (*.f64 x x))
(exp.f64 (*.f64 (*.f64 (log.f64 x) #s(literal 2 binary64)) #s(literal 1 binary64)))
(exp.f64 (*.f64 (log.f64 (*.f64 x x)) #s(literal 1 binary64)))
(exp.f64 (*.f64 (log.f64 x) #s(literal 2 binary64)))
(exp.f64 (*.f64 (log.f64 (fabs.f64 x)) #s(literal 2 binary64)))
(+.f64 (cosh.f64 (*.f64 (log.f64 (fabs.f64 x)) #s(literal 2 binary64))) (sinh.f64 (*.f64 (log.f64 (fabs.f64 x)) #s(literal 2 binary64))))
(+.f64 (cosh.f64 (*.f64 (log.f64 x) #s(literal 2 binary64))) (sinh.f64 (*.f64 (log.f64 x) #s(literal 2 binary64))))
#s(approx (- x (sqrt (- (* x x) eps))) (sqrt.f64 (neg.f64 eps)))
(*.f64 (pow.f64 (sqrt.f64 #s(literal -1 binary64)) #s(literal 1 binary64)) (pow.f64 (sqrt.f64 eps) #s(literal 1 binary64)))
(*.f64 (sqrt.f64 eps) (sqrt.f64 #s(literal -1 binary64)))
(*.f64 (sqrt.f64 #s(literal -1 binary64)) (sqrt.f64 eps))
(*.f64 (sqrt.f64 (/.f64 #s(literal -1 binary64) eps)) (neg.f64 eps))
(pow.f64 (/.f64 #s(literal -1 binary64) eps) #s(literal -1/2 binary64))
(pow.f64 (sqrt.f64 (neg.f64 eps)) #s(literal 1 binary64))
(pow.f64 (sqrt.f64 (/.f64 #s(literal -1 binary64) eps)) #s(literal -1 binary64))
(pow.f64 (neg.f64 eps) #s(literal 1/2 binary64))
(/.f64 #s(literal 1 binary64) (neg.f64 (neg.f64 (sqrt.f64 (/.f64 #s(literal -1 binary64) eps)))))
(/.f64 #s(literal 1 binary64) (sqrt.f64 (/.f64 #s(literal -1 binary64) eps)))
(/.f64 #s(literal -1 binary64) (neg.f64 (sqrt.f64 (/.f64 #s(literal -1 binary64) eps))))
(sqrt.f64 (neg.f64 eps))
(exp.f64 (*.f64 (log.f64 (sqrt.f64 (/.f64 #s(literal -1 binary64) eps))) #s(literal -1 binary64)))
(exp.f64 (*.f64 (log.f64 (neg.f64 eps)) #s(literal 1/2 binary64)))
(exp.f64 (*.f64 (log.f64 (sqrt.f64 (neg.f64 eps))) #s(literal 1 binary64)))
(*.f64 (fabs.f64 (sqrt.f64 (neg.f64 eps))) (fabs.f64 (sqrt.f64 (neg.f64 eps))))
(*.f64 (exp.f64 (log.f64 (sqrt.f64 (neg.f64 eps)))) (exp.f64 (log.f64 (sqrt.f64 (neg.f64 eps)))))
(*.f64 (pow.f64 (sqrt.f64 #s(literal -1 binary64)) #s(literal 2 binary64)) (pow.f64 (sqrt.f64 eps) #s(literal 2 binary64)))
(*.f64 (neg.f64 (sqrt.f64 (neg.f64 eps))) (neg.f64 (sqrt.f64 (neg.f64 eps))))
(*.f64 (sqrt.f64 eps) (sqrt.f64 eps))
(*.f64 #s(literal 1 binary64) (neg.f64 eps))
(*.f64 (sqrt.f64 (neg.f64 eps)) (sqrt.f64 (neg.f64 eps)))
(*.f64 #s(literal -1 binary64) eps)
(*.f64 (neg.f64 eps) #s(literal 1 binary64))
(*.f64 eps #s(literal -1 binary64))
(pow.f64 (exp.f64 (log.f64 (sqrt.f64 (neg.f64 eps)))) #s(literal 2 binary64))
(pow.f64 (/.f64 #s(literal -1 binary64) eps) #s(literal -1 binary64))
(pow.f64 (*.f64 eps eps) #s(literal 1/2 binary64))
(pow.f64 (sqrt.f64 (neg.f64 eps)) #s(literal 2 binary64))
(pow.f64 (sqrt.f64 (/.f64 #s(literal -1 binary64) eps)) #s(literal -2 binary64))
(pow.f64 (neg.f64 eps) #s(literal 1 binary64))
(/.f64 #s(literal 1 binary64) (/.f64 #s(literal -1 binary64) eps))
(neg.f64 eps)
(sqrt.f64 (*.f64 eps eps))
(fabs.f64 (neg.f64 (neg.f64 eps)))
(fabs.f64 (neg.f64 eps))
(fabs.f64 eps)
(exp.f64 (/.f64 (*.f64 (log.f64 eps) #s(literal 2 binary64)) #s(literal 2 binary64)))
