Numeric.LinearAlgebra.Util:formatSparse from hmatrix-0.16.1.5

Percentage Accurate: 100.0% → 100.0%

Time: 3.1s

Alternatives: 6

Speedup: 2.0×

Specification

Math

\[\begin{array}{l} \\ \frac{\left|x - y\right|}{\left|y\right|} \end{array} \]

FPCore

(FPCore (x y) :precision binary64 (/ (fabs (- x y)) (fabs y)))

C

double code(double x, double y) {
	return fabs((x - y)) / fabs(y);
}

Fortran

real(8) function code(x, y)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    code = abs((x - y)) / abs(y)
end function

Java

public static double code(double x, double y) {
	return Math.abs((x - y)) / Math.abs(y);
}

Python

def code(x, y):
	return math.fabs((x - y)) / math.fabs(y)

Julia

function code(x, y)
	return Float64(abs(Float64(x - y)) / abs(y))
end

MATLAB

function tmp = code(x, y)
	tmp = abs((x - y)) / abs(y);
end

Wolfram

code[x_, y_] := N[(N[Abs[N[(x - y), $MachinePrecision]], $MachinePrecision] / N[Abs[y], $MachinePrecision]), $MachinePrecision]

Initial Program: 100.0% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \frac{\left|x - y\right|}{\left|y\right|} \end{array} \]

FPCore

(FPCore (x y) :precision binary64 (/ (fabs (- x y)) (fabs y)))

C

double code(double x, double y) {
	return fabs((x - y)) / fabs(y);
}

Fortran

real(8) function code(x, y)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    code = abs((x - y)) / abs(y)
end function

Java

public static double code(double x, double y) {
	return Math.abs((x - y)) / Math.abs(y);
}

Python

def code(x, y):
	return math.fabs((x - y)) / math.fabs(y)

Julia

function code(x, y)
	return Float64(abs(Float64(x - y)) / abs(y))
end

MATLAB

function tmp = code(x, y)
	tmp = abs((x - y)) / abs(y);
end

Wolfram

code[x_, y_] := N[(N[Abs[N[(x - y), $MachinePrecision]], $MachinePrecision] / N[Abs[y], $MachinePrecision]), $MachinePrecision]

Alternative 1: 100.0% accurate, 2.0× speedup

Math

\[\begin{array}{l} \\ \left|\frac{y - x}{y}\right| \end{array} \]

FPCore

(FPCore (x y) :precision binary64 (fabs (/ (- y x) y)))

C

double code(double x, double y) {
	return fabs(((y - x) / y));
}

Fortran

real(8) function code(x, y)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    code = abs(((y - x) / y))
end function

Java

public static double code(double x, double y) {
	return Math.abs(((y - x) / y));
}

Python

def code(x, y):
	return math.fabs(((y - x) / y))

Julia

function code(x, y)
	return abs(Float64(Float64(y - x) / y))
end

MATLAB

function tmp = code(x, y)
	tmp = abs(((y - x) / y));
end

Wolfram

code[x_, y_] := N[Abs[N[(N[(y - x), $MachinePrecision] / y), $MachinePrecision]], $MachinePrecision]

Derivation

1. Initial program 100.0%

   \[\frac{\left|x - y\right|}{\left|y\right|} \]
2. Add Preprocessing
3. Step-by-step derivation

   1. fabs-sub 100.0%

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

   2. div-fabs 100.0%

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

4. Applied egg-rr 100.0%

   \[\leadsto \color{blue}{\left|\frac{y - x}{y}\right|} \]
5. Add Preprocessing

Alternative 2: 75.5% accurate, 1.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -6 \cdot 10^{-69} \lor \neg \left(x \leq 26000000000\right):\\ \;\;\;\;\left|\frac{x}{y}\right|\\ \mathbf{else}:\\ \;\;\;\;1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (if (or (<= x -6e-69) (not (<= x 26000000000.0))) (fabs (/ x y)) 1.0))

C

double code(double x, double y) {
	double tmp;
	if ((x <= -6e-69) || !(x <= 26000000000.0)) {
		tmp = fabs((x / y));
	} else {
		tmp = 1.0;
	}
	return tmp;
}

Fortran

real(8) function code(x, y)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8) :: tmp
    if ((x <= (-6d-69)) .or. (.not. (x <= 26000000000.0d0))) then
        tmp = abs((x / y))
    else
        tmp = 1.0d0
    end if
    code = tmp
end function

