fabs fraction 1

Percentage Accurate: 91.0% → 99.4%

Time: 8.0s

Alternatives: 13

Speedup: 1.0×

• 21.6% 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: 91.0% 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: 99.4% accurate, 0.5× speedup

Math

\[\begin{array}{l} y = |y|\\ \\ \begin{array}{l} \mathbf{if}\;y \leq 8 \cdot 10^{-82}:\\ \;\;\;\;\left|\frac{\left(x + 4\right) - x \cdot z}{y}\right|\\ \mathbf{else}:\\ \;\;\;\;\left|\mathsf{fma}\left(x, \frac{z}{y}, \frac{-4 - x}{y}\right)\right|\\ \end{array} \end{array} \]

FPCore

NOTE: y should be positive before calling this function
(FPCore (x y z)
 :precision binary64
 (if (<= y 8e-82)
   (fabs (/ (- (+ x 4.0) (* x z)) y))
   (fabs (fma x (/ z y) (/ (- -4.0 x) y)))))

C

y = abs(y);
double code(double x, double y, double z) {
	double tmp;
	if (y <= 8e-82) {
		tmp = fabs((((x + 4.0) - (x * z)) / y));
	} else {
		tmp = fabs(fma(x, (z / y), ((-4.0 - x) / y)));
	}
	return tmp;
}

Julia

y = abs(y)
function code(x, y, z)
	tmp = 0.0
	if (y <= 8e-82)
		tmp = abs(Float64(Float64(Float64(x + 4.0) - Float64(x * z)) / y));
	else
		tmp = abs(fma(x, Float64(z / y), Float64(Float64(-4.0 - x) / y)));
	end
	return tmp
end

Wolfram

NOTE: y should be positive before calling this function
code[x_, y_, z_] := If[LessEqual[y, 8e-82], N[Abs[N[(N[(N[(x + 4.0), $MachinePrecision] - N[(x * z), $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision]], $MachinePrecision], N[Abs[N[(x * N[(z / y), $MachinePrecision] + N[(N[(-4.0 - x), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision]], $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < 8e-82

   1. Initial program 88.5%

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

      1. associate-*l/ 89.2%

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

      2. sub-div 96.7%

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

   3. Applied egg-rr 96.7%

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

   if 8e-82 < y

   1. Initial program 95.1%

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

      1. fabs-sub 95.1%

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

      2. associate-*l/ 96.5%

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

      3. *-commutative 96.5%

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

      4. associate-*l/ 99.9%

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

      5. *-commutative 99.9%

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

      6. fma-neg 99.9%

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

      7. distribute-neg-frac 99.9%

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

      8. +-commutative 99.9%

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

      9. distribute-neg-in 99.9%

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

      10. unsub-neg 99.9%

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

      11. metadata-eval 99.9%

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

   3. Simplified 99.9%

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

4. Final simplification 97.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq 8 \cdot 10^{-82}:\\ \;\;\;\;\left|\frac{\left(x + 4\right) - x \cdot z}{y}\right|\\ \mathbf{else}:\\ \;\;\;\;\left|\mathsf{fma}\left(x, \frac{z}{y}, \frac{-4 - x}{y}\right)\right|\\ \end{array} \]

Alternative 2: 67.4% accurate, 0.9× speedup

Math

\[\begin{array}{l} y = |y|\\ \\ \begin{array}{l} t_0 := \left|z \cdot \frac{x}{y}\right|\\ t_1 := \left|\frac{x}{y}\right|\\ t_2 := \left|\frac{4}{y}\right|\\ \mathbf{if}\;x \leq -10.5:\\ \;\;\;\;t_1\\ \mathbf{elif}\;x \leq 6.5 \cdot 10^{-90}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;x \leq 3.25 \cdot 10^{-37}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;x \leq 4:\\ \;\;\;\;t_2\\ \mathbf{elif}\;x \leq 9.5 \cdot 10^{+48}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;x \leq 9 \cdot 10^{+81}:\\ \;\;\;\;\left|x \cdot \frac{z}{y}\right|\\ \mathbf{elif}\;x \leq 1.5 \cdot 10^{+163}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t_0\\ \end{array} \end{array} \]

FPCore

NOTE: y should be positive before calling this function
(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (fabs (* z (/ x y)))) (t_1 (fabs (/ x y))) (t_2 (fabs (/ 4.0 y))))
   (if (<= x -10.5)
     t_1
     (if (<= x 6.5e-90)
       t_2
       (if (<= x 3.25e-37)
         t_0
         (if (<= x 4.0)
           t_2
           (if (<= x 9.5e+48)
             t_1
             (if (<= x 9e+81)
               (fabs (* x (/ z y)))
               (if (<= x 1.5e+163) t_1 t_0)))))))))

C

y = abs(y);
double code(double x, double y, double z) {
	double t_0 = fabs((z * (x / y)));
	double t_1 = fabs((x / y));
	double t_2 = fabs((4.0 / y));
	double tmp;
	if (x <= -10.5) {
		tmp = t_1;
	} else if (x <= 6.5e-90) {
		tmp = t_2;
	} else if (x <= 3.25e-37) {
		tmp = t_0;
	} else if (x <= 4.0) {
		tmp = t_2;
	} else if (x <= 9.5e+48) {
		tmp = t_1;
	} else if (x <= 9e+81) {
		tmp = fabs((x * (z / y)));
	} else if (x <= 1.5e+163) {
		tmp = t_1;
	} else {
		tmp = t_0;
	}
	return tmp;
}

Fortran

NOTE: y should be positive before calling this function
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((z * (x / y)))
    t_1 = abs((x / y))
    t_2 = abs((4.0d0 / y))
    if (x <= (-10.5d0)) then
        tmp = t_1
    else if (x <= 6.5d-90) then
        tmp = t_2
    else if (x <= 3.25d-37) then
        tmp = t_0
    else if (x <= 4.0d0) then
        tmp = t_2
    else if (x <= 9.5d+48) then
        tmp = t_1
    else if (x <= 9d+81) then
        tmp = abs((x * (z / y)))
    else if (x <= 1.5d+163) then
        tmp = t_1
    else
        tmp = t_0
    end if
    code = tmp
end function

Java

y = Math.abs(y);
public static double code(double x, double y, double z) {
	double t_0 = Math.abs((z * (x / y)));
	double t_1 = Math.abs((x / y));
	double t_2 = Math.abs((4.0 / y));
	double tmp;
	if (x <= -10.5) {
		tmp = t_1;
	} else if (x <= 6.5e-90) {
		tmp = t_2;
	} else if (x <= 3.25e-37) {
		tmp = t_0;
	} else if (x <= 4.0) {
		tmp = t_2;
	} else if (x <= 9.5e+48) {
		tmp = t_1;
	} else if (x <= 9e+81) {
		tmp = Math.abs((x * (z / y)));
	} else if (x <= 1.5e+163) {
		tmp = t_1;
	} else {
		tmp = t_0;
	}
	return tmp;
}

