fabs fraction 1

Percentage Accurate: 91.9% → 97.6%

Time: 7.4s

Alternatives: 10

Speedup: 1.0×

• 20.3% of points produce a very large (infinite) output. You may want to add a precondition.

Specification

Math

\[\begin{array}{l} \\ \left|\frac{x + 4}{y} - \frac{x}{y} \cdot z\right| \end{array} \]

FPCore

(FPCore (x y z) :precision binary64 (fabs (- (/ (+ x 4.0) y) (* (/ x y) z))))

C

double code(double x, double y, double z) {
	return fabs((((x + 4.0) / y) - ((x / y) * z)));
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    code = abs((((x + 4.0d0) / y) - ((x / y) * z)))
end function

Java

public static double code(double x, double y, double z) {
	return Math.abs((((x + 4.0) / y) - ((x / y) * z)));
}

Python

def code(x, y, z):
	return math.fabs((((x + 4.0) / y) - ((x / y) * z)))

Julia

function code(x, y, z)
	return abs(Float64(Float64(Float64(x + 4.0) / y) - Float64(Float64(x / y) * z)))
end

MATLAB

function tmp = code(x, y, z)
	tmp = abs((((x + 4.0) / y) - ((x / y) * z)));
end

Wolfram

code[x_, y_, z_] := N[Abs[N[(N[(N[(x + 4.0), $MachinePrecision] / y), $MachinePrecision] - N[(N[(x / y), $MachinePrecision] * z), $MachinePrecision]), $MachinePrecision]], $MachinePrecision]

Initial Program: 91.9% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \left|\frac{x + 4}{y} - \frac{x}{y} \cdot z\right| \end{array} \]

FPCore

(FPCore (x y z) :precision binary64 (fabs (- (/ (+ x 4.0) y) (* (/ x y) z))))

C

double code(double x, double y, double z) {
	return fabs((((x + 4.0) / y) - ((x / y) * z)));
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    code = abs((((x + 4.0d0) / y) - ((x / y) * z)))
end function

Java

public static double code(double x, double y, double z) {
	return Math.abs((((x + 4.0) / y) - ((x / y) * z)));
}

Python

def code(x, y, z):
	return math.fabs((((x + 4.0) / y) - ((x / y) * z)))

Julia

function code(x, y, z)
	return abs(Float64(Float64(Float64(x + 4.0) / y) - Float64(Float64(x / y) * z)))
end

MATLAB

function tmp = code(x, y, z)
	tmp = abs((((x + 4.0) / y) - ((x / y) * z)));
end

Wolfram

code[x_, y_, z_] := N[Abs[N[(N[(N[(x + 4.0), $MachinePrecision] / y), $MachinePrecision] - N[(N[(x / y), $MachinePrecision] * z), $MachinePrecision]), $MachinePrecision]], $MachinePrecision]

Alternative 1: 97.6% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq 6.5 \cdot 10^{+81}:\\ \;\;\;\;\left|\frac{\left(x + 4\right) - x \cdot z}{y}\right|\\ \mathbf{else}:\\ \;\;\;\;\left|x \cdot \frac{1 - z}{y}\right|\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= x 6.5e+81)
   (fabs (/ (- (+ x 4.0) (* x z)) y))
   (fabs (* x (/ (- 1.0 z) y)))))

C

double code(double x, double y, double z) {
	double tmp;
	if (x <= 6.5e+81) {
		tmp = fabs((((x + 4.0) - (x * z)) / y));
	} else {
		tmp = fabs((x * ((1.0 - z) / y)));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: tmp
    if (x <= 6.5d+81) then
        tmp = abs((((x + 4.0d0) - (x * z)) / y))
    else
        tmp = abs((x * ((1.0d0 - z) / y)))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if (x <= 6.5e+81) {
		tmp = Math.abs((((x + 4.0) - (x * z)) / y));
	} else {
		tmp = Math.abs((x * ((1.0 - z) / y)));
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if x <= 6.5e+81:
		tmp = math.fabs((((x + 4.0) - (x * z)) / y))
	else:
		tmp = math.fabs((x * ((1.0 - z) / y)))
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (x <= 6.5e+81)
		tmp = abs(Float64(Float64(Float64(x + 4.0) - Float64(x * z)) / y));
	else
		tmp = abs(Float64(x * Float64(Float64(1.0 - z) / y)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (x <= 6.5e+81)
		tmp = abs((((x + 4.0) - (x * z)) / y));
	else
		tmp = abs((x * ((1.0 - z) / y)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[x, 6.5e+81], N[Abs[N[(N[(N[(x + 4.0), $MachinePrecision] - N[(x * z), $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision]], $MachinePrecision], N[Abs[N[(x * N[(N[(1.0 - z), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision]], $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < 6.4999999999999996e81

   1. Initial program 94.2%

      \[\left|\frac{x + 4}{y} - \frac{x}{y} \cdot z\right| \]
   2. Step-by-step derivation

      1. associate-*l/ 96.2%

         \[\leadsto \left|\frac{x + 4}{y} - \color{blue}{\frac{x \cdot z}{y}}\right| \]

      2. sub-div 98.6%

         \[\leadsto \left|\color{blue}{\frac{\left(x + 4\right) - x \cdot z}{y}}\right| \]

   3. Applied egg-rr 98.6%

      \[\leadsto \left|\color{blue}{\frac{\left(x + 4\right) - x \cdot z}{y}}\right| \]

   if 6.4999999999999996e81 < x

   1. Initial program 87.4%

      \[\left|\frac{x + 4}{y} - \frac{x}{y} \cdot z\right| \]

   2. Taylor expanded in x around inf 99.7%

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

      1. *-commutative 99.7%

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

      2. sub-neg 99.7%

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

      3. mul-1-neg 99.7%

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

      4. distribute-lft-in 93.5%

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

      5. associate-*r/ 93.7%

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

      6. *-rgt-identity 93.7%

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

      7. mul-1-neg 93.7%

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

      8. distribute-rgt-neg-in 93.7%

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

      9. unsub-neg 93.7%

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

      10. *-lft-identity 93.7%

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

      11. associate-/l* 93.5%

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

      12. *-commutative 93.5%

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

      13. associate-/r/ 89.3%

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

      14. div-sub 99.7%

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

      15. associate-/r/ 99.7%

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

   4. Simplified 99.7%

      \[\leadsto \left|\color{blue}{\frac{1 - z}{y} \cdot x}\right| \]
3. Recombined 2 regimes into one program.

4. Final simplification 98.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq 6.5 \cdot 10^{+81}:\\ \;\;\;\;\left|\frac{\left(x + 4\right) - x \cdot z}{y}\right|\\ \mathbf{else}:\\ \;\;\;\;\left|x \cdot \frac{1 - z}{y}\right|\\ \end{array} \]

Alternative 2: 64.7% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \left|\frac{4}{y}\right|\\ t_1 := \left|\frac{x}{y}\right|\\ t_2 := \left|x \cdot \frac{z}{y}\right|\\ \mathbf{if}\;x \leq -2.15 \cdot 10^{+172}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;x \leq -3.85 \cdot 10^{-32}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;x \leq 2.9 \cdot 10^{-124}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;x \leq 1.9 \cdot 10^{-51}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;x \leq 4:\\ \;\;\;\;t_0\\ \mathbf{elif}\;x \leq 2.6 \cdot 10^{+50} \lor \neg \left(x \leq 1.05 \cdot 10^{+120}\right) \land x \leq 1.35 \cdot 10^{+156}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (fabs (/ 4.0 y))) (t_1 (fabs (/ x y))) (t_2 (fabs (* x (/ z y)))))
   (if (<= x -2.15e+172)
     t_1
     (if (<= x -3.85e-32)
       t_2
       (if (<= x 2.9e-124)
         t_0
         (if (<= x 1.9e-51)
           t_2
           (if (<= x 4.0)
             t_0
             (if (or (<= x 2.6e+50)
                     (and (not (<= x 1.05e+120)) (<= x 1.35e+156)))
               t_1
               t_2))))))))