(exp.f64 (*.f64 (log.f64 (neg.f64 eps)) #s(literal 1 binary64)))
(exp.f64 (*.f64 (log.f64 (sqrt.f64 (neg.f64 eps))) #s(literal 2 binary64)))
(+.f64 (cosh.f64 (*.f64 (log.f64 (sqrt.f64 (neg.f64 eps))) #s(literal 2 binary64))) (sinh.f64 (*.f64 (log.f64 (sqrt.f64 (neg.f64 eps))) #s(literal 2 binary64))))
(/.f64 (neg.f64 (-.f64 (*.f64 x x) #s(approx (- (* x x) eps) (neg.f64 eps)))) (neg.f64 (+.f64 x (sqrt.f64 #s(approx (- (* x x) eps) (neg.f64 eps))))))
(/.f64 (neg.f64 (-.f64 (*.f64 (*.f64 x x) x) (*.f64 (sqrt.f64 #s(approx (- (* x x) eps) (neg.f64 eps))) #s(approx (- (* x x) eps) (neg.f64 eps))))) (neg.f64 (fma.f64 x x (+.f64 #s(approx (- (* x x) eps) (neg.f64 eps)) (*.f64 x (sqrt.f64 #s(approx (- (* x x) eps) (neg.f64 eps))))))))
(/.f64 (-.f64 (*.f64 x x) #s(approx (- (* x x) eps) (neg.f64 eps))) (+.f64 x (sqrt.f64 #s(approx (- (* x x) eps) (neg.f64 eps)))))
(/.f64 (-.f64 (*.f64 (*.f64 x x) x) (*.f64 (sqrt.f64 #s(approx (- (* x x) eps) (neg.f64 eps))) #s(approx (- (* x x) eps) (neg.f64 eps)))) (fma.f64 x x (+.f64 #s(approx (- (* x x) eps) (neg.f64 eps)) (*.f64 x (sqrt.f64 #s(approx (- (* x x) eps) (neg.f64 eps)))))))
(-.f64 x (sqrt.f64 #s(approx (- (* x x) eps) (neg.f64 eps))))
(*.f64 (pow.f64 #s(approx (- (* x x) eps) (neg.f64 eps)) #s(literal -1/2 binary64)) #s(approx (- (* x x) eps) (neg.f64 eps)))
(pow.f64 #s(approx (- (* x x) eps) (neg.f64 eps)) #s(literal 1/2 binary64))
(/.f64 #s(literal 1 binary64) (pow.f64 #s(approx (- (* x x) eps) (neg.f64 eps)) #s(literal -1/2 binary64)))
(sqrt.f64 #s(approx (- (* x x) eps) (neg.f64 eps)))
(exp.f64 (*.f64 (log.f64 #s(approx (- (* x x) eps) (neg.f64 eps))) #s(literal 1/2 binary64)))
(*.f64 (fabs.f64 (sqrt.f64 #s(approx (- (* x x) eps) (neg.f64 eps)))) (fabs.f64 (sqrt.f64 #s(approx (- (* x x) eps) (neg.f64 eps)))))
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(*.f64 (sqrt.f64 #s(approx (- (* x x) eps) (neg.f64 eps))) (sqrt.f64 #s(approx (- (* x x) eps) (neg.f64 eps))))
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#s(approx (- x (sqrt (- (* x x) eps))) (*.f64 (-.f64 (/.f64 (neg.f64 x) eps) (sqrt.f64 (/.f64 #s(literal -1 binary64) eps))) (neg.f64 eps)))
#s(approx (- x (sqrt (- (* x x) eps))) (*.f64 (neg.f64 eps) (-.f64 (neg.f64 (/.f64 (fma.f64 (/.f64 (*.f64 x x) (*.f64 (sqrt.f64 (/.f64 #s(literal -1 binary64) eps)) eps)) #s(literal 1/2 binary64) x) eps)) (sqrt.f64 (/.f64 #s(literal -1 binary64) eps)))))
#s(approx (- x (sqrt (- (* x x) eps))) (*.f64 (neg.f64 eps) (-.f64 (neg.f64 (/.f64 (+.f64 (neg.f64 (/.f64 (fma.f64 (/.f64 (*.f64 (*.f64 x x) (*.f64 x x)) (*.f64 (/.f64 #s(literal 1 binary64) (*.f64 (sqrt.f64 (neg.f64 eps)) (neg.f64 eps))) (*.f64 eps eps))) #s(literal 1/8 binary64) (*.f64 #s(literal -1/2 binary64) (/.f64 (*.f64 x x) (sqrt.f64 (/.f64 #s(literal -1 binary64) eps))))) eps)) x) eps)) (sqrt.f64 (/.f64 #s(literal -1 binary64) eps)))))
#s(approx (* (neg eps) (- (/ (neg x) eps) (sqrt (/ -1 eps)))) (*.f64 (neg.f64 eps) (+.f64 (neg.f64 (sqrt.f64 (/.f64 #s(literal -1 binary64) eps))) (/.f64 (neg.f64 x) eps))))