Python

y = abs(y)
def code(x, y, z):
	t_0 = math.fabs((z * (x / y)))
	t_1 = math.fabs((x / y))
	t_2 = math.fabs((4.0 / y))
	tmp = 0
	if x <= -10.5:
		tmp = t_1
	elif x <= 6.5e-90:
		tmp = t_2
	elif x <= 3.25e-37:
		tmp = t_0
	elif x <= 4.0:
		tmp = t_2
	elif x <= 9.5e+48:
		tmp = t_1
	elif x <= 9e+81:
		tmp = math.fabs((x * (z / y)))
	elif x <= 1.5e+163:
		tmp = t_1
	else:
		tmp = t_0
	return tmp

Julia

y = abs(y)
function code(x, y, z)
	t_0 = abs(Float64(z * Float64(x / y)))
	t_1 = abs(Float64(x / y))
	t_2 = abs(Float64(4.0 / y))
	tmp = 0.0
	if (x <= -10.5)
		tmp = t_1;
	elseif (x <= 6.5e-90)
		tmp = t_2;
	elseif (x <= 3.25e-37)
		tmp = t_0;
	elseif (x <= 4.0)
		tmp = t_2;
	elseif (x <= 9.5e+48)
		tmp = t_1;
	elseif (x <= 9e+81)
		tmp = abs(Float64(x * Float64(z / y)));
	elseif (x <= 1.5e+163)
		tmp = t_1;
	else
		tmp = t_0;
	end
	return tmp
end

MATLAB

y = abs(y)
function tmp_2 = code(x, y, z)
	t_0 = abs((z * (x / y)));
	t_1 = abs((x / y));
	t_2 = abs((4.0 / y));
	tmp = 0.0;
	if (x <= -10.5)
		tmp = t_1;
	elseif (x <= 6.5e-90)
		tmp = t_2;
	elseif (x <= 3.25e-37)
		tmp = t_0;
	elseif (x <= 4.0)
		tmp = t_2;
	elseif (x <= 9.5e+48)
		tmp = t_1;
	elseif (x <= 9e+81)
		tmp = abs((x * (z / y)));
	elseif (x <= 1.5e+163)
		tmp = t_1;
	else
		tmp = t_0;
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: y should be positive before calling this function
code[x_, y_, z_] := Block[{t$95$0 = N[Abs[N[(z * N[(x / y), $MachinePrecision]), $MachinePrecision]], $MachinePrecision]}, Block[{t$95$1 = N[Abs[N[(x / y), $MachinePrecision]], $MachinePrecision]}, Block[{t$95$2 = N[Abs[N[(4.0 / y), $MachinePrecision]], $MachinePrecision]}, If[LessEqual[x, -10.5], t$95$1, If[LessEqual[x, 6.5e-90], t$95$2, If[LessEqual[x, 3.25e-37], t$95$0, If[LessEqual[x, 4.0], t$95$2, If[LessEqual[x, 9.5e+48], t$95$1, If[LessEqual[x, 9e+81], N[Abs[N[(x * N[(z / y), $MachinePrecision]), $MachinePrecision]], $MachinePrecision], If[LessEqual[x, 1.5e+163], t$95$1, t$95$0]]]]]]]]]]

Derivation

1. Split input into 4 regimes

2. if x < -10.5 or 4 < x < 9.4999999999999997e48 or 9.00000000000000034e81 < x < 1.50000000000000007e163

   1. Initial program 84.1%

      \[\left|\frac{x + 4}{y} - \frac{x}{y} \cdot z\right| \]
   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 96.6%

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

   3. Applied egg-rr 96.6%

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

   4. Taylor expanded in x around inf 95.2%

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

      1. associate-/l* 98.4%

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

   6. Simplified 98.4%

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

   7. Taylor expanded in z around 0 71.5%

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

   if -10.5 < x < 6.4999999999999996e-90 or 3.2500000000000001e-37 < x < 4

   1. Initial program 96.3%

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

   2. Taylor expanded in x around 0 80.6%

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

   if 6.4999999999999996e-90 < x < 3.2500000000000001e-37 or 1.50000000000000007e163 < x

   1. Initial program 83.6%

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

   3. Simplified 84.4%

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

   4. Taylor expanded in x around inf 84.2%

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

   5. Taylor expanded in z around inf 61.4%

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

      1. associate-*r/ 81.8%

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

   7. Simplified 81.8%

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

   if 9.4999999999999997e48 < x < 9.00000000000000034e81

   1. Initial program 99.7%

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

   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 99.4%

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

      1. associate-*l/ 99.7%

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

      2. *-commutative 99.7%

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

   6. Simplified 99.7%

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

4. Final simplification 78.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -10.5:\\ \;\;\;\;\left|\frac{x}{y}\right|\\ \mathbf{elif}\;x \leq 6.5 \cdot 10^{-90}:\\ \;\;\;\;\left|\frac{4}{y}\right|\\ \mathbf{elif}\;x \leq 3.25 \cdot 10^{-37}:\\ \;\;\;\;\left|z \cdot \frac{x}{y}\right|\\ \mathbf{elif}\;x \leq 4:\\ \;\;\;\;\left|\frac{4}{y}\right|\\ \mathbf{elif}\;x \leq 9.5 \cdot 10^{+48}:\\ \;\;\;\;\left|\frac{x}{y}\right|\\ \mathbf{elif}\;x \leq 9 \cdot 10^{+81}:\\ \;\;\;\;\left|x \cdot \frac{z}{y}\right|\\ \mathbf{elif}\;x \leq 1.5 \cdot 10^{+163}:\\ \;\;\;\;\left|\frac{x}{y}\right|\\ \mathbf{else}:\\ \;\;\;\;\left|z \cdot \frac{x}{y}\right|\\ \end{array} \]

Alternative 3: 67.2% accurate, 0.9× speedup

Math

\[\begin{array}{l} y = |y|\\ \\ \begin{array}{l} t_0 := \left|\frac{x}{y}\right|\\ t_1 := \left|\frac{4}{y}\right|\\ \mathbf{if}\;x \leq -10.5:\\ \;\;\;\;t_0\\ \mathbf{elif}\;x \leq 6.5 \cdot 10^{-90}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;x \leq 4.2 \cdot 10^{-33}:\\ \;\;\;\;\left|z \cdot \frac{x}{y}\right|\\ \mathbf{elif}\;x \leq 4:\\ \;\;\;\;t_1\\ \mathbf{elif}\;x \leq 5.3 \cdot 10^{+48}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;x \leq 2.2 \cdot 10^{+81}:\\ \;\;\;\;\left|x \cdot \frac{z}{y}\right|\\ \mathbf{elif}\;x \leq 5.2 \cdot 10^{+155}:\\ \;\;\;\;t_0\\ \mathbf{else}:\\ \;\;\;\;\left|\frac{z}{\frac{y}{x}}\right|\\ \end{array} \end{array} \]

FPCore

NOTE: y should be positive before calling this function
(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (fabs (/ x y))) (t_1 (fabs (/ 4.0 y))))
   (if (<= x -10.5)
     t_0
     (if (<= x 6.5e-90)
       t_1
       (if (<= x 4.2e-33)
         (fabs (* z (/ x y)))
         (if (<= x 4.0)
           t_1
           (if (<= x 5.3e+48)
             t_0
             (if (<= x 2.2e+81)
               (fabs (* x (/ z y)))
               (if (<= x 5.2e+155) t_0 (fabs (/ z (/ y x))))))))))))