Java

public static double code(double x, double y) {
	double tmp;
	if ((x <= -6e-69) || !(x <= 26000000000.0)) {
		tmp = Math.abs((x / y));
	} else {
		tmp = 1.0;
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if (x <= -6e-69) or not (x <= 26000000000.0):
		tmp = math.fabs((x / y))
	else:
		tmp = 1.0
	return tmp

Julia

function code(x, y)
	tmp = 0.0
	if ((x <= -6e-69) || !(x <= 26000000000.0))
		tmp = abs(Float64(x / y));
	else
		tmp = 1.0;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y)
	tmp = 0.0;
	if ((x <= -6e-69) || ~((x <= 26000000000.0)))
		tmp = abs((x / y));
	else
		tmp = 1.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := If[Or[LessEqual[x, -6e-69], N[Not[LessEqual[x, 26000000000.0]], $MachinePrecision]], N[Abs[N[(x / y), $MachinePrecision]], $MachinePrecision], 1.0]

Derivation

1. Split input into 2 regimes

2. if x < -5.99999999999999978e-69 or 2.6e10 < x

   1. Initial program 100.0%

      \[\frac{\left|x - y\right|}{\left|y\right|} \]
   2. Add Preprocessing
   3. Step-by-step derivation

      1. fabs-sub 100.0%

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

      2. div-fabs 100.0%

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

   4. Applied egg-rr 100.0%

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

   5. Taylor expanded in y around 0 75.6%

      \[\leadsto \left|\color{blue}{-1 \cdot \frac{x}{y}}\right| \]
   6. Step-by-step derivation

      1. neg-mul-1 75.6%

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

      2. distribute-neg-frac2 75.6%

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

   7. Simplified 75.6%

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

   if -5.99999999999999978e-69 < x < 2.6e10

   1. Initial program 100.0%

      \[\frac{\left|x - y\right|}{\left|y\right|} \]
   2. Add Preprocessing
   3. Step-by-step derivation

      1. fabs-sub 100.0%

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

      2. div-fabs 100.0%

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

   4. Applied egg-rr 100.0%

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

   5. Taylor expanded in y around inf 81.6%

      \[\leadsto \left|\color{blue}{1}\right| \]
3. Recombined 2 regimes into one program.

4. Final simplification 78.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -6 \cdot 10^{-69} \lor \neg \left(x \leq 26000000000\right):\\ \;\;\;\;\left|\frac{x}{y}\right|\\ \mathbf{else}:\\ \;\;\;\;1\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 59.8% accurate, 13.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -1 \cdot 10^{+124}:\\ \;\;\;\;\frac{x}{y}\\ \mathbf{elif}\;x \leq 1.5 \cdot 10^{+96}:\\ \;\;\;\;1\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{y} + -1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (if (<= x -1e+124) (/ x y) (if (<= x 1.5e+96) 1.0 (+ (/ x y) -1.0))))

C

double code(double x, double y) {
	double tmp;
	if (x <= -1e+124) {
		tmp = x / y;
	} else if (x <= 1.5e+96) {
		tmp = 1.0;
	} else {
		tmp = (x / y) + -1.0;
	}
	return tmp;
}

Fortran

real(8) function code(x, y)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8) :: tmp
    if (x <= (-1d+124)) then
        tmp = x / y
    else if (x <= 1.5d+96) then
        tmp = 1.0d0
    else
        tmp = (x / y) + (-1.0d0)
    end if
    code = tmp
end function

Java

public static double code(double x, double y) {
	double tmp;
	if (x <= -1e+124) {
		tmp = x / y;
	} else if (x <= 1.5e+96) {
		tmp = 1.0;
	} else {
		tmp = (x / y) + -1.0;
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if x <= -1e+124:
		tmp = x / y
	elif x <= 1.5e+96:
		tmp = 1.0
	else:
		tmp = (x / y) + -1.0
	return tmp

Julia

function code(x, y)
	tmp = 0.0
	if (x <= -1e+124)
		tmp = Float64(x / y);
	elseif (x <= 1.5e+96)
		tmp = 1.0;
	else
		tmp = Float64(Float64(x / y) + -1.0);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y)
	tmp = 0.0;
	if (x <= -1e+124)
		tmp = x / y;
	elseif (x <= 1.5e+96)
		tmp = 1.0;
	else
		tmp = (x / y) + -1.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := If[LessEqual[x, -1e+124], N[(x / y), $MachinePrecision], If[LessEqual[x, 1.5e+96], 1.0, N[(N[(x / y), $MachinePrecision] + -1.0), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if x < -9.99999999999999948e123