C

double code(double x, double y, double z) {
	double t_0 = fabs((4.0 / y));
	double t_1 = fabs((x / y));
	double t_2 = fabs((x * (z / y)));
	double tmp;
	if (x <= -2.15e+172) {
		tmp = t_1;
	} else if (x <= -3.85e-32) {
		tmp = t_2;
	} else if (x <= 2.9e-124) {
		tmp = t_0;
	} else if (x <= 1.9e-51) {
		tmp = t_2;
	} else if (x <= 4.0) {
		tmp = t_0;
	} else if ((x <= 2.6e+50) || (!(x <= 1.05e+120) && (x <= 1.35e+156))) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: t_0
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_0 = abs((4.0d0 / y))
    t_1 = abs((x / y))
    t_2 = abs((x * (z / y)))
    if (x <= (-2.15d+172)) then
        tmp = t_1
    else if (x <= (-3.85d-32)) then
        tmp = t_2
    else if (x <= 2.9d-124) then
        tmp = t_0
    else if (x <= 1.9d-51) then
        tmp = t_2
    else if (x <= 4.0d0) then
        tmp = t_0
    else if ((x <= 2.6d+50) .or. (.not. (x <= 1.05d+120)) .and. (x <= 1.35d+156)) then
        tmp = t_1
    else
        tmp = t_2
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double t_0 = Math.abs((4.0 / y));
	double t_1 = Math.abs((x / y));
	double t_2 = Math.abs((x * (z / y)));
	double tmp;
	if (x <= -2.15e+172) {
		tmp = t_1;
	} else if (x <= -3.85e-32) {
		tmp = t_2;
	} else if (x <= 2.9e-124) {
		tmp = t_0;
	} else if (x <= 1.9e-51) {
		tmp = t_2;
	} else if (x <= 4.0) {
		tmp = t_0;
	} else if ((x <= 2.6e+50) || (!(x <= 1.05e+120) && (x <= 1.35e+156))) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = math.fabs((4.0 / y))
	t_1 = math.fabs((x / y))
	t_2 = math.fabs((x * (z / y)))
	tmp = 0
	if x <= -2.15e+172:
		tmp = t_1
	elif x <= -3.85e-32:
		tmp = t_2
	elif x <= 2.9e-124:
		tmp = t_0
	elif x <= 1.9e-51:
		tmp = t_2
	elif x <= 4.0:
		tmp = t_0
	elif (x <= 2.6e+50) or (not (x <= 1.05e+120) and (x <= 1.35e+156)):
		tmp = t_1
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z)
	t_0 = abs(Float64(4.0 / y))
	t_1 = abs(Float64(x / y))
	t_2 = abs(Float64(x * Float64(z / y)))
	tmp = 0.0
	if (x <= -2.15e+172)
		tmp = t_1;
	elseif (x <= -3.85e-32)
		tmp = t_2;
	elseif (x <= 2.9e-124)
		tmp = t_0;
	elseif (x <= 1.9e-51)
		tmp = t_2;
	elseif (x <= 4.0)
		tmp = t_0;
	elseif ((x <= 2.6e+50) || (!(x <= 1.05e+120) && (x <= 1.35e+156)))
		tmp = t_1;
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	t_0 = abs((4.0 / y));
	t_1 = abs((x / y));
	t_2 = abs((x * (z / y)));
	tmp = 0.0;
	if (x <= -2.15e+172)
		tmp = t_1;
	elseif (x <= -3.85e-32)
		tmp = t_2;
	elseif (x <= 2.9e-124)
		tmp = t_0;
	elseif (x <= 1.9e-51)
		tmp = t_2;
	elseif (x <= 4.0)
		tmp = t_0;
	elseif ((x <= 2.6e+50) || (~((x <= 1.05e+120)) && (x <= 1.35e+156)))
		tmp = t_1;
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := Block[{t$95$0 = N[Abs[N[(4.0 / y), $MachinePrecision]], $MachinePrecision]}, Block[{t$95$1 = N[Abs[N[(x / y), $MachinePrecision]], $MachinePrecision]}, Block[{t$95$2 = N[Abs[N[(x * N[(z / y), $MachinePrecision]), $MachinePrecision]], $MachinePrecision]}, If[LessEqual[x, -2.15e+172], t$95$1, If[LessEqual[x, -3.85e-32], t$95$2, If[LessEqual[x, 2.9e-124], t$95$0, If[LessEqual[x, 1.9e-51], t$95$2, If[LessEqual[x, 4.0], t$95$0, If[Or[LessEqual[x, 2.6e+50], And[N[Not[LessEqual[x, 1.05e+120]], $MachinePrecision], LessEqual[x, 1.35e+156]]], t$95$1, t$95$2]]]]]]]]]

Derivation

1. Split input into 3 regimes

2. if x < -2.1500000000000001e172 or 4 < x < 2.6000000000000002e50 or 1.05e120 < x < 1.35e156

   1. Initial program 89.3%

      \[\left|\frac{x + 4}{y} - \frac{x}{y} \cdot z\right| \]
   2. Step-by-step derivation

      1. associate-*l/ 90.0%

         \[\leadsto \left|\frac{x + 4}{y} - \color{blue}{\frac{x \cdot z}{y}}\right| \]

      2. sub-div 94.3%

         \[\leadsto \left|\color{blue}{\frac{\left(x + 4\right) - x \cdot z}{y}}\right| \]

   3. Applied egg-rr 94.3%

      \[\leadsto \left|\color{blue}{\frac{\left(x + 4\right) - x \cdot z}{y}}\right| \]

   4. Taylor expanded in x around inf 93.9%

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

      1. sub-neg 93.9%

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

      2. +-commutative 93.9%

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

      3. distribute-rgt1-in 93.9%

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

      4. cancel-sign-sub-inv 93.9%

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

   6. Simplified 93.9%

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

   7. Taylor expanded in z around 0 73.7%

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

   if -2.1500000000000001e172 < x < -3.8499999999999998e-32 or 2.9000000000000002e-124 < x < 1.90000000000000001e-51 or 2.6000000000000002e50 < x < 1.05e120 or 1.35e156 < x

   1. Initial program 88.2%

      \[\left|\frac{x + 4}{y} - \frac{x}{y} \cdot z\right| \]

   3. Simplified 92.7%

      \[\leadsto \color{blue}{\left|\frac{1}{y} \cdot \mathsf{fma}\left(x, z, -4 - x\right)\right|} \]

   4. Taylor expanded in z around inf 69.0%

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

      1. associate-*l/ 74.2%

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

      2. *-commutative 74.2%

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

   6. Simplified 74.2%

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

   if -3.8499999999999998e-32 < x < 2.9000000000000002e-124 or 1.90000000000000001e-51 < x < 4

   1. Initial program 98.3%

      \[\left|\frac{x + 4}{y} - \frac{x}{y} \cdot z\right| \]

   2. Taylor expanded in x around 0 83.6%

      \[\leadsto \left|\color{blue}{\frac{4}{y}}\right| \]
3. Recombined 3 regimes into one program.