C

y = abs(y);
double code(double x, double y, double z) {
	double t_0 = fabs((x / y));
	double t_1 = fabs((4.0 / y));
	double tmp;
	if (x <= -10.5) {
		tmp = t_0;
	} else if (x <= 6.5e-90) {
		tmp = t_1;
	} else if (x <= 4.2e-33) {
		tmp = fabs((z * (x / y)));
	} else if (x <= 4.0) {
		tmp = t_1;
	} else if (x <= 5.3e+48) {
		tmp = t_0;
	} else if (x <= 2.2e+81) {
		tmp = fabs((x * (z / y)));
	} else if (x <= 5.2e+155) {
		tmp = t_0;
	} else {
		tmp = fabs((z / (y / x)));
	}
	return tmp;
}

Fortran

NOTE: y should be positive before calling this function
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((x / y))
    t_1 = abs((4.0d0 / y))
    if (x <= (-10.5d0)) then
        tmp = t_0
    else if (x <= 6.5d-90) then
        tmp = t_1
    else if (x <= 4.2d-33) then
        tmp = abs((z * (x / y)))
    else if (x <= 4.0d0) then
        tmp = t_1
    else if (x <= 5.3d+48) then
        tmp = t_0
    else if (x <= 2.2d+81) then
        tmp = abs((x * (z / y)))
    else if (x <= 5.2d+155) then
        tmp = t_0
    else
        tmp = abs((z / (y / x)))
    end if
    code = tmp
end function

Java

y = Math.abs(y);
public static double code(double x, double y, double z) {
	double t_0 = Math.abs((x / y));
	double t_1 = Math.abs((4.0 / y));
	double tmp;
	if (x <= -10.5) {
		tmp = t_0;
	} else if (x <= 6.5e-90) {
		tmp = t_1;
	} else if (x <= 4.2e-33) {
		tmp = Math.abs((z * (x / y)));
	} else if (x <= 4.0) {
		tmp = t_1;
	} else if (x <= 5.3e+48) {
		tmp = t_0;
	} else if (x <= 2.2e+81) {
		tmp = Math.abs((x * (z / y)));
	} else if (x <= 5.2e+155) {
		tmp = t_0;
	} else {
		tmp = Math.abs((z / (y / x)));
	}
	return tmp;
}

Python

y = abs(y)
def code(x, y, z):
	t_0 = math.fabs((x / y))
	t_1 = math.fabs((4.0 / y))
	tmp = 0
	if x <= -10.5:
		tmp = t_0
	elif x <= 6.5e-90:
		tmp = t_1
	elif x <= 4.2e-33:
		tmp = math.fabs((z * (x / y)))
	elif x <= 4.0:
		tmp = t_1
	elif x <= 5.3e+48:
		tmp = t_0
	elif x <= 2.2e+81:
		tmp = math.fabs((x * (z / y)))
	elif x <= 5.2e+155:
		tmp = t_0
	else:
		tmp = math.fabs((z / (y / x)))
	return tmp

Julia

y = abs(y)
function code(x, y, z)
	t_0 = abs(Float64(x / y))
	t_1 = abs(Float64(4.0 / y))
	tmp = 0.0
	if (x <= -10.5)
		tmp = t_0;
	elseif (x <= 6.5e-90)
		tmp = t_1;
	elseif (x <= 4.2e-33)
		tmp = abs(Float64(z * Float64(x / y)));
	elseif (x <= 4.0)
		tmp = t_1;
	elseif (x <= 5.3e+48)
		tmp = t_0;
	elseif (x <= 2.2e+81)
		tmp = abs(Float64(x * Float64(z / y)));
	elseif (x <= 5.2e+155)
		tmp = t_0;
	else
		tmp = abs(Float64(z / Float64(y / x)));
	end
	return tmp
end

MATLAB

y = abs(y)
function tmp_2 = code(x, y, z)
	t_0 = abs((x / y));
	t_1 = abs((4.0 / y));
	tmp = 0.0;
	if (x <= -10.5)
		tmp = t_0;
	elseif (x <= 6.5e-90)
		tmp = t_1;
	elseif (x <= 4.2e-33)
		tmp = abs((z * (x / y)));
	elseif (x <= 4.0)
		tmp = t_1;
	elseif (x <= 5.3e+48)
		tmp = t_0;
	elseif (x <= 2.2e+81)
		tmp = abs((x * (z / y)));
	elseif (x <= 5.2e+155)
		tmp = t_0;
	else
		tmp = abs((z / (y / x)));
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: y should be positive before calling this function
code[x_, y_, z_] := Block[{t$95$0 = N[Abs[N[(x / y), $MachinePrecision]], $MachinePrecision]}, Block[{t$95$1 = N[Abs[N[(4.0 / y), $MachinePrecision]], $MachinePrecision]}, If[LessEqual[x, -10.5], t$95$0, If[LessEqual[x, 6.5e-90], t$95$1, If[LessEqual[x, 4.2e-33], N[Abs[N[(z * N[(x / y), $MachinePrecision]), $MachinePrecision]], $MachinePrecision], If[LessEqual[x, 4.0], t$95$1, If[LessEqual[x, 5.3e+48], t$95$0, If[LessEqual[x, 2.2e+81], N[Abs[N[(x * N[(z / y), $MachinePrecision]), $MachinePrecision]], $MachinePrecision], If[LessEqual[x, 5.2e+155], t$95$0, N[Abs[N[(z / N[(y / x), $MachinePrecision]), $MachinePrecision]], $MachinePrecision]]]]]]]]]]

Derivation

1. Split input into 5 regimes

2. if x < -10.5 or 4 < x < 5.3e48 or 2.19999999999999987e81 < x < 5.2000000000000004e155

   1. Initial program 83.5%

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

      1. associate-*l/ 86.3%

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

      2. sub-div 97.6%

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

   3. Applied egg-rr 97.6%

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

   4. Taylor expanded in x around inf 96.2%

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

      1. associate-/l* 98.3%

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

   6. Simplified 98.3%

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

   7. Taylor expanded in z around 0 71.7%

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

   if -10.5 < x < 6.4999999999999996e-90 or 4.2e-33 < x < 4

   1. Initial program 96.3%

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

   2. Taylor expanded in x around 0 80.6%

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

   if 6.4999999999999996e-90 < x < 4.2e-33

   1. Initial program 99.4%

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

   3. Simplified 99.4%

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

   4. Taylor expanded in x around inf 97.3%

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

   5. Taylor expanded in z around inf 97.3%

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

      1. associate-*r/ 97.0%

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

   7. Simplified 97.0%

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

   if 5.3e48 < x < 2.19999999999999987e81

   1. Initial program 99.7%

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

   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 99.4%

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

      1. associate-*l/ 99.7%

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

      2. *-commutative 99.7%

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

   6. Simplified 99.7%

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

   if 5.2000000000000004e155 < x

   1. Initial program 82.7%

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

   3. Simplified 80.8%

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

      1. associate-*l/ 81.0%

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

      2. associate-/l* 80.8%

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

      3. fma-udef 80.8%

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

      4. associate-+r- 80.8%

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

      5. fma-udef 80.8%

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

   5. Applied egg-rr 80.8%

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

   6. Taylor expanded in z around inf 51.4%

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

      1. associate-/l* 78.5%

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

   8. Simplified 78.5%

      \[\leadsto \left|\color{blue}{\frac{z}{\frac{y}{x}}}\right| \]
3. Recombined 5 regimes into one program.

