sqrt sqr

Average Error: 32.2 → 0

Time: 3.0s

Precision: binary64

Cost: 196

Math

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

↓

\[\begin{array}{l} \mathbf{if}\;x \leq -5 \cdot 10^{-311}:\\ \;\;\;\;2\\ \mathbf{else}:\\ \;\;\;\;0\\ \end{array} \]

FPCore

(FPCore (x) :precision binary64 (- (/ x x) (* (/ 1.0 x) (sqrt (* x x)))))

↓

(FPCore (x) :precision binary64 (if (<= x -5e-311) 2.0 0.0))

C

double code(double x) {
	return (x / x) - ((1.0 / x) * sqrt((x * x)));
}

↓

double code(double x) {
	double tmp;
	if (x <= -5e-311) {
		tmp = 2.0;
	} else {
		tmp = 0.0;
	}
	return tmp;
}

Fortran

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
    real(8) :: tmp
    if (x <= (-5d-311)) then
        tmp = 2.0d0
    else
        tmp = 0.0d0
    end if
    code = tmp
end function

Java

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

↓

public static double code(double x) {
	double tmp;
	if (x <= -5e-311) {
		tmp = 2.0;
	} else {
		tmp = 0.0;
	}
	return tmp;
}

Python

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

↓

def code(x):
	tmp = 0
	if x <= -5e-311:
		tmp = 2.0
	else:
		tmp = 0.0
	return tmp

Julia

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

↓

function code(x)
	tmp = 0.0
	if (x <= -5e-311)
		tmp = 2.0;
	else
		tmp = 0.0;
	end
	return tmp
end

MATLAB

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

↓

function tmp_2 = code(x)
	tmp = 0.0;
	if (x <= -5e-311)
		tmp = 2.0;
	else
		tmp = 0.0;
	end
	tmp_2 = tmp;
end

Wolfram

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

↓

code[x_] := If[LessEqual[x, -5e-311], 2.0, 0.0]

Target

Original	32.2
Target	0
Herbie	0

\[\begin{array}{l} \mathbf{if}\;x < 0:\\ \;\;\;\;2\\ \mathbf{else}:\\ \;\;\;\;0\\ \end{array} \]

Derivation

1. Split input into 2 regimes

2. if x < -5.00000000000023e-311

   1. Initial program 27.9

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

   2. Taylor expanded in x around -inf 0

      \[\leadsto \color{blue}{2} \]

   if -5.00000000000023e-311 < x

   1. Initial program 36.5

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

   2. Taylor expanded in x around 0 0

      \[\leadsto \color{blue}{0} \]
3. Recombined 2 regimes into one program.

4. Final simplification 0

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -5 \cdot 10^{-311}:\\ \;\;\;\;2\\ \mathbf{else}:\\ \;\;\;\;0\\ \end{array} \]

Alternatives

Alternative 1
Error	31.3
Cost	64

\[0 \]

Reproduce

herbie shell --seed 2023067 
(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)))))