eval77.0ms (2.6%)

Memory
1.7MiB live, 56.8MiB allocated; 74ms collecting garbage
Compiler

Compiled 3 447 to 1 335 computations (61.3% saved)

prune12.0ms (0.4%)

Memory
23.6MiB live, 23.6MiB allocated; 0ms collecting garbage
Pruning

15 alts after pruning (5 fresh and 10 done)

PrunedKeptTotal
New2844288
Fresh112
Picked235
Done178
Total28815303
Accuracy
100.0%
Counts
303 → 15
Alt Table
Click to see full alt table
StatusAccuracyProgram
87.0%
(/.f64 #s(approx (- (* x x) (- (* x x) eps)) eps) (/.f64 (fma.f64 (*.f64 x x) x (*.f64 (sqrt.f64 (-.f64 (*.f64 x x) eps)) (-.f64 (*.f64 x x) eps))) (fma.f64 x x (-.f64 (-.f64 (*.f64 x x) eps) (*.f64 x (sqrt.f64 (-.f64 (*.f64 x x) eps)))))))
✓99.5%
(/.f64 #s(approx (- (* x x) (- (* x x) eps)) eps) (+.f64 x (sqrt.f64 (-.f64 (*.f64 x x) eps))))
59.5%
(/.f64 #s(approx (- (* x x) (- (* x x) eps)) eps) #s(approx (+ x (sqrt (- (* x x) eps))) (+.f64 (sqrt.f64 (neg.f64 eps)) x)))
44.7%
(/.f64 #s(approx (- (* x x) (- (* x x) eps)) eps) #s(approx (+ x (sqrt (- (* x x) eps))) (+.f64 x x)))
✓61.5%
(-.f64 x (sqrt.f64 (-.f64 (*.f64 x x) eps)))
✓61.5%
(-.f64 x (sqrt.f64 #s(approx (- (* x x) eps) (fma.f64 x x (neg.f64 eps)))))
✓61.5%
(-.f64 x (sqrt.f64 #s(approx (- (* x x) eps) (*.f64 (-.f64 (/.f64 (*.f64 x x) eps) #s(literal 1 binary64)) eps))))
✓57.1%
(-.f64 x (sqrt.f64 #s(approx (- (* x x) eps) (neg.f64 eps))))
✓4.2%
(-.f64 x #s(approx (sqrt (- (* x x) eps)) (fabs.f64 x)))
42.3%
#s(approx (- x (sqrt (- (* x x) eps))) (/.f64 #s(approx (+ (* (/ (* eps eps) (* x x)) 1/8) (* 1/2 eps)) (*.f64 (fma.f64 (/.f64 eps (*.f64 x x)) #s(literal 1/8 binary64) #s(literal 1/2 binary64)) eps)) x))
✓3.7%
#s(approx (- x (sqrt (- (* x x) eps))) (+.f64 x x))
✓1.7%
#s(approx (- x (sqrt (- (* x x) eps))) (sqrt.f64 (neg.f64 eps)))
3.7%
#s(approx (- x (sqrt (- (* x x) eps))) (sqrt.f64 (fabs.f64 eps)))
✓56.9%
#s(approx (- x (sqrt (- (* x x) eps))) (neg.f64 (sqrt.f64 (neg.f64 eps))))
✓56.9%
#s(approx (- x (sqrt (- (* x x) eps))) #s(approx (* (neg eps) (- (/ (neg x) eps) (sqrt (/ -1 eps)))) (fma.f64 (sqrt.f64 (/.f64 #s(literal -1 binary64) eps)) eps x)))
Compiler

