Exception for ENA, Section 1.4, Exercise 4d

\[\left(0 \leq x \land x \leq 1000000000\right) \land \left(-1 \leq \varepsilon \land \varepsilon \leq 1\right)\]

Math

\[x - \sqrt{x \cdot x - \varepsilon} \]

FPCore

(FPCore (x eps) :precision binary64 (- x (sqrt (- (* x x) eps))))

C

double code(double x, double eps) {
	return x - sqrt(((x * x) - eps));
}

Fortran

real(8) function code(x, eps)
    real(8), intent (in) :: x
    real(8), intent (in) :: eps
    code = x - sqrt(((x * x) - eps))
end function

Java

public static double code(double x, double eps) {
	return x - Math.sqrt(((x * x) - eps));
}

Python

def code(x, eps):
	return x - math.sqrt(((x * x) - eps))

Julia

function code(x, eps)
	return Float64(x - sqrt(Float64(Float64(x * x) - eps)))
end

MATLAB

function tmp = code(x, eps)
	tmp = x - sqrt(((x * x) - eps));
end

Wolfram

code[x_, eps_] := N[(x - N[Sqrt[N[(N[(x * x), $MachinePrecision] - eps), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]

Reproduce

Please include this information when filing a bug report:

herbie shell --seed 2022203 
(FPCore (x eps)
  :name "ENA, Section 1.4, Exercise 4d"
  :precision binary64
  :pre (and (and (<= 0.0 x) (<= x 1000000000.0)) (and (<= -1.0 eps) (<= eps 1.0)))

  :herbie-target
  (/ eps (+ x (sqrt (- (* x x) eps))))

  (- x (sqrt (- (* x x) eps))))

Backtrace

hash-ref: no value found for key key: '~		L	C
get-parametric-operator	/data/pavpan/nightlies/herbie/enumo-rat/src/syntax/syntax.rkt	218	0
f336	.../match/compiler.rkt	548	40
expand-parametric	/data/pavpan/nightlies/herbie/enumo-rat/src/syntax/sugar.rkt	62	0
(unnamed)	/data/pavpan/nightlies/herbie/enumo-rat/src/syntax/rules.rkt	176	8
generate-rules-for	/data/pavpan/nightlies/herbie/enumo-rat/src/syntax/rules.rkt	161	0
generate-missing-rules	/data/pavpan/nightlies/herbie/enumo-rat/src/syntax/rules.rkt	187	0
(unnamed)	/data/pavpan/nightlies/herbie/enumo-rat/src/syntax/rules.rkt	29	26
get-swaps	/data/pavpan/nightlies/herbie/enumo-rat/src/symmetry.rkt	6	0
connected-components	/data/pavpan/nightlies/herbie/enumo-rat/src/symmetry.rkt	17	0
run-improve!	/data/pavpan/nightlies/herbie/enumo-rat/src/mainloop.rkt	296	0
(unnamed)	/data/pavpan/nightlies/herbie/enumo-rat/src/sandbox.rkt	55	6
(unnamed)	/usr/share/racket/pkgs/profile-lib/main.rkt	40	10
profile-thunk	/usr/share/racket/pkgs/profile-lib/main.rkt	9	0
(unnamed)	/usr/share/racket/collects/racket/engine.rkt	42	24