   1. Initial program 100.0%

      \[\frac{\left|x - y\right|}{\left|y\right|} \]
   2. Add Preprocessing
   3. Step-by-step derivation

      1. div-inv 99.9%

         \[\leadsto \color{blue}{\left|x - y\right| \cdot \frac{1}{\left|y\right|}} \]

      2. add-sqr-sqrt 5.6%

         \[\leadsto \left|\color{blue}{\sqrt{x - y} \cdot \sqrt{x - y}}\right| \cdot \frac{1}{\left|y\right|} \]

      3. fabs-sqr 5.6%

         \[\leadsto \color{blue}{\left(\sqrt{x - y} \cdot \sqrt{x - y}\right)} \cdot \frac{1}{\left|y\right|} \]

      4. add-sqr-sqrt 6.1%

         \[\leadsto \color{blue}{\left(x - y\right)} \cdot \frac{1}{\left|y\right|} \]

      5. *-commutative 6.1%

         \[\leadsto \color{blue}{\frac{1}{\left|y\right|} \cdot \left(x - y\right)} \]

      6. add-sqr-sqrt 0.2%

         \[\leadsto \frac{1}{\left|\color{blue}{\sqrt{y} \cdot \sqrt{y}}\right|} \cdot \left(x - y\right) \]

      7. fabs-sqr 0.2%

         \[\leadsto \frac{1}{\color{blue}{\sqrt{y} \cdot \sqrt{y}}} \cdot \left(x - y\right) \]

      8. add-sqr-sqrt 43.1%

         \[\leadsto \frac{1}{\color{blue}{y}} \cdot \left(x - y\right) \]

   4. Applied egg-rr 43.1%

      \[\leadsto \color{blue}{\frac{1}{y} \cdot \left(x - y\right)} \]

   5. Taylor expanded in y around 0 43.7%

      \[\leadsto \color{blue}{\frac{x}{y}} \]

   if -9.99999999999999948e123 < x < 1.5e96

   1. Initial program 100.0%

      \[\frac{\left|x - y\right|}{\left|y\right|} \]
   2. Add Preprocessing
   3. Step-by-step derivation

      1. fabs-sub 100.0%

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

      2. div-fabs 100.0%

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

   4. Applied egg-rr 100.0%

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

   5. Taylor expanded in y around inf 68.5%

      \[\leadsto \left|\color{blue}{1}\right| \]

   if 1.5e96 < x

   1. Initial program 100.0%

      \[\frac{\left|x - y\right|}{\left|y\right|} \]
   2. Add Preprocessing

   3. Taylor expanded in x around -inf 100.0%

      \[\leadsto \color{blue}{\frac{\left|-\left(y + -1 \cdot x\right)\right|}{\left|y\right|}} \]
   4. Step-by-step derivation

      1. fabs-neg 100.0%

         \[\leadsto \frac{\color{blue}{\left|y + -1 \cdot x\right|}}{\left|y\right|} \]

      2. mul-1-neg 100.0%

         \[\leadsto \frac{\left|y + \color{blue}{\left(-x\right)}\right|}{\left|y\right|} \]

      3. sub-neg 100.0%

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

      4. fabs-sub 100.0%

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

      5. fabs-div 100.0%

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

      6. rem-square-sqrt 51.1%

         \[\leadsto \left|\color{blue}{\sqrt{\frac{x - y}{y}} \cdot \sqrt{\frac{x - y}{y}}}\right| \]

      7. fabs-sqr 51.1%

         \[\leadsto \color{blue}{\sqrt{\frac{x - y}{y}} \cdot \sqrt{\frac{x - y}{y}}} \]

      8. rem-square-sqrt 51.6%

         \[\leadsto \color{blue}{\frac{x - y}{y}} \]

      9. div-sub 51.6%

         \[\leadsto \color{blue}{\frac{x}{y} - \frac{y}{y}} \]

      10. sub-neg 51.6%

          \[\leadsto \color{blue}{\frac{x}{y} + \left(-\frac{y}{y}\right)} \]

      11. *-inverses 51.6%

          \[\leadsto \frac{x}{y} + \left(-\color{blue}{1}\right) \]

      12. metadata-eval 51.6%

          \[\leadsto \frac{x}{y} + \color{blue}{-1} \]

      13. +-commutative 51.6%

          \[\leadsto \color{blue}{-1 + \frac{x}{y}} \]

   5. Simplified 51.6%

      \[\leadsto \color{blue}{-1 + \frac{x}{y}} \]
3. Recombined 3 regimes into one program.