4. Final simplification 78.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -2.15 \cdot 10^{+172}:\\ \;\;\;\;\left|\frac{x}{y}\right|\\ \mathbf{elif}\;x \leq -3.85 \cdot 10^{-32}:\\ \;\;\;\;\left|x \cdot \frac{z}{y}\right|\\ \mathbf{elif}\;x \leq 2.9 \cdot 10^{-124}:\\ \;\;\;\;\left|\frac{4}{y}\right|\\ \mathbf{elif}\;x \leq 1.9 \cdot 10^{-51}:\\ \;\;\;\;\left|x \cdot \frac{z}{y}\right|\\ \mathbf{elif}\;x \leq 4:\\ \;\;\;\;\left|\frac{4}{y}\right|\\ \mathbf{elif}\;x \leq 2.6 \cdot 10^{+50} \lor \neg \left(x \leq 1.05 \cdot 10^{+120}\right) \land x \leq 1.35 \cdot 10^{+156}:\\ \;\;\;\;\left|\frac{x}{y}\right|\\ \mathbf{else}:\\ \;\;\;\;\left|x \cdot \frac{z}{y}\right|\\ \end{array} \]

Alternative 3: 85.1% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \left|\frac{-4 - x}{y}\right|\\ t_1 := \left|x \cdot \frac{1 - z}{y}\right|\\ \mathbf{if}\;x \leq -3.5 \cdot 10^{-32}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;x \leq 4 \cdot 10^{-125}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;x \leq 2.25 \cdot 10^{-51}:\\ \;\;\;\;\left|\frac{x \cdot z}{y}\right|\\ \mathbf{elif}\;x \leq 0.00335:\\ \;\;\;\;t_0\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (fabs (/ (- -4.0 x) y))) (t_1 (fabs (* x (/ (- 1.0 z) y)))))
   (if (<= x -3.5e-32)
     t_1
     (if (<= x 4e-125)
       t_0
       (if (<= x 2.25e-51)
         (fabs (/ (* x z) y))
         (if (<= x 0.00335) t_0 t_1))))))

C

double code(double x, double y, double z) {
	double t_0 = fabs(((-4.0 - x) / y));
	double t_1 = fabs((x * ((1.0 - z) / y)));
	double tmp;
	if (x <= -3.5e-32) {
		tmp = t_1;
	} else if (x <= 4e-125) {
		tmp = t_0;
	} else if (x <= 2.25e-51) {
		tmp = fabs(((x * z) / y));
	} else if (x <= 0.00335) {
		tmp = t_0;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: t_0
    real(8) :: t_1
    real(8) :: tmp
    t_0 = abs((((-4.0d0) - x) / y))
    t_1 = abs((x * ((1.0d0 - z) / y)))
    if (x <= (-3.5d-32)) then
        tmp = t_1
    else if (x <= 4d-125) then
        tmp = t_0
    else if (x <= 2.25d-51) then
        tmp = abs(((x * z) / y))
    else if (x <= 0.00335d0) then
        tmp = t_0
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double t_0 = Math.abs(((-4.0 - x) / y));
	double t_1 = Math.abs((x * ((1.0 - z) / y)));
	double tmp;
	if (x <= -3.5e-32) {
		tmp = t_1;
	} else if (x <= 4e-125) {
		tmp = t_0;
	} else if (x <= 2.25e-51) {
		tmp = Math.abs(((x * z) / y));
	} else if (x <= 0.00335) {
		tmp = t_0;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = math.fabs(((-4.0 - x) / y))
	t_1 = math.fabs((x * ((1.0 - z) / y)))
	tmp = 0
	if x <= -3.5e-32:
		tmp = t_1
	elif x <= 4e-125:
		tmp = t_0
	elif x <= 2.25e-51:
		tmp = math.fabs(((x * z) / y))
	elif x <= 0.00335:
		tmp = t_0
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z)
	t_0 = abs(Float64(Float64(-4.0 - x) / y))
	t_1 = abs(Float64(x * Float64(Float64(1.0 - z) / y)))
	tmp = 0.0
	if (x <= -3.5e-32)
		tmp = t_1;
	elseif (x <= 4e-125)
		tmp = t_0;
	elseif (x <= 2.25e-51)
		tmp = abs(Float64(Float64(x * z) / y));
	elseif (x <= 0.00335)
		tmp = t_0;
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	t_0 = abs(((-4.0 - x) / y));
	t_1 = abs((x * ((1.0 - z) / y)));
	tmp = 0.0;
	if (x <= -3.5e-32)
		tmp = t_1;
	elseif (x <= 4e-125)
		tmp = t_0;
	elseif (x <= 2.25e-51)
		tmp = abs(((x * z) / y));
	elseif (x <= 0.00335)
		tmp = t_0;
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := Block[{t$95$0 = N[Abs[N[(N[(-4.0 - x), $MachinePrecision] / y), $MachinePrecision]], $MachinePrecision]}, Block[{t$95$1 = N[Abs[N[(x * N[(N[(1.0 - z), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision]], $MachinePrecision]}, If[LessEqual[x, -3.5e-32], t$95$1, If[LessEqual[x, 4e-125], t$95$0, If[LessEqual[x, 2.25e-51], N[Abs[N[(N[(x * z), $MachinePrecision] / y), $MachinePrecision]], $MachinePrecision], If[LessEqual[x, 0.00335], t$95$0, t$95$1]]]]]]

Derivation

1. Split input into 3 regimes

2. if x < -3.4999999999999999e-32 or 0.00335000000000000011 < x

   1. Initial program 88.1%

      \[\left|\frac{x + 4}{y} - \frac{x}{y} \cdot z\right| \]

   2. Taylor expanded in x around inf 98.3%

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

      1. *-commutative 98.3%

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

      2. sub-neg 98.3%

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

      3. mul-1-neg 98.3%

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

      4. distribute-lft-in 92.1%

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

      5. associate-*r/ 92.3%

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

      6. *-rgt-identity 92.3%

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

      7. mul-1-neg 92.3%

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

      8. distribute-rgt-neg-in 92.3%

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

      9. unsub-neg 92.3%

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

      10. *-lft-identity 92.3%

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

      11. associate-/l* 92.2%

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

      12. *-commutative 92.2%

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

      13. associate-/r/ 89.0%

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

      14. div-sub 98.4%

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

      15. associate-/r/ 98.3%

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

   4. Simplified 98.3%

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

   if -3.4999999999999999e-32 < x < 4.00000000000000005e-125 or 2.24999999999999987e-51 < x < 0.00335000000000000011

   1. Initial program 98.3%

      \[\left|\frac{x + 4}{y} - \frac{x}{y} \cdot z\right| \]

   3. Simplified 99.9%

      \[\leadsto \color{blue}{\left|\frac{1}{y} \cdot \mathsf{fma}\left(x, z, -4 - x\right)\right|} \]

   4. Taylor expanded in z around 0 84.3%

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

      1. associate-*r/ 84.3%

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

      2. distribute-lft-in 84.3%

         \[\leadsto \left|\frac{\color{blue}{-1 \cdot 4 + -1 \cdot x}}{y}\right| \]

      3. metadata-eval 84.3%

         \[\leadsto \left|\frac{\color{blue}{-4} + -1 \cdot x}{y}\right| \]

      4. neg-mul-1 84.3%

         \[\leadsto \left|\frac{-4 + \color{blue}{\left(-x\right)}}{y}\right| \]

      5. sub-neg 84.3%

         \[\leadsto \left|\frac{\color{blue}{-4 - x}}{y}\right| \]

   6. Simplified 84.3%

      \[\leadsto \left|\color{blue}{\frac{-4 - x}{y}}\right| \]

   if 4.00000000000000005e-125 < x < 2.24999999999999987e-51

   1. Initial program 93.0%

      \[\left|\frac{x + 4}{y} - \frac{x}{y} \cdot z\right| \]

   3. Simplified 100.0%

      \[\leadsto \color{blue}{\left|\frac{1}{y} \cdot \mathsf{fma}\left(x, z, -4 - x\right)\right|} \]

   4. Taylor expanded in z around inf 77.3%

      \[\leadsto \left|\color{blue}{\frac{z \cdot x}{y}}\right| \]
3. Recombined 3 regimes into one program.

