Average Error: 32.6 → 0
Time: 2.5s
Precision: binary64
Cost: 6720
\[\frac{x}{x} - \frac{1}{x} \cdot \sqrt{x \cdot x} \]
↓
\[\frac{x - \left|x\right|}{x} \]
(FPCore (x) :precision binary64 (- (/ x x) (* (/ 1.0 x) (sqrt (* x x)))))
↓
(FPCore (x) :precision binary64 (/ (- x (fabs x)) x))
double code(double x) {
	return (x / x) - ((1.0 / x) * sqrt((x * x)));
}
↓
double code(double x) {
	return (x - fabs(x)) / x;
}

real(8) function code(x)
    real(8), intent (in) :: x
    code = (x / x) - ((1.0d0 / x) * sqrt((x * x)))
end function
↓
real(8) function code(x)
    real(8), intent (in) :: x
    code = (x - abs(x)) / x
end function

public static double code(double x) {
	return (x / x) - ((1.0 / x) * Math.sqrt((x * x)));
}
↓
public static double code(double x) {
	return (x - Math.abs(x)) / x;
}

def code(x):
	return (x / x) - ((1.0 / x) * math.sqrt((x * x)))
↓
def code(x):
	return (x - math.fabs(x)) / x

function code(x)
	return Float64(Float64(x / x) - Float64(Float64(1.0 / x) * sqrt(Float64(x * x))))
end
↓
function code(x)
	return Float64(Float64(x - abs(x)) / x)
end

function tmp = code(x)
	tmp = (x / x) - ((1.0 / x) * sqrt((x * x)));
end
↓
function tmp = code(x)
	tmp = (x - abs(x)) / x;
end

code[x_] := N[(N[(x / x), $MachinePrecision] - N[(N[(1.0 / x), $MachinePrecision] * N[Sqrt[N[(x * x), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]
↓
code[x_] := N[(N[(x - N[Abs[x], $MachinePrecision]), $MachinePrecision] / x), $MachinePrecision]

\frac{x}{x} - \frac{1}{x} \cdot \sqrt{x \cdot x}
↓
\frac{x - \left|x\right|}{x}

Error

Try it out

Your Program's Arguments

Results

Enter valid numbers for all inputs

Target

Original32.6
Target0
Herbie0
\[\begin{array}{l} \mathbf{if}\;x < 0:\\ \;\;\;\;2\\ \mathbf{else}:\\ \;\;\;\;0\\ \end{array} \]

Derivation

  1. Initial program 32.6

    \[\frac{x}{x} - \frac{1}{x} \cdot \sqrt{x \cdot x} \]

  2. Simplified0

    \[\leadsto \color{blue}{\frac{x - \left|x\right|}{x}} \]
    Proof

Reproduce

herbie shell --seed 2023010 
(FPCore (x)
  :name "sqrt sqr"
  :precision binary64

  :herbie-target
  (if (< x 0.0) 2.0 0.0)

  (- (/ x x) (* (/ 1.0 x) (sqrt (* x x)))))