4. Final simplification 62.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -1 \cdot 10^{+124}:\\ \;\;\;\;\frac{x}{y}\\ \mathbf{elif}\;x \leq 1.5 \cdot 10^{+96}:\\ \;\;\;\;1\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{y} + -1\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 25.1% accurate, 41.0× speedup

Math

\[\begin{array}{l} \\ \frac{x}{y} + -1 \end{array} \]

FPCore

(FPCore (x y) :precision binary64 (+ (/ x y) -1.0))

C

double code(double x, double y) {
	return (x / y) + -1.0;
}

Fortran

real(8) function code(x, y)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    code = (x / y) + (-1.0d0)
end function

Java

public static double code(double x, double y) {
	return (x / y) + -1.0;
}

Python

def code(x, y):
	return (x / y) + -1.0

Julia

function code(x, y)
	return Float64(Float64(x / y) + -1.0)
end

MATLAB

function tmp = code(x, y)
	tmp = (x / y) + -1.0;
end

Wolfram

code[x_, y_] := N[(N[(x / y), $MachinePrecision] + -1.0), $MachinePrecision]

Derivation

1. Initial program 100.0%

   \[\frac{\left|x - y\right|}{\left|y\right|} \]
2. Add Preprocessing

3. Taylor expanded in x around -inf 100.0%

   \[\leadsto \color{blue}{\frac{\left|-\left(y + -1 \cdot x\right)\right|}{\left|y\right|}} \]
4. Step-by-step derivation

   1. fabs-neg 100.0%

      \[\leadsto \frac{\color{blue}{\left|y + -1 \cdot x\right|}}{\left|y\right|} \]

   2. mul-1-neg 100.0%

      \[\leadsto \frac{\left|y + \color{blue}{\left(-x\right)}\right|}{\left|y\right|} \]

   3. sub-neg 100.0%

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

   4. fabs-sub 100.0%

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

   5. fabs-div 100.0%

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

   6. rem-square-sqrt 23.7%

      \[\leadsto \left|\color{blue}{\sqrt{\frac{x - y}{y}} \cdot \sqrt{\frac{x - y}{y}}}\right| \]

   7. fabs-sqr 23.7%

      \[\leadsto \color{blue}{\sqrt{\frac{x - y}{y}} \cdot \sqrt{\frac{x - y}{y}}} \]

   8. rem-square-sqrt 24.8%

      \[\leadsto \color{blue}{\frac{x - y}{y}} \]

   9. div-sub 24.8%

      \[\leadsto \color{blue}{\frac{x}{y} - \frac{y}{y}} \]

   10. sub-neg 24.8%

       \[\leadsto \color{blue}{\frac{x}{y} + \left(-\frac{y}{y}\right)} \]

   11. *-inverses 24.8%

       \[\leadsto \frac{x}{y} + \left(-\color{blue}{1}\right) \]

   12. metadata-eval 24.8%

       \[\leadsto \frac{x}{y} + \color{blue}{-1} \]

   13. +-commutative 24.8%

       \[\leadsto \color{blue}{-1 + \frac{x}{y}} \]

5. Simplified 24.8%

   \[\leadsto \color{blue}{-1 + \frac{x}{y}} \]

6. Final simplification 24.8%

   \[\leadsto \frac{x}{y} + -1 \]
7. Add Preprocessing

Alternative 5: 25.8% accurate, 68.3× speedup

Math

\[\begin{array}{l} \\ \frac{x}{y} \end{array} \]

FPCore

(FPCore (x y) :precision binary64 (/ x y))

C

double code(double x, double y) {
	return x / y;
}

Fortran

real(8) function code(x, y)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    code = x / y
end function

Java

public static double code(double x, double y) {
	return x / y;
}

Python

def code(x, y):
	return x / y

Julia

function code(x, y)
	return Float64(x / y)
end

MATLAB

function tmp = code(x, y)
	tmp = x / y;
end

Wolfram

code[x_, y_] := N[(x / y), $MachinePrecision]

Derivation

1. Initial program 100.0%

   \[\frac{\left|x - y\right|}{\left|y\right|} \]
2. Add Preprocessing
3. Step-by-step derivation

   1. div-inv 99.7%

      \[\leadsto \color{blue}{\left|x - y\right| \cdot \frac{1}{\left|y\right|}} \]