4. Final simplification 78.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -10.5:\\ \;\;\;\;\left|\frac{x}{y}\right|\\ \mathbf{elif}\;x \leq 6.5 \cdot 10^{-90}:\\ \;\;\;\;\left|\frac{4}{y}\right|\\ \mathbf{elif}\;x \leq 4.2 \cdot 10^{-33}:\\ \;\;\;\;\left|z \cdot \frac{x}{y}\right|\\ \mathbf{elif}\;x \leq 4:\\ \;\;\;\;\left|\frac{4}{y}\right|\\ \mathbf{elif}\;x \leq 5.3 \cdot 10^{+48}:\\ \;\;\;\;\left|\frac{x}{y}\right|\\ \mathbf{elif}\;x \leq 2.2 \cdot 10^{+81}:\\ \;\;\;\;\left|x \cdot \frac{z}{y}\right|\\ \mathbf{elif}\;x \leq 5.2 \cdot 10^{+155}:\\ \;\;\;\;\left|\frac{x}{y}\right|\\ \mathbf{else}:\\ \;\;\;\;\left|\frac{z}{\frac{y}{x}}\right|\\ \end{array} \]

Alternative 4: 67.4% accurate, 0.9× speedup

Math

\[\begin{array}{l} y = |y|\\ \\ \begin{array}{l} t_0 := \left|\frac{x}{y}\right|\\ t_1 := \left|\frac{4}{y}\right|\\ \mathbf{if}\;x \leq -10.5:\\ \;\;\;\;t_0\\ \mathbf{elif}\;x \leq 6 \cdot 10^{-90}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;x \leq 7.2 \cdot 10^{-30}:\\ \;\;\;\;\left|\frac{x \cdot z}{y}\right|\\ \mathbf{elif}\;x \leq 4:\\ \;\;\;\;t_1\\ \mathbf{elif}\;x \leq 5.3 \cdot 10^{+48}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;x \leq 2.2 \cdot 10^{+81}:\\ \;\;\;\;\left|x \cdot \frac{z}{y}\right|\\ \mathbf{elif}\;x \leq 1.32 \cdot 10^{+156}:\\ \;\;\;\;t_0\\ \mathbf{else}:\\ \;\;\;\;\left|\frac{z}{\frac{y}{x}}\right|\\ \end{array} \end{array} \]

FPCore

NOTE: y should be positive before calling this function
(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (fabs (/ x y))) (t_1 (fabs (/ 4.0 y))))
   (if (<= x -10.5)
     t_0
     (if (<= x 6e-90)
       t_1
       (if (<= x 7.2e-30)
         (fabs (/ (* x z) y))
         (if (<= x 4.0)
           t_1
           (if (<= x 5.3e+48)
             t_0
             (if (<= x 2.2e+81)
               (fabs (* x (/ z y)))
               (if (<= x 1.32e+156) t_0 (fabs (/ z (/ y x))))))))))))

C

y = abs(y);
double code(double x, double y, double z) {
	double t_0 = fabs((x / y));
	double t_1 = fabs((4.0 / y));
	double tmp;
	if (x <= -10.5) {
		tmp = t_0;
	} else if (x <= 6e-90) {
		tmp = t_1;
	} else if (x <= 7.2e-30) {
		tmp = fabs(((x * z) / y));
	} else if (x <= 4.0) {
		tmp = t_1;
	} else if (x <= 5.3e+48) {
		tmp = t_0;
	} else if (x <= 2.2e+81) {
		tmp = fabs((x * (z / y)));
	} else if (x <= 1.32e+156) {
		tmp = t_0;
	} else {
		tmp = fabs((z / (y / x)));
	}
	return tmp;
}

Fortran

NOTE: y should be positive before calling this function
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((x / y))
    t_1 = abs((4.0d0 / y))
    if (x <= (-10.5d0)) then
        tmp = t_0
    else if (x <= 6d-90) then
        tmp = t_1
    else if (x <= 7.2d-30) then
        tmp = abs(((x * z) / y))
    else if (x <= 4.0d0) then
        tmp = t_1
    else if (x <= 5.3d+48) then
        tmp = t_0
    else if (x <= 2.2d+81) then
        tmp = abs((x * (z / y)))
    else if (x <= 1.32d+156) then
        tmp = t_0
    else
        tmp = abs((z / (y / x)))
    end if
    code = tmp
end function

Java

y = Math.abs(y);
public static double code(double x, double y, double z) {
	double t_0 = Math.abs((x / y));
	double t_1 = Math.abs((4.0 / y));
	double tmp;
	if (x <= -10.5) {
		tmp = t_0;
	} else if (x <= 6e-90) {
		tmp = t_1;
	} else if (x <= 7.2e-30) {
		tmp = Math.abs(((x * z) / y));
	} else if (x <= 4.0) {
		tmp = t_1;
	} else if (x <= 5.3e+48) {
		tmp = t_0;
	} else if (x <= 2.2e+81) {
		tmp = Math.abs((x * (z / y)));
	} else if (x <= 1.32e+156) {
		tmp = t_0;
	} else {
		tmp = Math.abs((z / (y / x)));
	}
	return tmp;
}

Python

y = abs(y)
def code(x, y, z):
	t_0 = math.fabs((x / y))
	t_1 = math.fabs((4.0 / y))
	tmp = 0
	if x <= -10.5:
		tmp = t_0
	elif x <= 6e-90:
		tmp = t_1
	elif x <= 7.2e-30:
		tmp = math.fabs(((x * z) / y))
	elif x <= 4.0:
		tmp = t_1
	elif x <= 5.3e+48:
		tmp = t_0
	elif x <= 2.2e+81:
		tmp = math.fabs((x * (z / y)))
	elif x <= 1.32e+156:
		tmp = t_0
	else:
		tmp = math.fabs((z / (y / x)))
	return tmp

Julia

y = abs(y)
function code(x, y, z)
	t_0 = abs(Float64(x / y))
	t_1 = abs(Float64(4.0 / y))
	tmp = 0.0
	if (x <= -10.5)
		tmp = t_0;
	elseif (x <= 6e-90)
		tmp = t_1;
	elseif (x <= 7.2e-30)
		tmp = abs(Float64(Float64(x * z) / y));
	elseif (x <= 4.0)
		tmp = t_1;
	elseif (x <= 5.3e+48)
		tmp = t_0;
	elseif (x <= 2.2e+81)
		tmp = abs(Float64(x * Float64(z / y)));
	elseif (x <= 1.32e+156)
		tmp = t_0;
	else
		tmp = abs(Float64(z / Float64(y / x)));
	end
	return tmp
end