4. Final simplification 90.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -3.5 \cdot 10^{-32}:\\ \;\;\;\;\left|x \cdot \frac{1 - z}{y}\right|\\ \mathbf{elif}\;x \leq 4 \cdot 10^{-125}:\\ \;\;\;\;\left|\frac{-4 - x}{y}\right|\\ \mathbf{elif}\;x \leq 2.25 \cdot 10^{-51}:\\ \;\;\;\;\left|\frac{x \cdot z}{y}\right|\\ \mathbf{elif}\;x \leq 0.00335:\\ \;\;\;\;\left|\frac{-4 - x}{y}\right|\\ \mathbf{else}:\\ \;\;\;\;\left|x \cdot \frac{1 - z}{y}\right|\\ \end{array} \]

Alternative 4: 85.2% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \left|x \cdot \frac{1 - z}{y}\right|\\ \mathbf{if}\;x \leq -4.8 \cdot 10^{-32}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;x \leq 5.6 \cdot 10^{-124}:\\ \;\;\;\;\left|\frac{-4 - x}{y}\right|\\ \mathbf{elif}\;x \leq 3 \cdot 10^{-51}:\\ \;\;\;\;\left|\frac{x \cdot z}{y}\right|\\ \mathbf{elif}\;x \leq 0.00385:\\ \;\;\;\;\left|\frac{4}{y} + \frac{x}{y}\right|\\ \mathbf{else}:\\ \;\;\;\;t_0\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (fabs (* x (/ (- 1.0 z) y)))))
   (if (<= x -4.8e-32)
     t_0
     (if (<= x 5.6e-124)
       (fabs (/ (- -4.0 x) y))
       (if (<= x 3e-51)
         (fabs (/ (* x z) y))
         (if (<= x 0.00385) (fabs (+ (/ 4.0 y) (/ x y))) t_0))))))

C

double code(double x, double y, double z) {
	double t_0 = fabs((x * ((1.0 - z) / y)));
	double tmp;
	if (x <= -4.8e-32) {
		tmp = t_0;
	} else if (x <= 5.6e-124) {
		tmp = fabs(((-4.0 - x) / y));
	} else if (x <= 3e-51) {
		tmp = fabs(((x * z) / y));
	} else if (x <= 0.00385) {
		tmp = fabs(((4.0 / y) + (x / y)));
	} else {
		tmp = t_0;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: t_0
    real(8) :: tmp
    t_0 = abs((x * ((1.0d0 - z) / y)))
    if (x <= (-4.8d-32)) then
        tmp = t_0
    else if (x <= 5.6d-124) then
        tmp = abs((((-4.0d0) - x) / y))
    else if (x <= 3d-51) then
        tmp = abs(((x * z) / y))
    else if (x <= 0.00385d0) then
        tmp = abs(((4.0d0 / y) + (x / y)))
    else
        tmp = t_0
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double t_0 = Math.abs((x * ((1.0 - z) / y)));
	double tmp;
	if (x <= -4.8e-32) {
		tmp = t_0;
	} else if (x <= 5.6e-124) {
		tmp = Math.abs(((-4.0 - x) / y));
	} else if (x <= 3e-51) {
		tmp = Math.abs(((x * z) / y));
	} else if (x <= 0.00385) {
		tmp = Math.abs(((4.0 / y) + (x / y)));
	} else {
		tmp = t_0;
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = math.fabs((x * ((1.0 - z) / y)))
	tmp = 0
	if x <= -4.8e-32:
		tmp = t_0
	elif x <= 5.6e-124:
		tmp = math.fabs(((-4.0 - x) / y))
	elif x <= 3e-51:
		tmp = math.fabs(((x * z) / y))
	elif x <= 0.00385:
		tmp = math.fabs(((4.0 / y) + (x / y)))
	else:
		tmp = t_0
	return tmp

Julia

function code(x, y, z)
	t_0 = abs(Float64(x * Float64(Float64(1.0 - z) / y)))
	tmp = 0.0
	if (x <= -4.8e-32)
		tmp = t_0;
	elseif (x <= 5.6e-124)
		tmp = abs(Float64(Float64(-4.0 - x) / y));
	elseif (x <= 3e-51)
		tmp = abs(Float64(Float64(x * z) / y));
	elseif (x <= 0.00385)
		tmp = abs(Float64(Float64(4.0 / y) + Float64(x / y)));
	else
		tmp = t_0;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	t_0 = abs((x * ((1.0 - z) / y)));
	tmp = 0.0;
	if (x <= -4.8e-32)
		tmp = t_0;
	elseif (x <= 5.6e-124)
		tmp = abs(((-4.0 - x) / y));
	elseif (x <= 3e-51)
		tmp = abs(((x * z) / y));
	elseif (x <= 0.00385)
		tmp = abs(((4.0 / y) + (x / y)));
	else
		tmp = t_0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := Block[{t$95$0 = N[Abs[N[(x * N[(N[(1.0 - z), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision]], $MachinePrecision]}, If[LessEqual[x, -4.8e-32], t$95$0, If[LessEqual[x, 5.6e-124], N[Abs[N[(N[(-4.0 - x), $MachinePrecision] / y), $MachinePrecision]], $MachinePrecision], If[LessEqual[x, 3e-51], N[Abs[N[(N[(x * z), $MachinePrecision] / y), $MachinePrecision]], $MachinePrecision], If[LessEqual[x, 0.00385], N[Abs[N[(N[(4.0 / y), $MachinePrecision] + N[(x / y), $MachinePrecision]), $MachinePrecision]], $MachinePrecision], t$95$0]]]]]

Derivation

1. Split input into 4 regimes

2. if x < -4.8000000000000003e-32 or 0.0038500000000000001 < x

   1. Initial program 88.1%

      \[\left|\frac{x + 4}{y} - \frac{x}{y} \cdot z\right| \]

   2. Taylor expanded in x around inf 98.3%

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

      1. *-commutative 98.3%

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

      2. sub-neg 98.3%

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

      3. mul-1-neg 98.3%

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

      4. distribute-lft-in 92.1%

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

      5. associate-*r/ 92.3%

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

      6. *-rgt-identity 92.3%

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

      7. mul-1-neg 92.3%

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

      8. distribute-rgt-neg-in 92.3%

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

      9. unsub-neg 92.3%

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

      10. *-lft-identity 92.3%

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

      11. associate-/l* 92.2%

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

      12. *-commutative 92.2%

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

      13. associate-/r/ 89.0%

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

      14. div-sub 98.4%

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

      15. associate-/r/ 98.3%

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

   4. Simplified 98.3%

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

   if -4.8000000000000003e-32 < x < 5.59999999999999996e-124

   1. Initial program 98.2%

      \[\left|\frac{x + 4}{y} - \frac{x}{y} \cdot z\right| \]

   3. Simplified 99.9%

      \[\leadsto \color{blue}{\left|\frac{1}{y} \cdot \mathsf{fma}\left(x, z, -4 - x\right)\right|} \]

   4. Taylor expanded in z around 0 85.8%

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

      1. associate-*r/ 85.8%

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

      2. distribute-lft-in 85.8%

         \[\leadsto \left|\frac{\color{blue}{-1 \cdot 4 + -1 \cdot x}}{y}\right| \]

      3. metadata-eval 85.8%

         \[\leadsto \left|\frac{\color{blue}{-4} + -1 \cdot x}{y}\right| \]

      4. neg-mul-1 85.8%

         \[\leadsto \left|\frac{-4 + \color{blue}{\left(-x\right)}}{y}\right| \]

      5. sub-neg 85.8%

         \[\leadsto \left|\frac{\color{blue}{-4 - x}}{y}\right| \]

   6. Simplified 85.8%

      \[\leadsto \left|\color{blue}{\frac{-4 - x}{y}}\right| \]

   if 5.59999999999999996e-124 < x < 3.00000000000000002e-51

   1. Initial program 93.0%

      \[\left|\frac{x + 4}{y} - \frac{x}{y} \cdot z\right| \]

   3. Simplified 100.0%

      \[\leadsto \color{blue}{\left|\frac{1}{y} \cdot \mathsf{fma}\left(x, z, -4 - x\right)\right|} \]

   4. Taylor expanded in z around inf 77.3%

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

   if 3.00000000000000002e-51 < x < 0.0038500000000000001

   1. Initial program 99.7%

      \[\left|\frac{x + 4}{y} - \frac{x}{y} \cdot z\right| \]

   2. Taylor expanded in z around 0 67.8%

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

      1. associate-*r/ 67.8%

         \[\leadsto \left|\color{blue}{\frac{4 \cdot 1}{y}} + \frac{x}{y}\right| \]

      2. metadata-eval 67.8%

         \[\leadsto \left|\frac{\color{blue}{4}}{y} + \frac{x}{y}\right| \]

   4. Simplified 67.8%

      \[\leadsto \left|\color{blue}{\frac{4}{y} + \frac{x}{y}}\right| \]
3. Recombined 4 regimes into one program.