   2. add-sqr-sqrt 54.2%

      \[\leadsto \left|\color{blue}{\sqrt{x - y} \cdot \sqrt{x - y}}\right| \cdot \frac{1}{\left|y\right|} \]

   3. fabs-sqr 54.2%

      \[\leadsto \color{blue}{\left(\sqrt{x - y} \cdot \sqrt{x - y}\right)} \cdot \frac{1}{\left|y\right|} \]

   4. add-sqr-sqrt 55.0%

      \[\leadsto \color{blue}{\left(x - y\right)} \cdot \frac{1}{\left|y\right|} \]

   5. *-commutative 55.0%

      \[\leadsto \color{blue}{\frac{1}{\left|y\right|} \cdot \left(x - y\right)} \]

   6. add-sqr-sqrt 14.0%

      \[\leadsto \frac{1}{\left|\color{blue}{\sqrt{y} \cdot \sqrt{y}}\right|} \cdot \left(x - y\right) \]

   7. fabs-sqr 14.0%

      \[\leadsto \frac{1}{\color{blue}{\sqrt{y} \cdot \sqrt{y}}} \cdot \left(x - y\right) \]

   8. add-sqr-sqrt 24.7%

      \[\leadsto \frac{1}{\color{blue}{y}} \cdot \left(x - y\right) \]

4. Applied egg-rr 24.7%

   \[\leadsto \color{blue}{\frac{1}{y} \cdot \left(x - y\right)} \]

5. Taylor expanded in y around 0 24.7%

   \[\leadsto \color{blue}{\frac{x}{y}} \]
6. Add Preprocessing

Alternative 6: 1.3% accurate, 205.0× speedup

Math

\[\begin{array}{l} \\ -1 \end{array} \]

FPCore

(FPCore (x y) :precision binary64 -1.0)

C

double code(double x, double y) {
	return -1.0;
}

Fortran

real(8) function code(x, y)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    code = -1.0d0
end function

Java

public static double code(double x, double y) {
	return -1.0;
}

Python

def code(x, y):
	return -1.0

Julia

function code(x, y)
	return -1.0
end

MATLAB

function tmp = code(x, y)
	tmp = -1.0;
end

Wolfram

code[x_, y_] := -1.0

Derivation

1. Initial program 100.0%

   \[\frac{\left|x - y\right|}{\left|y\right|} \]
2. Add Preprocessing
3. Step-by-step derivation

   1. div-inv 99.7%

      \[\leadsto \color{blue}{\left|x - y\right| \cdot \frac{1}{\left|y\right|}} \]

   2. add-sqr-sqrt 54.2%

      \[\leadsto \left|\color{blue}{\sqrt{x - y} \cdot \sqrt{x - y}}\right| \cdot \frac{1}{\left|y\right|} \]

   3. fabs-sqr 54.2%

      \[\leadsto \color{blue}{\left(\sqrt{x - y} \cdot \sqrt{x - y}\right)} \cdot \frac{1}{\left|y\right|} \]

   4. add-sqr-sqrt 55.0%

      \[\leadsto \color{blue}{\left(x - y\right)} \cdot \frac{1}{\left|y\right|} \]

   5. *-commutative 55.0%

      \[\leadsto \color{blue}{\frac{1}{\left|y\right|} \cdot \left(x - y\right)} \]

   6. add-sqr-sqrt 14.0%

      \[\leadsto \frac{1}{\left|\color{blue}{\sqrt{y} \cdot \sqrt{y}}\right|} \cdot \left(x - y\right) \]

   7. fabs-sqr 14.0%

      \[\leadsto \frac{1}{\color{blue}{\sqrt{y} \cdot \sqrt{y}}} \cdot \left(x - y\right) \]

   8. add-sqr-sqrt 24.7%

      \[\leadsto \frac{1}{\color{blue}{y}} \cdot \left(x - y\right) \]

4. Applied egg-rr 24.7%

   \[\leadsto \color{blue}{\frac{1}{y} \cdot \left(x - y\right)} \]

5. Taylor expanded in y around inf 1.3%

   \[\leadsto \color{blue}{-1} \]
6. Add Preprocessing

Reproduce

herbie shell --seed 2024086 
(FPCore (x y)
  :name "Numeric.LinearAlgebra.Util:formatSparse from hmatrix-0.16.1.5"
  :precision binary64
  (/ (fabs (- x y)) (fabs y)))