MATLAB

y = abs(y)
function tmp_2 = code(x, y, z)
	t_0 = abs((x / y));
	t_1 = abs((4.0 / y));
	tmp = 0.0;
	if (x <= -10.5)
		tmp = t_0;
	elseif (x <= 6e-90)
		tmp = t_1;
	elseif (x <= 7.2e-30)
		tmp = abs(((x * z) / y));
	elseif (x <= 4.0)
		tmp = t_1;
	elseif (x <= 5.3e+48)
		tmp = t_0;
	elseif (x <= 2.2e+81)
		tmp = abs((x * (z / y)));
	elseif (x <= 1.32e+156)
		tmp = t_0;
	else
		tmp = abs((z / (y / x)));
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: y should be positive before calling this function
code[x_, y_, z_] := Block[{t$95$0 = N[Abs[N[(x / y), $MachinePrecision]], $MachinePrecision]}, Block[{t$95$1 = N[Abs[N[(4.0 / y), $MachinePrecision]], $MachinePrecision]}, If[LessEqual[x, -10.5], t$95$0, If[LessEqual[x, 6e-90], t$95$1, If[LessEqual[x, 7.2e-30], N[Abs[N[(N[(x * z), $MachinePrecision] / y), $MachinePrecision]], $MachinePrecision], If[LessEqual[x, 4.0], t$95$1, If[LessEqual[x, 5.3e+48], t$95$0, If[LessEqual[x, 2.2e+81], N[Abs[N[(x * N[(z / y), $MachinePrecision]), $MachinePrecision]], $MachinePrecision], If[LessEqual[x, 1.32e+156], t$95$0, N[Abs[N[(z / N[(y / x), $MachinePrecision]), $MachinePrecision]], $MachinePrecision]]]]]]]]]]

Derivation

1. Split input into 5 regimes

2. if x < -10.5 or 4 < x < 5.3e48 or 2.19999999999999987e81 < x < 1.3199999999999999e156

   1. Initial program 83.5%

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

      1. associate-*l/ 86.3%

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

      2. sub-div 97.6%

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

   3. Applied egg-rr 97.6%

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

   4. Taylor expanded in x around inf 96.2%

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

      1. associate-/l* 98.3%

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

   6. Simplified 98.3%

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

   7. Taylor expanded in z around 0 71.7%

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

   if -10.5 < x < 6.00000000000000041e-90 or 7.2000000000000006e-30 < x < 4

   1. Initial program 96.3%

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

   2. Taylor expanded in x around 0 80.6%

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

   if 6.00000000000000041e-90 < x < 7.2000000000000006e-30

   1. Initial program 99.4%

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

   3. Simplified 99.4%

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

   4. Taylor expanded in z around inf 97.3%

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

   if 5.3e48 < x < 2.19999999999999987e81

   1. Initial program 99.7%

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

   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 99.4%

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

      1. associate-*l/ 99.7%

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

      2. *-commutative 99.7%

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

   6. Simplified 99.7%

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

   if 1.3199999999999999e156 < x

   1. Initial program 82.7%

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

   3. Simplified 80.8%

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

      1. associate-*l/ 81.0%

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

      2. associate-/l* 80.8%

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

      3. fma-udef 80.8%

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

      4. associate-+r- 80.8%

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

      5. fma-udef 80.8%

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

   5. Applied egg-rr 80.8%

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

   6. Taylor expanded in z around inf 51.4%

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

      1. associate-/l* 78.5%

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

   8. Simplified 78.5%

      \[\leadsto \left|\color{blue}{\frac{z}{\frac{y}{x}}}\right| \]
3. Recombined 5 regimes into one program.

4. Final simplification 78.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -10.5:\\ \;\;\;\;\left|\frac{x}{y}\right|\\ \mathbf{elif}\;x \leq 6 \cdot 10^{-90}:\\ \;\;\;\;\left|\frac{4}{y}\right|\\ \mathbf{elif}\;x \leq 7.2 \cdot 10^{-30}:\\ \;\;\;\;\left|\frac{x \cdot z}{y}\right|\\ \mathbf{elif}\;x \leq 4:\\ \;\;\;\;\left|\frac{4}{y}\right|\\ \mathbf{elif}\;x \leq 5.3 \cdot 10^{+48}:\\ \;\;\;\;\left|\frac{x}{y}\right|\\ \mathbf{elif}\;x \leq 2.2 \cdot 10^{+81}:\\ \;\;\;\;\left|x \cdot \frac{z}{y}\right|\\ \mathbf{elif}\;x \leq 1.32 \cdot 10^{+156}:\\ \;\;\;\;\left|\frac{x}{y}\right|\\ \mathbf{else}:\\ \;\;\;\;\left|\frac{z}{\frac{y}{x}}\right|\\ \end{array} \]

Alternative 5: 98.4% accurate, 1.0× speedup

Math

\[\begin{array}{l} y = |y|\\ \\ \begin{array}{l} \mathbf{if}\;x \leq -1.15 \cdot 10^{+24} \lor \neg \left(x \leq 3.7\right):\\ \;\;\;\;\left|\left(z + -1\right) \cdot \frac{x}{y}\right|\\ \mathbf{else}:\\ \;\;\;\;\left|\frac{1}{\frac{y}{x \cdot z - 4}}\right|\\ \end{array} \end{array} \]

FPCore

NOTE: y should be positive before calling this function
(FPCore (x y z)
 :precision binary64
 (if (or (<= x -1.15e+24) (not (<= x 3.7)))
   (fabs (* (+ z -1.0) (/ x y)))
   (fabs (/ 1.0 (/ y (- (* x z) 4.0))))))

C

y = abs(y);
double code(double x, double y, double z) {
	double tmp;
	if ((x <= -1.15e+24) || !(x <= 3.7)) {
		tmp = fabs(((z + -1.0) * (x / y)));
	} else {
		tmp = fabs((1.0 / (y / ((x * z) - 4.0))));
	}
	return tmp;
}

Fortran

NOTE: y should be positive before calling this function
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 <= (-1.15d+24)) .or. (.not. (x <= 3.7d0))) then
        tmp = abs(((z + (-1.0d0)) * (x / y)))
    else
        tmp = abs((1.0d0 / (y / ((x * z) - 4.0d0))))
    end if
    code = tmp
end function

Java

y = Math.abs(y);
public static double code(double x, double y, double z) {
	double tmp;
	if ((x <= -1.15e+24) || !(x <= 3.7)) {
		tmp = Math.abs(((z + -1.0) * (x / y)));
	} else {
		tmp = Math.abs((1.0 / (y / ((x * z) - 4.0))));
	}
	return tmp;
}

Python

y = abs(y)
def code(x, y, z):
	tmp = 0
	if (x <= -1.15e+24) or not (x <= 3.7):
		tmp = math.fabs(((z + -1.0) * (x / y)))
	else:
		tmp = math.fabs((1.0 / (y / ((x * z) - 4.0))))
	return tmp

Julia

y = abs(y)
function code(x, y, z)
	tmp = 0.0
	if ((x <= -1.15e+24) || !(x <= 3.7))
		tmp = abs(Float64(Float64(z + -1.0) * Float64(x / y)));
	else
		tmp = abs(Float64(1.0 / Float64(y / Float64(Float64(x * z) - 4.0))));
	end
	return tmp
end