4. Final simplification 90.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -4.8 \cdot 10^{-32}:\\ \;\;\;\;\left|x \cdot \frac{1 - z}{y}\right|\\ \mathbf{elif}\;x \leq 5.6 \cdot 10^{-124}:\\ \;\;\;\;\left|\frac{-4 - x}{y}\right|\\ \mathbf{elif}\;x \leq 3 \cdot 10^{-51}:\\ \;\;\;\;\left|\frac{x \cdot z}{y}\right|\\ \mathbf{elif}\;x \leq 0.00385:\\ \;\;\;\;\left|\frac{4}{y} + \frac{x}{y}\right|\\ \mathbf{else}:\\ \;\;\;\;\left|x \cdot \frac{1 - z}{y}\right|\\ \end{array} \]

Alternative 5: 67.2% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \left|z \cdot \frac{x}{y}\right|\\ \mathbf{if}\;x \leq -8.2 \cdot 10^{-32}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;x \leq 5.6 \cdot 10^{-124}:\\ \;\;\;\;\left|\frac{4}{y}\right|\\ \mathbf{elif}\;x \leq 1.06 \cdot 10^{+119} \lor \neg \left(x \leq 1.2 \cdot 10^{+156}\right):\\ \;\;\;\;t_0\\ \mathbf{else}:\\ \;\;\;\;\left|\frac{x}{y}\right|\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (fabs (* z (/ x y)))))
   (if (<= x -8.2e-32)
     t_0
     (if (<= x 5.6e-124)
       (fabs (/ 4.0 y))
       (if (or (<= x 1.06e+119) (not (<= x 1.2e+156))) t_0 (fabs (/ x y)))))))

C

double code(double x, double y, double z) {
	double t_0 = fabs((z * (x / y)));
	double tmp;
	if (x <= -8.2e-32) {
		tmp = t_0;
	} else if (x <= 5.6e-124) {
		tmp = fabs((4.0 / y));
	} else if ((x <= 1.06e+119) || !(x <= 1.2e+156)) {
		tmp = t_0;
	} else {
		tmp = fabs((x / y));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: t_0
    real(8) :: tmp
    t_0 = abs((z * (x / y)))
    if (x <= (-8.2d-32)) then
        tmp = t_0
    else if (x <= 5.6d-124) then
        tmp = abs((4.0d0 / y))
    else if ((x <= 1.06d+119) .or. (.not. (x <= 1.2d+156))) then
        tmp = t_0
    else
        tmp = abs((x / y))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double t_0 = Math.abs((z * (x / y)));
	double tmp;
	if (x <= -8.2e-32) {
		tmp = t_0;
	} else if (x <= 5.6e-124) {
		tmp = Math.abs((4.0 / y));
	} else if ((x <= 1.06e+119) || !(x <= 1.2e+156)) {
		tmp = t_0;
	} else {
		tmp = Math.abs((x / y));
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = math.fabs((z * (x / y)))
	tmp = 0
	if x <= -8.2e-32:
		tmp = t_0
	elif x <= 5.6e-124:
		tmp = math.fabs((4.0 / y))
	elif (x <= 1.06e+119) or not (x <= 1.2e+156):
		tmp = t_0
	else:
		tmp = math.fabs((x / y))
	return tmp

Julia

function code(x, y, z)
	t_0 = abs(Float64(z * Float64(x / y)))
	tmp = 0.0
	if (x <= -8.2e-32)
		tmp = t_0;
	elseif (x <= 5.6e-124)
		tmp = abs(Float64(4.0 / y));
	elseif ((x <= 1.06e+119) || !(x <= 1.2e+156))
		tmp = t_0;
	else
		tmp = abs(Float64(x / y));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	t_0 = abs((z * (x / y)));
	tmp = 0.0;
	if (x <= -8.2e-32)
		tmp = t_0;
	elseif (x <= 5.6e-124)
		tmp = abs((4.0 / y));
	elseif ((x <= 1.06e+119) || ~((x <= 1.2e+156)))
		tmp = t_0;
	else
		tmp = abs((x / y));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := Block[{t$95$0 = N[Abs[N[(z * N[(x / y), $MachinePrecision]), $MachinePrecision]], $MachinePrecision]}, If[LessEqual[x, -8.2e-32], t$95$0, If[LessEqual[x, 5.6e-124], N[Abs[N[(4.0 / y), $MachinePrecision]], $MachinePrecision], If[Or[LessEqual[x, 1.06e+119], N[Not[LessEqual[x, 1.2e+156]], $MachinePrecision]], t$95$0, N[Abs[N[(x / y), $MachinePrecision]], $MachinePrecision]]]]]

Derivation

1. Split input into 3 regimes

2. if x < -8.1999999999999995e-32 or 5.59999999999999996e-124 < x < 1.0599999999999999e119 or 1.2000000000000001e156 < x

   1. Initial program 88.5%

      \[\left|\frac{x + 4}{y} - \frac{x}{y} \cdot z\right| \]

   3. Simplified 93.1%

      \[\leadsto \color{blue}{\left|\frac{1}{y} \cdot \mathsf{fma}\left(x, z, -4 - x\right)\right|} \]

   4. Taylor expanded in z around inf 59.8%

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

      1. *-commutative 59.8%

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

      2. associate-*l/ 72.6%

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

      3. *-commutative 72.6%

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

   6. Simplified 72.6%

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

   if -8.1999999999999995e-32 < x < 5.59999999999999996e-124

   1. Initial program 98.2%

      \[\left|\frac{x + 4}{y} - \frac{x}{y} \cdot z\right| \]

   2. Taylor expanded in x around 0 85.8%

      \[\leadsto \left|\color{blue}{\frac{4}{y}}\right| \]

   if 1.0599999999999999e119 < x < 1.2000000000000001e156

   1. Initial program 100.0%

      \[\left|\frac{x + 4}{y} - \frac{x}{y} \cdot z\right| \]
   2. Step-by-step derivation

      1. associate-*l/ 100.0%

         \[\leadsto \left|\frac{x + 4}{y} - \color{blue}{\frac{x \cdot z}{y}}\right| \]

      2. sub-div 100.0%

         \[\leadsto \left|\color{blue}{\frac{\left(x + 4\right) - x \cdot z}{y}}\right| \]

   3. Applied egg-rr 100.0%

      \[\leadsto \left|\color{blue}{\frac{\left(x + 4\right) - x \cdot z}{y}}\right| \]

   4. Taylor expanded in x around inf 100.0%

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

      1. sub-neg 100.0%

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

      2. +-commutative 100.0%

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

      3. distribute-rgt1-in 100.0%

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

      4. cancel-sign-sub-inv 100.0%

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

   6. Simplified 100.0%

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

   7. Taylor expanded in z around 0 91.4%

      \[\leadsto \left|\color{blue}{\frac{x}{y}}\right| \]
3. Recombined 3 regimes into one program.