Compiled 457 to 313 computations (31.5% saved)

regimes26.0ms (0.9%)

Memory
-15.9MiB live, 31.4MiB allocated; 8ms collecting garbage
Counts
24 → 1
Calls
Call 1
Inputs
#s(approx (- x (sqrt (- (* x x) eps))) (+.f64 x x))
#s(approx (- x (sqrt (- (* x x) eps))) (sqrt.f64 (neg.f64 eps)))
#s(approx (- x (sqrt (- (* x x) eps))) (sqrt.f64 (fabs.f64 eps)))
#s(approx (- x (sqrt (- (* x x) eps))) (neg.f64 (sqrt.f64 (neg.f64 eps))))
(-.f64 x #s(approx (sqrt (- (* x x) eps)) (fabs.f64 x)))
(-.f64 x (sqrt.f64 #s(approx (- (* x x) eps) (neg.f64 eps))))
(-.f64 x (sqrt.f64 #s(approx (- (* x x) eps) (fabs.f64 eps))))
(/.f64 #s(approx (- (* x x) (- (* x x) eps)) eps) #s(approx (+ x (sqrt (- (* x x) eps))) (+.f64 x x)))
#s(approx (- x (sqrt (- (* x x) eps))) (/.f64 eps (sqrt.f64 (neg.f64 eps))))
#s(approx (- x (sqrt (- (* x x) eps))) (*.f64 (/.f64 eps x) #s(literal 1/2 binary64)))
(/.f64 #s(approx (- (* x x) (- (* x x) eps)) eps) #s(approx (+ x (sqrt (- (* x x) eps))) (+.f64 (sqrt.f64 (neg.f64 eps)) x)))
(-.f64 x (sqrt.f64 (-.f64 (*.f64 x x) eps)))
#s(approx (- x (sqrt (- (* x x) eps))) #s(approx (* (neg eps) (- (/ (neg x) eps) (sqrt (/ -1 eps)))) (fma.f64 (sqrt.f64 (/.f64 #s(literal -1 binary64) eps)) eps x)))
(-.f64 x (sqrt.f64 #s(approx (- (* x x) eps) (fma.f64 x x (neg.f64 eps)))))
(/.f64 #s(approx (- (* x x) (- (* x x) eps)) eps) (+.f64 x (sqrt.f64 (-.f64 (*.f64 x x) eps))))
#s(approx (- x (sqrt (- (* x x) eps))) (*.f64 (neg.f64 eps) (-.f64 (/.f64 (neg.f64 x) eps) (sqrt.f64 (/.f64 #s(literal -1 binary64) eps)))))
(-.f64 x (sqrt.f64 #s(approx (- (* x x) eps) (*.f64 (-.f64 (/.f64 (*.f64 x x) eps) #s(literal 1 binary64)) eps))))
#s(approx (- x (sqrt (- (* x x) eps))) (/.f64 #s(approx (+ (* (/ (* eps eps) (* x x)) 1/8) (* 1/2 eps)) (*.f64 (fma.f64 (/.f64 eps (*.f64 x x)) #s(literal 1/8 binary64) #s(literal 1/2 binary64)) eps)) x))