MATLAB

y = abs(y)
function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if ((x <= -1.15e+24) || ~((x <= 3.7)))
		tmp = abs(((z + -1.0) * (x / y)));
	else
		tmp = abs((1.0 / (y / ((x * z) - 4.0))));
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: y should be positive before calling this function
code[x_, y_, z_] := If[Or[LessEqual[x, -1.15e+24], N[Not[LessEqual[x, 3.7]], $MachinePrecision]], N[Abs[N[(N[(z + -1.0), $MachinePrecision] * N[(x / y), $MachinePrecision]), $MachinePrecision]], $MachinePrecision], N[Abs[N[(1.0 / N[(y / N[(N[(x * z), $MachinePrecision] - 4.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]], $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < -1.15e24 or 3.7000000000000002 < x

   1. Initial program 83.5%

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

   3. Simplified 92.4%

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

   4. Taylor expanded in x around inf 91.7%

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

      1. associate-/l* 98.8%

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

      2. div-inv 98.7%

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

      3. sub-neg 98.7%

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

      4. metadata-eval 98.7%

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

      5. clear-num 99.0%

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

   6. Applied egg-rr 99.0%

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

   if -1.15e24 < x < 3.7000000000000002

   1. Initial program 96.5%

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

   3. Simplified 99.9%

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

      1. associate-*l/ 99.9%

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

      2. associate-/l* 99.8%

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

      3. fma-udef 99.8%

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

      4. associate-+r- 99.8%

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

      5. fma-udef 99.8%

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

   5. Applied egg-rr 99.8%

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

   6. Taylor expanded in x around 0 99.8%

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

   7. Taylor expanded in z around inf 98.3%

      \[\leadsto \left|\frac{1}{\frac{y}{\color{blue}{z \cdot x} - 4}}\right| \]
3. Recombined 2 regimes into one program.

4. Final simplification 98.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -1.15 \cdot 10^{+24} \lor \neg \left(x \leq 3.7\right):\\ \;\;\;\;\left|\left(z + -1\right) \cdot \frac{x}{y}\right|\\ \mathbf{else}:\\ \;\;\;\;\left|\frac{1}{\frac{y}{x \cdot z - 4}}\right|\\ \end{array} \]

Alternative 6: 99.9% accurate, 1.0× speedup

Math

\[\begin{array}{l} y = |y|\\ \\ \begin{array}{l} \mathbf{if}\;y \leq 20000000:\\ \;\;\;\;\left|\frac{\left(x + 4\right) - x \cdot z}{y}\right|\\ \mathbf{else}:\\ \;\;\;\;\left|\frac{x + 4}{y} - \frac{x}{\frac{y}{z}}\right|\\ \end{array} \end{array} \]

FPCore

NOTE: y should be positive before calling this function
(FPCore (x y z)
 :precision binary64
 (if (<= y 20000000.0)
   (fabs (/ (- (+ x 4.0) (* x z)) y))
   (fabs (- (/ (+ x 4.0) y) (/ x (/ y z))))))

C

y = abs(y);
double code(double x, double y, double z) {
	double tmp;
	if (y <= 20000000.0) {
		tmp = fabs((((x + 4.0) - (x * z)) / y));
	} else {
		tmp = fabs((((x + 4.0) / y) - (x / (y / z))));
	}
	return tmp;
}

Fortran

NOTE: y should be positive before calling this function
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 (y <= 20000000.0d0) then
        tmp = abs((((x + 4.0d0) - (x * z)) / y))
    else
        tmp = abs((((x + 4.0d0) / y) - (x / (y / z))))
    end if
    code = tmp
end function

Java

y = Math.abs(y);
public static double code(double x, double y, double z) {
	double tmp;
	if (y <= 20000000.0) {
		tmp = Math.abs((((x + 4.0) - (x * z)) / y));
	} else {
		tmp = Math.abs((((x + 4.0) / y) - (x / (y / z))));
	}
	return tmp;
}

Python

y = abs(y)
def code(x, y, z):
	tmp = 0
	if y <= 20000000.0:
		tmp = math.fabs((((x + 4.0) - (x * z)) / y))
	else:
		tmp = math.fabs((((x + 4.0) / y) - (x / (y / z))))
	return tmp

Julia

y = abs(y)
function code(x, y, z)
	tmp = 0.0
	if (y <= 20000000.0)
		tmp = abs(Float64(Float64(Float64(x + 4.0) - Float64(x * z)) / y));
	else
		tmp = abs(Float64(Float64(Float64(x + 4.0) / y) - Float64(x / Float64(y / z))));
	end
	return tmp
end

MATLAB

y = abs(y)
function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (y <= 20000000.0)
		tmp = abs((((x + 4.0) - (x * z)) / y));
	else
		tmp = abs((((x + 4.0) / y) - (x / (y / z))));
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: y should be positive before calling this function
code[x_, y_, z_] := If[LessEqual[y, 20000000.0], N[Abs[N[(N[(N[(x + 4.0), $MachinePrecision] - N[(x * z), $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision]], $MachinePrecision], N[Abs[N[(N[(N[(x + 4.0), $MachinePrecision] / y), $MachinePrecision] - N[(x / N[(y / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]], $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < 2e7

   1. Initial program 89.2%

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

      1. associate-*l/ 90.3%

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

      2. sub-div 97.0%

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

   3. Applied egg-rr 97.0%

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

   if 2e7 < y

   1. Initial program 95.0%

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

      1. associate-*l/ 95.3%

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

      2. associate-/l* 99.8%

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

   3. Applied egg-rr 99.8%

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

4. Final simplification 97.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq 20000000:\\ \;\;\;\;\left|\frac{\left(x + 4\right) - x \cdot z}{y}\right|\\ \mathbf{else}:\\ \;\;\;\;\left|\frac{x + 4}{y} - \frac{x}{\frac{y}{z}}\right|\\ \end{array} \]

Alternative 7: 67.2% accurate, 1.0× speedup

Math

\[\begin{array}{l} y = |y|\\ \\ \begin{array}{l} t_0 := \left|\frac{x}{y}\right|\\ \mathbf{if}\;x \leq -10.5:\\ \;\;\;\;t_0\\ \mathbf{elif}\;x \leq 26000000:\\ \;\;\;\;\left|\frac{4}{y}\right|\\ \mathbf{elif}\;x \leq 5.6 \cdot 10^{+253}:\\ \;\;\;\;\left|x \cdot \frac{z}{y}\right|\\ \mathbf{else}:\\ \;\;\;\;t_0\\ \end{array} \end{array} \]

FPCore

NOTE: y should be positive before calling this function
(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (fabs (/ x y))))
   (if (<= x -10.5)
     t_0
     (if (<= x 26000000.0)
       (fabs (/ 4.0 y))
       (if (<= x 5.6e+253) (fabs (* x (/ z y))) t_0)))))

C

y = abs(y);
double code(double x, double y, double z) {
	double t_0 = fabs((x / y));
	double tmp;
	if (x <= -10.5) {
		tmp = t_0;
	} else if (x <= 26000000.0) {
		tmp = fabs((4.0 / y));
	} else if (x <= 5.6e+253) {
		tmp = fabs((x * (z / y)));
	} else {
		tmp = t_0;
	}
	return tmp;
}

Fortran

NOTE: y should be positive before calling this function
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 / y))
    if (x <= (-10.5d0)) then
        tmp = t_0
    else if (x <= 26000000.0d0) then
        tmp = abs((4.0d0 / y))
    else if (x <= 5.6d+253) then
        tmp = abs((x * (z / y)))
    else
        tmp = t_0
    end if
    code = tmp
end function