4. Final simplification 78.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -8.2 \cdot 10^{-32}:\\ \;\;\;\;\left|z \cdot \frac{x}{y}\right|\\ \mathbf{elif}\;x \leq 5.6 \cdot 10^{-124}:\\ \;\;\;\;\left|\frac{4}{y}\right|\\ \mathbf{elif}\;x \leq 1.06 \cdot 10^{+119} \lor \neg \left(x \leq 1.2 \cdot 10^{+156}\right):\\ \;\;\;\;\left|z \cdot \frac{x}{y}\right|\\ \mathbf{else}:\\ \;\;\;\;\left|\frac{x}{y}\right|\\ \end{array} \]

Alternative 6: 67.0% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \left|z \cdot \frac{x}{y}\right|\\ \mathbf{if}\;x \leq -9.3 \cdot 10^{-32}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;x \leq 5.5 \cdot 10^{-124}:\\ \;\;\;\;\left|\frac{4}{y}\right|\\ \mathbf{elif}\;x \leq 2.1 \cdot 10^{+119}:\\ \;\;\;\;\left|\frac{z}{\frac{y}{x}}\right|\\ \mathbf{elif}\;x \leq 1.2 \cdot 10^{+156}:\\ \;\;\;\;\left|\frac{x}{y}\right|\\ \mathbf{else}:\\ \;\;\;\;t_0\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (fabs (* z (/ x y)))))
   (if (<= x -9.3e-32)
     t_0
     (if (<= x 5.5e-124)
       (fabs (/ 4.0 y))
       (if (<= x 2.1e+119)
         (fabs (/ z (/ y x)))
         (if (<= x 1.2e+156) (fabs (/ x y)) t_0))))))

C

double code(double x, double y, double z) {
	double t_0 = fabs((z * (x / y)));
	double tmp;
	if (x <= -9.3e-32) {
		tmp = t_0;
	} else if (x <= 5.5e-124) {
		tmp = fabs((4.0 / y));
	} else if (x <= 2.1e+119) {
		tmp = fabs((z / (y / x)));
	} else if (x <= 1.2e+156) {
		tmp = fabs((x / y));
	} else {
		tmp = t_0;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: t_0
    real(8) :: tmp
    t_0 = abs((z * (x / y)))
    if (x <= (-9.3d-32)) then
        tmp = t_0
    else if (x <= 5.5d-124) then
        tmp = abs((4.0d0 / y))
    else if (x <= 2.1d+119) then
        tmp = abs((z / (y / x)))
    else if (x <= 1.2d+156) then
        tmp = abs((x / y))
    else
        tmp = t_0
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double t_0 = Math.abs((z * (x / y)));
	double tmp;
	if (x <= -9.3e-32) {
		tmp = t_0;
	} else if (x <= 5.5e-124) {
		tmp = Math.abs((4.0 / y));
	} else if (x <= 2.1e+119) {
		tmp = Math.abs((z / (y / x)));
	} else if (x <= 1.2e+156) {
		tmp = Math.abs((x / y));
	} else {
		tmp = t_0;
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = math.fabs((z * (x / y)))
	tmp = 0
	if x <= -9.3e-32:
		tmp = t_0
	elif x <= 5.5e-124:
		tmp = math.fabs((4.0 / y))
	elif x <= 2.1e+119:
		tmp = math.fabs((z / (y / x)))
	elif x <= 1.2e+156:
		tmp = math.fabs((x / y))
	else:
		tmp = t_0
	return tmp

Julia

function code(x, y, z)
	t_0 = abs(Float64(z * Float64(x / y)))
	tmp = 0.0
	if (x <= -9.3e-32)
		tmp = t_0;
	elseif (x <= 5.5e-124)
		tmp = abs(Float64(4.0 / y));
	elseif (x <= 2.1e+119)
		tmp = abs(Float64(z / Float64(y / x)));
	elseif (x <= 1.2e+156)
		tmp = abs(Float64(x / y));
	else
		tmp = t_0;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	t_0 = abs((z * (x / y)));
	tmp = 0.0;
	if (x <= -9.3e-32)
		tmp = t_0;
	elseif (x <= 5.5e-124)
		tmp = abs((4.0 / y));
	elseif (x <= 2.1e+119)
		tmp = abs((z / (y / x)));
	elseif (x <= 1.2e+156)
		tmp = abs((x / y));
	else
		tmp = t_0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := Block[{t$95$0 = N[Abs[N[(z * N[(x / y), $MachinePrecision]), $MachinePrecision]], $MachinePrecision]}, If[LessEqual[x, -9.3e-32], t$95$0, If[LessEqual[x, 5.5e-124], N[Abs[N[(4.0 / y), $MachinePrecision]], $MachinePrecision], If[LessEqual[x, 2.1e+119], N[Abs[N[(z / N[(y / x), $MachinePrecision]), $MachinePrecision]], $MachinePrecision], If[LessEqual[x, 1.2e+156], N[Abs[N[(x / y), $MachinePrecision]], $MachinePrecision], t$95$0]]]]]

Derivation

1. Split input into 4 regimes

2. if x < -9.29999999999999977e-32 or 1.2000000000000001e156 < x

   1. Initial program 85.7%

      \[\left|\frac{x + 4}{y} - \frac{x}{y} \cdot z\right| \]

   3. Simplified 91.3%

      \[\leadsto \color{blue}{\left|\frac{1}{y} \cdot \mathsf{fma}\left(x, z, -4 - x\right)\right|} \]

   4. Taylor expanded in z around inf 58.5%

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

      1. *-commutative 58.5%

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

      2. associate-*l/ 76.3%

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

      3. *-commutative 76.3%

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

   6. Simplified 76.3%

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

   if -9.29999999999999977e-32 < x < 5.50000000000000016e-124

   1. Initial program 98.2%

      \[\left|\frac{x + 4}{y} - \frac{x}{y} \cdot z\right| \]

   2. Taylor expanded in x around 0 85.8%

      \[\leadsto \left|\color{blue}{\frac{4}{y}}\right| \]

   if 5.50000000000000016e-124 < x < 2.09999999999999983e119

   1. Initial program 95.2%

      \[\left|\frac{x + 4}{y} - \frac{x}{y} \cdot z\right| \]

   3. Simplified 97.5%

      \[\leadsto \color{blue}{\left|\frac{1}{y} \cdot \mathsf{fma}\left(x, z, -4 - x\right)\right|} \]

   4. Taylor expanded in z around inf 62.8%

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

      1. *-commutative 62.8%

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

      2. associate-*l/ 63.5%

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

      3. *-commutative 63.5%

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

   6. Simplified 63.5%

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

      1. clear-num 63.4%

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

      2. un-div-inv 63.6%

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

   8. Applied egg-rr 63.6%

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

   if 2.09999999999999983e119 < x < 1.2000000000000001e156

   1. Initial program 100.0%

      \[\left|\frac{x + 4}{y} - \frac{x}{y} \cdot z\right| \]
   2. Step-by-step derivation

      1. associate-*l/ 100.0%

         \[\leadsto \left|\frac{x + 4}{y} - \color{blue}{\frac{x \cdot z}{y}}\right| \]

      2. sub-div 100.0%

         \[\leadsto \left|\color{blue}{\frac{\left(x + 4\right) - x \cdot z}{y}}\right| \]

   3. Applied egg-rr 100.0%

      \[\leadsto \left|\color{blue}{\frac{\left(x + 4\right) - x \cdot z}{y}}\right| \]

   4. Taylor expanded in x around inf 100.0%

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

      1. sub-neg 100.0%

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

      2. +-commutative 100.0%

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

      3. distribute-rgt1-in 100.0%

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

      4. cancel-sign-sub-inv 100.0%

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

   6. Simplified 100.0%

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

   7. Taylor expanded in z around 0 91.4%

      \[\leadsto \left|\color{blue}{\frac{x}{y}}\right| \]
3. Recombined 4 regimes into one program.