#s(approx (- x (sqrt (- (* x x) eps))) (/.f64 (fma.f64 (/.f64 (*.f64 eps eps) (*.f64 x x)) #s(literal 1/8 binary64) (*.f64 #s(literal 1/2 binary64) eps)) x))
(/.f64 (-.f64 (*.f64 x x) (-.f64 (*.f64 x x) eps)) (+.f64 x (sqrt.f64 (-.f64 (*.f64 x x) eps))))
#s(approx (- x (sqrt (- (* x x) eps))) (/.f64 (-.f64 (/.f64 (*.f64 #s(literal 1/16 binary64) (*.f64 (*.f64 eps eps) eps)) (*.f64 (*.f64 x x) (*.f64 x x))) (fma.f64 (/.f64 (*.f64 eps eps) (*.f64 x x)) #s(literal -1/8 binary64) (*.f64 #s(literal -1/2 binary64) eps))) x))
(/.f64 #s(approx (- (* x x) (- (* x x) eps)) eps) (/.f64 (fma.f64 (*.f64 x x) x (*.f64 (sqrt.f64 (-.f64 (*.f64 x x) eps)) (-.f64 (*.f64 x x) eps))) (fma.f64 x x (-.f64 (-.f64 (*.f64 x x) eps) (*.f64 x (sqrt.f64 (-.f64 (*.f64 x x) eps)))))))
#s(approx (- x (sqrt (- (* x x) eps))) (/.f64 (-.f64 (fma.f64 #s(literal 1/2 binary64) eps (neg.f64 (/.f64 (*.f64 (*.f64 (*.f64 eps eps) (*.f64 eps eps)) #s(literal -5/128 binary64)) (*.f64 (*.f64 (*.f64 x x) (*.f64 x x)) (*.f64 x x))))) (fma.f64 #s(literal -1/16 binary64) (/.f64 (*.f64 (*.f64 eps eps) eps) (*.f64 (*.f64 x x) (*.f64 x x))) (/.f64 (*.f64 #s(literal -1/8 binary64) (*.f64 eps eps)) (*.f64 x x)))) x))
#s(approx (- x (sqrt (- (* x x) eps))) (/.f64 (-.f64 (*.f64 (/.f64 (*.f64 (*.f64 (*.f64 eps eps) (*.f64 eps eps)) #s(literal 5/64 binary64)) (*.f64 (*.f64 (*.f64 x x) x) (*.f64 (*.f64 x x) x))) #s(literal 1/2 binary64)) (fma.f64 #s(literal -1/2 binary64) eps (fma.f64 #s(literal -1/16 binary64) (/.f64 (*.f64 (*.f64 eps eps) eps) (*.f64 (*.f64 x x) (*.f64 x x))) (/.f64 (*.f64 #s(literal -1/8 binary64) (*.f64 eps eps)) (*.f64 x x))))) x))
Outputs
(/.f64 #s(approx (- (* x x) (- (* x x) eps)) eps) (+.f64 x (sqrt.f64 (-.f64 (*.f64 x x) eps))))
Calls