Java

y = Math.abs(y);
public static double code(double x, double y, double z) {
	double t_0 = Math.abs((x / y));
	double tmp;
	if (x <= -10.5) {
		tmp = t_0;
	} else if (x <= 26000000.0) {
		tmp = Math.abs((4.0 / y));
	} else if (x <= 5.6e+253) {
		tmp = Math.abs((x * (z / y)));
	} else {
		tmp = t_0;
	}
	return tmp;
}

Python

y = abs(y)
def code(x, y, z):
	t_0 = math.fabs((x / y))
	tmp = 0
	if x <= -10.5:
		tmp = t_0
	elif x <= 26000000.0:
		tmp = math.fabs((4.0 / y))
	elif x <= 5.6e+253:
		tmp = math.fabs((x * (z / y)))
	else:
		tmp = t_0
	return tmp

Julia

y = abs(y)
function code(x, y, z)
	t_0 = abs(Float64(x / y))
	tmp = 0.0
	if (x <= -10.5)
		tmp = t_0;
	elseif (x <= 26000000.0)
		tmp = abs(Float64(4.0 / y));
	elseif (x <= 5.6e+253)
		tmp = abs(Float64(x * Float64(z / y)));
	else
		tmp = t_0;
	end
	return tmp
end

MATLAB

y = abs(y)
function tmp_2 = code(x, y, z)
	t_0 = abs((x / y));
	tmp = 0.0;
	if (x <= -10.5)
		tmp = t_0;
	elseif (x <= 26000000.0)
		tmp = abs((4.0 / y));
	elseif (x <= 5.6e+253)
		tmp = abs((x * (z / y)));
	else
		tmp = t_0;
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: y should be positive before calling this function
code[x_, y_, z_] := Block[{t$95$0 = N[Abs[N[(x / y), $MachinePrecision]], $MachinePrecision]}, If[LessEqual[x, -10.5], t$95$0, If[LessEqual[x, 26000000.0], N[Abs[N[(4.0 / y), $MachinePrecision]], $MachinePrecision], If[LessEqual[x, 5.6e+253], N[Abs[N[(x * N[(z / y), $MachinePrecision]), $MachinePrecision]], $MachinePrecision], t$95$0]]]]

Derivation

1. Split input into 3 regimes

2. if x < -10.5 or 5.5999999999999999e253 < x

   1. Initial program 78.8%

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

      1. associate-*l/ 80.6%

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

      2. sub-div 95.8%

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

   3. Applied egg-rr 95.8%

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

   4. Taylor expanded in x around inf 95.7%

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

      1. associate-/l* 99.7%

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

   6. Simplified 99.7%

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

   7. Taylor expanded in z around 0 77.1%

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

   if -10.5 < x < 2.6e7

   1. Initial program 96.5%

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

   2. Taylor expanded in x around 0 77.0%

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

   if 2.6e7 < x < 5.5999999999999999e253

   1. Initial program 90.0%

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

   3. Simplified 88.6%

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

   4. Taylor expanded in z around inf 52.0%

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

      1. associate-*l/ 63.0%

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

      2. *-commutative 63.0%

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

   6. Simplified 63.0%

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

4. Final simplification 74.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -10.5:\\ \;\;\;\;\left|\frac{x}{y}\right|\\ \mathbf{elif}\;x \leq 26000000:\\ \;\;\;\;\left|\frac{4}{y}\right|\\ \mathbf{elif}\;x \leq 5.6 \cdot 10^{+253}:\\ \;\;\;\;\left|x \cdot \frac{z}{y}\right|\\ \mathbf{else}:\\ \;\;\;\;\left|\frac{x}{y}\right|\\ \end{array} \]

Alternative 8: 84.8% accurate, 1.0× speedup

Math

\[\begin{array}{l} y = |y|\\ \\ \begin{array}{l} \mathbf{if}\;z \leq -3.6 \cdot 10^{+127}:\\ \;\;\;\;\left|\frac{x \cdot z}{y}\right|\\ \mathbf{elif}\;z \leq 1.9 \cdot 10^{+32}:\\ \;\;\;\;\left|\frac{x}{y} + \frac{4}{y}\right|\\ \mathbf{else}:\\ \;\;\;\;\left|\frac{z}{\frac{y}{x}}\right|\\ \end{array} \end{array} \]

FPCore

NOTE: y should be positive before calling this function
(FPCore (x y z)
 :precision binary64
 (if (<= z -3.6e+127)
   (fabs (/ (* x z) y))
   (if (<= z 1.9e+32) (fabs (+ (/ x y) (/ 4.0 y))) (fabs (/ z (/ y x))))))

C

y = abs(y);
double code(double x, double y, double z) {
	double tmp;
	if (z <= -3.6e+127) {
		tmp = fabs(((x * z) / y));
	} else if (z <= 1.9e+32) {
		tmp = fabs(((x / y) + (4.0 / y)));
	} else {
		tmp = fabs((z / (y / x)));
	}
	return tmp;
}

Fortran

NOTE: y should be positive before calling this function
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 <= (-3.6d+127)) then
        tmp = abs(((x * z) / y))
    else if (z <= 1.9d+32) then
        tmp = abs(((x / y) + (4.0d0 / y)))
    else
        tmp = abs((z / (y / x)))
    end if
    code = tmp
end function

Java

y = Math.abs(y);
public static double code(double x, double y, double z) {
	double tmp;
	if (z <= -3.6e+127) {
		tmp = Math.abs(((x * z) / y));
	} else if (z <= 1.9e+32) {
		tmp = Math.abs(((x / y) + (4.0 / y)));
	} else {
		tmp = Math.abs((z / (y / x)));
	}
	return tmp;
}

Python

y = abs(y)
def code(x, y, z):
	tmp = 0
	if z <= -3.6e+127:
		tmp = math.fabs(((x * z) / y))
	elif z <= 1.9e+32:
		tmp = math.fabs(((x / y) + (4.0 / y)))
	else:
		tmp = math.fabs((z / (y / x)))
	return tmp

Julia

y = abs(y)
function code(x, y, z)
	tmp = 0.0
	if (z <= -3.6e+127)
		tmp = abs(Float64(Float64(x * z) / y));
	elseif (z <= 1.9e+32)
		tmp = abs(Float64(Float64(x / y) + Float64(4.0 / y)));
	else
		tmp = abs(Float64(z / Float64(y / x)));
	end
	return tmp
end

MATLAB

y = abs(y)
function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (z <= -3.6e+127)
		tmp = abs(((x * z) / y));
	elseif (z <= 1.9e+32)
		tmp = abs(((x / y) + (4.0 / y)));
	else
		tmp = abs((z / (y / x)));
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: y should be positive before calling this function
code[x_, y_, z_] := If[LessEqual[z, -3.6e+127], N[Abs[N[(N[(x * z), $MachinePrecision] / y), $MachinePrecision]], $MachinePrecision], If[LessEqual[z, 1.9e+32], N[Abs[N[(N[(x / y), $MachinePrecision] + N[(4.0 / y), $MachinePrecision]), $MachinePrecision]], $MachinePrecision], N[Abs[N[(z / N[(y / x), $MachinePrecision]), $MachinePrecision]], $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if z < -3.59999999999999979e127