4. Final simplification 78.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -9.3 \cdot 10^{-32}:\\ \;\;\;\;\left|z \cdot \frac{x}{y}\right|\\ \mathbf{elif}\;x \leq 5.5 \cdot 10^{-124}:\\ \;\;\;\;\left|\frac{4}{y}\right|\\ \mathbf{elif}\;x \leq 2.1 \cdot 10^{+119}:\\ \;\;\;\;\left|\frac{z}{\frac{y}{x}}\right|\\ \mathbf{elif}\;x \leq 1.2 \cdot 10^{+156}:\\ \;\;\;\;\left|\frac{x}{y}\right|\\ \mathbf{else}:\\ \;\;\;\;\left|z \cdot \frac{x}{y}\right|\\ \end{array} \]

Alternative 7: 84.8% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -5 \cdot 10^{-32} \lor \neg \left(x \leq 5.6 \cdot 10^{-124}\right):\\ \;\;\;\;\left|\frac{z + -1}{\frac{y}{x}}\right|\\ \mathbf{else}:\\ \;\;\;\;\left|\frac{-4 - x}{y}\right|\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= x -5e-32) (not (<= x 5.6e-124)))
   (fabs (/ (+ z -1.0) (/ y x)))
   (fabs (/ (- -4.0 x) y))))

C

double code(double x, double y, double z) {
	double tmp;
	if ((x <= -5e-32) || !(x <= 5.6e-124)) {
		tmp = fabs(((z + -1.0) / (y / x)));
	} else {
		tmp = fabs(((-4.0 - x) / y));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: tmp
    if ((x <= (-5d-32)) .or. (.not. (x <= 5.6d-124))) then
        tmp = abs(((z + (-1.0d0)) / (y / x)))
    else
        tmp = abs((((-4.0d0) - x) / y))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if ((x <= -5e-32) || !(x <= 5.6e-124)) {
		tmp = Math.abs(((z + -1.0) / (y / x)));
	} else {
		tmp = Math.abs(((-4.0 - x) / y));
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (x <= -5e-32) or not (x <= 5.6e-124):
		tmp = math.fabs(((z + -1.0) / (y / x)))
	else:
		tmp = math.fabs(((-4.0 - x) / y))
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((x <= -5e-32) || !(x <= 5.6e-124))
		tmp = abs(Float64(Float64(z + -1.0) / Float64(y / x)));
	else
		tmp = abs(Float64(Float64(-4.0 - x) / y));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if ((x <= -5e-32) || ~((x <= 5.6e-124)))
		tmp = abs(((z + -1.0) / (y / x)));
	else
		tmp = abs(((-4.0 - x) / y));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[x, -5e-32], N[Not[LessEqual[x, 5.6e-124]], $MachinePrecision]], N[Abs[N[(N[(z + -1.0), $MachinePrecision] / N[(y / x), $MachinePrecision]), $MachinePrecision]], $MachinePrecision], N[Abs[N[(N[(-4.0 - x), $MachinePrecision] / y), $MachinePrecision]], $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < -5e-32 or 5.59999999999999996e-124 < x

   1. Initial program 89.3%

      \[\left|\frac{x + 4}{y} - \frac{x}{y} \cdot z\right| \]

   3. Simplified 93.5%

      \[\leadsto \color{blue}{\left|\frac{1}{y} \cdot \mathsf{fma}\left(x, z, -4 - x\right)\right|} \]

   4. Taylor expanded in x around inf 86.4%

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

      1. associate-/l* 92.1%

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

      2. sub-neg 92.1%

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

      3. metadata-eval 92.1%

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

   6. Simplified 92.1%

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

   if -5e-32 < x < 5.59999999999999996e-124

   1. Initial program 98.2%

      \[\left|\frac{x + 4}{y} - \frac{x}{y} \cdot z\right| \]

   3. Simplified 99.9%

      \[\leadsto \color{blue}{\left|\frac{1}{y} \cdot \mathsf{fma}\left(x, z, -4 - x\right)\right|} \]

   4. Taylor expanded in z around 0 85.8%

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

      1. associate-*r/ 85.8%

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

      2. distribute-lft-in 85.8%

         \[\leadsto \left|\frac{\color{blue}{-1 \cdot 4 + -1 \cdot x}}{y}\right| \]

      3. metadata-eval 85.8%

         \[\leadsto \left|\frac{\color{blue}{-4} + -1 \cdot x}{y}\right| \]

      4. neg-mul-1 85.8%

         \[\leadsto \left|\frac{-4 + \color{blue}{\left(-x\right)}}{y}\right| \]

      5. sub-neg 85.8%

         \[\leadsto \left|\frac{\color{blue}{-4 - x}}{y}\right| \]

   6. Simplified 85.8%

      \[\leadsto \left|\color{blue}{\frac{-4 - x}{y}}\right| \]
3. Recombined 2 regimes into one program.

4. Final simplification 89.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -5 \cdot 10^{-32} \lor \neg \left(x \leq 5.6 \cdot 10^{-124}\right):\\ \;\;\;\;\left|\frac{z + -1}{\frac{y}{x}}\right|\\ \mathbf{else}:\\ \;\;\;\;\left|\frac{-4 - x}{y}\right|\\ \end{array} \]

Alternative 8: 86.6% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -9 \cdot 10^{+42}:\\ \;\;\;\;\left|\frac{z}{\frac{y}{x}}\right|\\ \mathbf{elif}\;z \leq 3.6 \cdot 10^{+34}:\\ \;\;\;\;\left|\frac{-4 - x}{y}\right|\\ \mathbf{else}:\\ \;\;\;\;\left|\frac{x}{\frac{y}{z}}\right|\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= z -9e+42)
   (fabs (/ z (/ y x)))
   (if (<= z 3.6e+34) (fabs (/ (- -4.0 x) y)) (fabs (/ x (/ y z))))))

C

double code(double x, double y, double z) {
	double tmp;
	if (z <= -9e+42) {
		tmp = fabs((z / (y / x)));
	} else if (z <= 3.6e+34) {
		tmp = fabs(((-4.0 - x) / y));
	} else {
		tmp = fabs((x / (y / z)));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: tmp
    if (z <= (-9d+42)) then
        tmp = abs((z / (y / x)))
    else if (z <= 3.6d+34) then
        tmp = abs((((-4.0d0) - x) / y))
    else
        tmp = abs((x / (y / z)))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if (z <= -9e+42) {
		tmp = Math.abs((z / (y / x)));
	} else if (z <= 3.6e+34) {
		tmp = Math.abs(((-4.0 - x) / y));
	} else {
		tmp = Math.abs((x / (y / z)));
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if z <= -9e+42:
		tmp = math.fabs((z / (y / x)))
	elif z <= 3.6e+34:
		tmp = math.fabs(((-4.0 - x) / y))
	else:
		tmp = math.fabs((x / (y / z)))
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (z <= -9e+42)
		tmp = abs(Float64(z / Float64(y / x)));
	elseif (z <= 3.6e+34)
		tmp = abs(Float64(Float64(-4.0 - x) / y));
	else
		tmp = abs(Float64(x / Float64(y / z)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (z <= -9e+42)
		tmp = abs((z / (y / x)));
	elseif (z <= 3.6e+34)
		tmp = abs(((-4.0 - x) / y));
	else
		tmp = abs((x / (y / z)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[z, -9e+42], N[Abs[N[(z / N[(y / x), $MachinePrecision]), $MachinePrecision]], $MachinePrecision], If[LessEqual[z, 3.6e+34], N[Abs[N[(N[(-4.0 - x), $MachinePrecision] / y), $MachinePrecision]], $MachinePrecision], N[Abs[N[(x / N[(y / z), $MachinePrecision]), $MachinePrecision]], $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if z < -9.00000000000000025e42

   1. Initial program 98.4%

      \[\left|\frac{x + 4}{y} - \frac{x}{y} \cdot z\right| \]