3 calls:

12.0ms
eps
7.0ms
x
6.0ms
(-.f64 x (sqrt.f64 (-.f64 (*.f64 x x) eps)))
Results
AccuracySegmentsBranch
99.5%1(-.f64 x (sqrt.f64 (-.f64 (*.f64 x x) eps)))
99.5%1x
99.5%1eps
Compiler

Compiled 8 to 10 computations (-25% saved)

regimes13.0ms (0.5%)

Memory
14.7MiB live, 14.7MiB allocated; 0ms collecting garbage
Counts
14 → 2
Calls
Call 1
Inputs
#s(approx (- x (sqrt (- (* x x) eps))) (+.f64 x x))
#s(approx (- x (sqrt (- (* x x) eps))) (sqrt.f64 (neg.f64 eps)))
#s(approx (- x (sqrt (- (* x x) eps))) (sqrt.f64 (fabs.f64 eps)))
#s(approx (- x (sqrt (- (* x x) eps))) (neg.f64 (sqrt.f64 (neg.f64 eps))))
(-.f64 x #s(approx (sqrt (- (* x x) eps)) (fabs.f64 x)))
(-.f64 x (sqrt.f64 #s(approx (- (* x x) eps) (neg.f64 eps))))
(-.f64 x (sqrt.f64 #s(approx (- (* x x) eps) (fabs.f64 eps))))
(/.f64 #s(approx (- (* x x) (- (* x x) eps)) eps) #s(approx (+ x (sqrt (- (* x x) eps))) (+.f64 x x)))
#s(approx (- x (sqrt (- (* x x) eps))) (/.f64 eps (sqrt.f64 (neg.f64 eps))))
#s(approx (- x (sqrt (- (* x x) eps))) (*.f64 (/.f64 eps x) #s(literal 1/2 binary64)))
(/.f64 #s(approx (- (* x x) (- (* x x) eps)) eps) #s(approx (+ x (sqrt (- (* x x) eps))) (+.f64 (sqrt.f64 (neg.f64 eps)) x)))
(-.f64 x (sqrt.f64 (-.f64 (*.f64 x x) eps)))
#s(approx (- x (sqrt (- (* x x) eps))) #s(approx (* (neg eps) (- (/ (neg x) eps) (sqrt (/ -1 eps)))) (fma.f64 (sqrt.f64 (/.f64 #s(literal -1 binary64) eps)) eps x)))
(-.f64 x (sqrt.f64 #s(approx (- (* x x) eps) (fma.f64 x x (neg.f64 eps)))))
Outputs
(-.f64 x (sqrt.f64 (-.f64 (*.f64 x x) eps)))
(/.f64 #s(approx (- (* x x) (- (* x x) eps)) eps) #s(approx (+ x (sqrt (- (* x x) eps))) (+.f64 x x)))
Calls

3 calls:

4.0ms
x
4.0ms
eps
4.0ms
(-.f64 x (sqrt.f64 (-.f64 (*.f64 x x) eps)))
Results
AccuracySegmentsBranch
98.8%2(-.f64 x (sqrt.f64 (-.f64 (*.f64 x x) eps)))
90.1%2x
83.7%2eps
Compiler

Compiled 8 to 10 computations (-25% saved)

regimes4.0ms (0.1%)

Memory
5.4MiB live, 5.4MiB allocated; 0ms collecting garbage
Counts
11 → 2
Calls
Call 1
Inputs
#s(approx (- x (sqrt (- (* x x) eps))) (+.f64 x x))
#s(approx (- x (sqrt (- (* x x) eps))) (sqrt.f64 (neg.f64 eps)))
#s(approx (- x (sqrt (- (* x x) eps))) (sqrt.f64 (fabs.f64 eps)))
#s(approx (- x (sqrt (- (* x x) eps))) (neg.f64 (sqrt.f64 (neg.f64 eps))))
(-.f64 x #s(approx (sqrt (- (* x x) eps)) (fabs.f64 x)))
(-.f64 x (sqrt.f64 #s(approx (- (* x x) eps) (neg.f64 eps))))
(-.f64 x (sqrt.f64 #s(approx (- (* x x) eps) (fabs.f64 eps))))
(/.f64 #s(approx (- (* x x) (- (* x x) eps)) eps) #s(approx (+ x (sqrt (- (* x x) eps))) (+.f64 x x)))
#s(approx (- x (sqrt (- (* x x) eps))) (/.f64 eps (sqrt.f64 (neg.f64 eps))))
#s(approx (- x (sqrt (- (* x x) eps))) (*.f64 (/.f64 eps x) #s(literal 1/2 binary64)))
(/.f64 #s(approx (- (* x x) (- (* x x) eps)) eps) #s(approx (+ x (sqrt (- (* x x) eps))) (+.f64 (sqrt.f64 (neg.f64 eps)) x)))
Outputs
(-.f64 x (sqrt.f64 #s(approx (- (* x x) eps) (neg.f64 eps))))
(/.f64 #s(approx (- (* x x) (- (* x x) eps)) eps) #s(approx (+ x (sqrt (- (* x x) eps))) (+.f64 x x)))
Calls

1 calls:

3.0ms
(-.f64 x (sqrt.f64 (-.f64 (*.f64 x x) eps)))
Results
AccuracySegmentsBranch
97.3%2(-.f64 x (sqrt.f64 (-.f64 (*.f64 x x) eps)))
Compiler

Compiled 6 to 6 computations (0% saved)

regimes10.0ms (0.3%)

Memory
-34.0MiB live, 12.5MiB allocated; 3ms collecting garbage
Counts
7 → 1
Calls
Call 1
Inputs
#s(approx (- x (sqrt (- (* x x) eps))) (+.f64 x x))
#s(approx (- x (sqrt (- (* x x) eps))) (sqrt.f64 (neg.f64 eps)))
#s(approx (- x (sqrt (- (* x x) eps))) (sqrt.f64 (fabs.f64 eps)))
#s(approx (- x (sqrt (- (* x x) eps))) (neg.f64 (sqrt.f64 (neg.f64 eps))))
(-.f64 x #s(approx (sqrt (- (* x x) eps)) (fabs.f64 x)))
(-.f64 x (sqrt.f64 #s(approx (- (* x x) eps) (neg.f64 eps))))
(-.f64 x (sqrt.f64 #s(approx (- (* x x) eps) (fabs.f64 eps))))
Outputs
(-.f64 x (sqrt.f64 #s(approx (- (* x x) eps) (fabs.f64 eps))))
Calls

3 calls:

5.0ms
x
3.0ms
eps
2.0ms
(-.f64 x (sqrt.f64 (-.f64 (*.f64 x x) eps)))
Results
AccuracySegmentsBranch
58.7%1eps
58.7%1x
58.7%1(-.f64 x (sqrt.f64 (-.f64 (*.f64 x x) eps)))
Compiler

Compiled 8 to 10 computations (-25% saved)

regimes7.0ms (0.3%)

Memory
13.1MiB live, 13.1MiB allocated; 0ms collecting garbage
Counts
6 → 2
Calls
Call 1
Inputs
#s(approx (- x (sqrt (- (* x x) eps))) (+.f64 x x))
#s(approx (- x (sqrt (- (* x x) eps))) (sqrt.f64 (neg.f64 eps)))
#s(approx (- x (sqrt (- (* x x) eps))) (sqrt.f64 (fabs.f64 eps)))
#s(approx (- x (sqrt (- (* x x) eps))) (neg.f64 (sqrt.f64 (neg.f64 eps))))
(-.f64 x #s(approx (sqrt (- (* x x) eps)) (fabs.f64 x)))
(-.f64 x (sqrt.f64 #s(approx (- (* x x) eps) (neg.f64 eps))))
Outputs
(-.f64 x (sqrt.f64 #s(approx (- (* x x) eps) (neg.f64 eps))))
#s(approx (- x (sqrt (- (* x x) eps))) (sqrt.f64 (fabs.f64 eps)))
Calls

3 calls:

2.0ms
x
2.0ms
eps
2.0ms
(-.f64 x (sqrt.f64 (-.f64 (*.f64 x x) eps)))
Results
AccuracySegmentsBranch
59.1%2eps
59.1%2(-.f64 x (sqrt.f64 (-.f64 (*.f64 x x) eps)))
57.1%1x
Compiler

Compiled 8 to 10 computations (-25% saved)

regimes4.0ms (0.1%)

Memory
6.1MiB live, 6.1MiB allocated; 0ms collecting garbage
Counts
5 → 2
Calls
Call 1
Inputs
#s(approx (- x (sqrt (- (* x x) eps))) (+.f64 x x))
#s(approx (- x (sqrt (- (* x x) eps))) (sqrt.f64 (neg.f64 eps)))
#s(approx (- x (sqrt (- (* x x) eps))) (sqrt.f64 (fabs.f64 eps)))
#s(approx (- x (sqrt (- (* x x) eps))) (neg.f64 (sqrt.f64 (neg.f64 eps))))
(-.f64 x #s(approx (sqrt (- (* x x) eps)) (fabs.f64 x)))
Outputs
#s(approx (- x (sqrt (- (* x x) eps))) (neg.f64 (sqrt.f64 (neg.f64 eps))))
#s(approx (- x (sqrt (- (* x x) eps))) (sqrt.f64 (fabs.f64 eps)))
Calls

2 calls:

2.0ms
eps
2.0ms
(-.f64 x (sqrt.f64 (-.f64 (*.f64 x x) eps)))
Results
AccuracySegmentsBranch
58.9%2eps
56.9%1(-.f64 x (sqrt.f64 (-.f64 (*.f64 x x) eps)))
Compiler

Compiled 7 to 8 computations (-14.3% saved)

regimes5.0ms (0.2%)