   3. Simplified 94.0%

      \[\leadsto \color{blue}{\left|\frac{1}{y} \cdot \mathsf{fma}\left(x, z, -4 - x\right)\right|} \]

   4. Taylor expanded in z around inf 67.0%

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

      1. *-commutative 67.0%

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

      2. associate-*l/ 71.7%

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

      3. *-commutative 71.7%

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

   6. Simplified 71.7%

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

      1. clear-num 71.6%

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

      2. un-div-inv 71.7%

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

   8. Applied egg-rr 71.7%

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

   if -9.00000000000000025e42 < z < 3.6e34

   1. Initial program 92.9%

      \[\left|\frac{x + 4}{y} - \frac{x}{y} \cdot z\right| \]

   3. Simplified 99.8%

      \[\leadsto \color{blue}{\left|\frac{1}{y} \cdot \mathsf{fma}\left(x, z, -4 - x\right)\right|} \]

   4. Taylor expanded in z around 0 95.7%

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

      1. associate-*r/ 95.7%

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

      2. distribute-lft-in 95.7%

         \[\leadsto \left|\frac{\color{blue}{-1 \cdot 4 + -1 \cdot x}}{y}\right| \]

      3. metadata-eval 95.7%

         \[\leadsto \left|\frac{\color{blue}{-4} + -1 \cdot x}{y}\right| \]

      4. neg-mul-1 95.7%

         \[\leadsto \left|\frac{-4 + \color{blue}{\left(-x\right)}}{y}\right| \]

      5. sub-neg 95.7%

         \[\leadsto \left|\frac{\color{blue}{-4 - x}}{y}\right| \]

   6. Simplified 95.7%

      \[\leadsto \left|\color{blue}{\frac{-4 - x}{y}}\right| \]

   if 3.6e34 < z

   1. Initial program 87.8%

      \[\left|\frac{x + 4}{y} - \frac{x}{y} \cdot z\right| \]

   3. Simplified 91.2%

      \[\leadsto \color{blue}{\left|\frac{1}{y} \cdot \mathsf{fma}\left(x, z, -4 - x\right)\right|} \]

   4. Taylor expanded in z around inf 73.0%

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

      1. *-commutative 73.0%

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

      2. associate-*l/ 78.7%

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

      3. *-commutative 78.7%

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

   6. Simplified 78.7%

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

      1. associate-*r/ 73.0%

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

      2. *-commutative 73.0%

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

      3. associate-/l* 78.9%

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

   8. Applied egg-rr 78.9%

      \[\leadsto \left|\color{blue}{\frac{x}{\frac{y}{z}}}\right| \]
3. Recombined 3 regimes into one program.

4. Final simplification 85.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -9 \cdot 10^{+42}:\\ \;\;\;\;\left|\frac{z}{\frac{y}{x}}\right|\\ \mathbf{elif}\;z \leq 3.6 \cdot 10^{+34}:\\ \;\;\;\;\left|\frac{-4 - x}{y}\right|\\ \mathbf{else}:\\ \;\;\;\;\left|\frac{x}{\frac{y}{z}}\right|\\ \end{array} \]

Alternative 9: 69.1% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -1.55 \lor \neg \left(x \leq 4\right):\\ \;\;\;\;\left|\frac{x}{y}\right|\\ \mathbf{else}:\\ \;\;\;\;\left|\frac{4}{y}\right|\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= x -1.55) (not (<= x 4.0))) (fabs (/ x y)) (fabs (/ 4.0 y))))

C

double code(double x, double y, double z) {
	double tmp;
	if ((x <= -1.55) || !(x <= 4.0)) {
		tmp = fabs((x / y));
	} else {
		tmp = fabs((4.0 / y));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: tmp
    if ((x <= (-1.55d0)) .or. (.not. (x <= 4.0d0))) then
        tmp = abs((x / y))
    else
        tmp = abs((4.0d0 / y))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if ((x <= -1.55) || !(x <= 4.0)) {
		tmp = Math.abs((x / y));
	} else {
		tmp = Math.abs((4.0 / y));
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (x <= -1.55) or not (x <= 4.0):
		tmp = math.fabs((x / y))
	else:
		tmp = math.fabs((4.0 / y))
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((x <= -1.55) || !(x <= 4.0))
		tmp = abs(Float64(x / y));
	else
		tmp = abs(Float64(4.0 / y));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if ((x <= -1.55) || ~((x <= 4.0)))
		tmp = abs((x / y));
	else
		tmp = abs((4.0 / y));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[x, -1.55], N[Not[LessEqual[x, 4.0]], $MachinePrecision]], N[Abs[N[(x / y), $MachinePrecision]], $MachinePrecision], N[Abs[N[(4.0 / y), $MachinePrecision]], $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < -1.55000000000000004 or 4 < x

   1. Initial program 87.4%

      \[\left|\frac{x + 4}{y} - \frac{x}{y} \cdot z\right| \]
   2. Step-by-step derivation

      1. associate-*l/ 85.6%

         \[\leadsto \left|\frac{x + 4}{y} - \color{blue}{\frac{x \cdot z}{y}}\right| \]

      2. sub-div 92.2%

         \[\leadsto \left|\color{blue}{\frac{\left(x + 4\right) - x \cdot z}{y}}\right| \]

   3. Applied egg-rr 92.2%

      \[\leadsto \left|\color{blue}{\frac{\left(x + 4\right) - x \cdot z}{y}}\right| \]

   4. Taylor expanded in x around inf 91.5%

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

      1. sub-neg 91.5%

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

      2. +-commutative 91.5%

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

      3. distribute-rgt1-in 91.5%

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

      4. cancel-sign-sub-inv 91.5%

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

   6. Simplified 91.5%

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

   7. Taylor expanded in z around 0 55.0%

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

   if -1.55000000000000004 < x < 4

   1. Initial program 97.9%

      \[\left|\frac{x + 4}{y} - \frac{x}{y} \cdot z\right| \]

   2. Taylor expanded in x around 0 73.7%

      \[\leadsto \left|\color{blue}{\frac{4}{y}}\right| \]
3. Recombined 2 regimes into one program.

4. Final simplification 64.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -1.55 \lor \neg \left(x \leq 4\right):\\ \;\;\;\;\left|\frac{x}{y}\right|\\ \mathbf{else}:\\ \;\;\;\;\left|\frac{4}{y}\right|\\ \end{array} \]

Alternative 10: 40.5% accurate, 1.1× speedup

Math

\[\begin{array}{l} \\ \left|\frac{4}{y}\right| \end{array} \]

FPCore

(FPCore (x y z) :precision binary64 (fabs (/ 4.0 y)))

C

double code(double x, double y, double z) {
	return fabs((4.0 / y));
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    code = abs((4.0d0 / y))
end function

Java

public static double code(double x, double y, double z) {
	return Math.abs((4.0 / y));
}

Python

def code(x, y, z):
	return math.fabs((4.0 / y))

Julia

function code(x, y, z)
	return abs(Float64(4.0 / y))
end

MATLAB

function tmp = code(x, y, z)
	tmp = abs((4.0 / y));
end

Wolfram

code[x_, y_, z_] := N[Abs[N[(4.0 / y), $MachinePrecision]], $MachinePrecision]

Derivation

1. Initial program 92.9%

   \[\left|\frac{x + 4}{y} - \frac{x}{y} \cdot z\right| \]

2. Taylor expanded in x around 0 41.2%

   \[\leadsto \left|\color{blue}{\frac{4}{y}}\right| \]

3. Final simplification 41.2%

   \[\leadsto \left|\frac{4}{y}\right| \]

Reproduce

herbie shell --seed 2023187 
(FPCore (x y z)
  :name "fabs fraction 1"
  :precision binary64
  (fabs (- (/ (+ x 4.0) y) (* (/ x y) z))))