Memory
7.1MiB live, 7.1MiB allocated; 0ms collecting garbage
Counts
3 → 1
Calls
Call 1
Inputs
#s(approx (- x (sqrt (- (* x x) eps))) (+.f64 x x))
#s(approx (- x (sqrt (- (* x x) eps))) (sqrt.f64 (neg.f64 eps)))
#s(approx (- x (sqrt (- (* x x) eps))) (sqrt.f64 (fabs.f64 eps)))
Outputs
#s(approx (- x (sqrt (- (* x x) eps))) (sqrt.f64 (fabs.f64 eps)))
Calls

3 calls:

1.0ms
x
1.0ms
eps
1.0ms
(-.f64 x (sqrt.f64 (-.f64 (*.f64 x x) eps)))
Results
AccuracySegmentsBranch
3.7%1(-.f64 x (sqrt.f64 (-.f64 (*.f64 x x) eps)))
3.7%1x
3.7%1eps
Compiler

Compiled 8 to 10 computations (-25% saved)

regimes4.0ms (0.1%)

Memory
6.4MiB live, 6.4MiB allocated; 0ms collecting garbage
Accuracy

Total -1.3b remaining (-2.1%)

Threshold costs -1.3b (-2.1%)

Counts
2 → 1
Calls
Call 1
Inputs
#s(approx (- x (sqrt (- (* x x) eps))) (+.f64 x x))
#s(approx (- x (sqrt (- (* x x) eps))) (sqrt.f64 (neg.f64 eps)))
Outputs
#s(approx (- x (sqrt (- (* x x) eps))) (+.f64 x x))
Calls

3 calls:

1.0ms
eps
1.0ms
x
1.0ms
(-.f64 x (sqrt.f64 (-.f64 (*.f64 x x) eps)))
Results
AccuracySegmentsBranch
3.7%1x
3.7%1(-.f64 x (sqrt.f64 (-.f64 (*.f64 x x) eps)))
3.7%1eps
Compiler

Compiled 8 to 10 computations (-25% saved)

bsearch0.0ms (0%)

Memory
0.4MiB live, 0.4MiB allocated; 0ms collecting garbage
Algorithm
1×left-value
Steps
TimeLeftRight
0.0ms
-3.2945112864892916e-154
0.0
Compiler

Compiled 9 to 11 computations (-22.2% saved)

bsearch0.0ms (0%)

Memory
0.2MiB live, 0.2MiB allocated; 0ms collecting garbage
Algorithm
1×left-value
Steps
TimeLeftRight
0.0ms
-3.2945112864892916e-154
0.0
Compiler

Compiled 9 to 11 computations (-22.2% saved)

bsearch0.0ms (0%)

Memory
0.2MiB live, 0.2MiB allocated; 0ms collecting garbage
Algorithm
1×left-value
Steps
TimeLeftRight
0.0ms
-3.2945112864892916e-154
0.0
Compiler

Compiled 9 to 11 computations (-22.2% saved)

bsearch19.0ms (0.6%)

Memory
-32.3MiB live, 14.2MiB allocated; 4ms collecting garbage
Algorithm
1×binary-search
Stop Event
1×narrow-enough
Steps
TimeLeftRight
17.0ms
-1.0853804616805327e-307
2.2765273989176625e-308
Samples
8.0ms52×2valid
3.0ms34×1valid
1.0ms30×0invalid
1.0ms26×0valid
Compiler

Compiled 144 to 158 computations (-9.7% saved)

Precisions
Click to see histograms. Total time spent on operations: 9.0ms
ival-sub!: 3.0ms (33.4% of total)
adjust: 2.0ms (22.3% of total)
ival-sqrt: 2.0ms (22.3% of total)
ival-mult!: 1.0ms (11.1% of total)

derivations247.0ms (8.4%)

Memory
0.6MiB live, 141.9MiB allocated; 15ms collecting garbage
Stop Event
1×fuel
Compiler

Compiled 66 to 40 computations (39.4% saved)

preprocess84.0ms (2.9%)

Memory
24.0MiB live, 119.2MiB allocated; 14ms collecting garbage
Compiler

Compiled 79 to 53 computations (32.9% saved)

end0.0ms (0%)

Memory
0.0MiB live, 0.0MiB allocated; 0ms collecting garbage

Profiling

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