   1. Initial program 93.3%

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

   3. Simplified 95.4%

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

   4. Taylor expanded in z around inf 81.8%

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

   if -3.59999999999999979e127 < z < 1.9000000000000002e32

   1. Initial program 94.3%

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

   2. Taylor expanded in z around 0 95.0%

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

      1. associate-*r/ 95.0%

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

      2. metadata-eval 95.0%

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

   4. Simplified 95.0%

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

   if 1.9000000000000002e32 < z

   1. Initial program 77.5%

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

   3. Simplified 92.8%

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

      1. associate-*l/ 92.8%

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

      2. associate-/l* 92.7%

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

      3. fma-udef 92.7%

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

      4. associate-+r- 92.7%

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

      5. fma-udef 92.7%

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

   5. Applied egg-rr 92.7%

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

   6. Taylor expanded in z around inf 74.1%

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

      1. associate-/l* 79.1%

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

   8. Simplified 79.1%

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

4. Final simplification 89.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -3.6 \cdot 10^{+127}:\\ \;\;\;\;\left|\frac{x \cdot z}{y}\right|\\ \mathbf{elif}\;z \leq 1.9 \cdot 10^{+32}:\\ \;\;\;\;\left|\frac{x}{y} + \frac{4}{y}\right|\\ \mathbf{else}:\\ \;\;\;\;\left|\frac{z}{\frac{y}{x}}\right|\\ \end{array} \]

Alternative 9: 84.7% accurate, 1.0× speedup

Math

\[\begin{array}{l} y = |y|\\ \\ \begin{array}{l} \mathbf{if}\;z \leq -2.1 \cdot 10^{+130}:\\ \;\;\;\;\left|\frac{x \cdot z}{y}\right|\\ \mathbf{elif}\;z \leq 3 \cdot 10^{+33}:\\ \;\;\;\;\left|\frac{x}{y} + \frac{4}{y}\right|\\ \mathbf{else}:\\ \;\;\;\;\left|\frac{z + -1}{\frac{y}{x}}\right|\\ \end{array} \end{array} \]

FPCore

NOTE: y should be positive before calling this function
(FPCore (x y z)
 :precision binary64
 (if (<= z -2.1e+130)
   (fabs (/ (* x z) y))
   (if (<= z 3e+33)
     (fabs (+ (/ x y) (/ 4.0 y)))
     (fabs (/ (+ z -1.0) (/ y x))))))

C

y = abs(y);
double code(double x, double y, double z) {
	double tmp;
	if (z <= -2.1e+130) {
		tmp = fabs(((x * z) / y));
	} else if (z <= 3e+33) {
		tmp = fabs(((x / y) + (4.0 / y)));
	} else {
		tmp = fabs(((z + -1.0) / (y / x)));
	}
	return tmp;
}

Fortran

NOTE: y should be positive before calling this function
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 <= (-2.1d+130)) then
        tmp = abs(((x * z) / y))
    else if (z <= 3d+33) then
        tmp = abs(((x / y) + (4.0d0 / y)))
    else
        tmp = abs(((z + (-1.0d0)) / (y / x)))
    end if
    code = tmp
end function

Java

y = Math.abs(y);
public static double code(double x, double y, double z) {
	double tmp;
	if (z <= -2.1e+130) {
		tmp = Math.abs(((x * z) / y));
	} else if (z <= 3e+33) {
		tmp = Math.abs(((x / y) + (4.0 / y)));
	} else {
		tmp = Math.abs(((z + -1.0) / (y / x)));
	}
	return tmp;
}

Python

y = abs(y)
def code(x, y, z):
	tmp = 0
	if z <= -2.1e+130:
		tmp = math.fabs(((x * z) / y))
	elif z <= 3e+33:
		tmp = math.fabs(((x / y) + (4.0 / y)))
	else:
		tmp = math.fabs(((z + -1.0) / (y / x)))
	return tmp

Julia

y = abs(y)
function code(x, y, z)
	tmp = 0.0
	if (z <= -2.1e+130)
		tmp = abs(Float64(Float64(x * z) / y));
	elseif (z <= 3e+33)
		tmp = abs(Float64(Float64(x / y) + Float64(4.0 / y)));
	else
		tmp = abs(Float64(Float64(z + -1.0) / Float64(y / x)));
	end
	return tmp
end

MATLAB

y = abs(y)
function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (z <= -2.1e+130)
		tmp = abs(((x * z) / y));
	elseif (z <= 3e+33)
		tmp = abs(((x / y) + (4.0 / y)));
	else
		tmp = abs(((z + -1.0) / (y / x)));
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: y should be positive before calling this function
code[x_, y_, z_] := If[LessEqual[z, -2.1e+130], N[Abs[N[(N[(x * z), $MachinePrecision] / y), $MachinePrecision]], $MachinePrecision], If[LessEqual[z, 3e+33], N[Abs[N[(N[(x / y), $MachinePrecision] + N[(4.0 / y), $MachinePrecision]), $MachinePrecision]], $MachinePrecision], N[Abs[N[(N[(z + -1.0), $MachinePrecision] / N[(y / x), $MachinePrecision]), $MachinePrecision]], $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if z < -2.0999999999999999e130

   1. Initial program 93.3%

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

   3. Simplified 95.4%

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

   4. Taylor expanded in z around inf 81.8%

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

   if -2.0999999999999999e130 < z < 2.99999999999999984e33

   1. Initial program 94.3%

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

   2. Taylor expanded in z around 0 95.0%

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

      1. associate-*r/ 95.0%

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

      2. metadata-eval 95.0%

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

   4. Simplified 95.0%

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

   if 2.99999999999999984e33 < z

   1. Initial program 77.5%

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

   3. Simplified 92.8%

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

   4. Taylor expanded in x around inf 74.1%

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

      1. associate-/l* 79.1%

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

      2. sub-neg 79.1%

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

      3. metadata-eval 79.1%

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

   6. Simplified 79.1%

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

4. Final simplification 89.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -2.1 \cdot 10^{+130}:\\ \;\;\;\;\left|\frac{x \cdot z}{y}\right|\\ \mathbf{elif}\;z \leq 3 \cdot 10^{+33}:\\ \;\;\;\;\left|\frac{x}{y} + \frac{4}{y}\right|\\ \mathbf{else}:\\ \;\;\;\;\left|\frac{z + -1}{\frac{y}{x}}\right|\\ \end{array} \]

Alternative 10: 98.1% accurate, 1.0× speedup

Math

\[\begin{array}{l} y = |y|\\ \\ \begin{array}{l} \mathbf{if}\;x \leq 4.4 \cdot 10^{+15}:\\ \;\;\;\;\left|\frac{\left(x + 4\right) - x \cdot z}{y}\right|\\ \mathbf{else}:\\ \;\;\;\;\left|\left(z + -1\right) \cdot \frac{x}{y}\right|\\ \end{array} \end{array} \]

FPCore

NOTE: y should be positive before calling this function
(FPCore (x y z)
 :precision binary64
 (if (<= x 4.4e+15)
   (fabs (/ (- (+ x 4.0) (* x z)) y))
   (fabs (* (+ z -1.0) (/ x y)))))

C

y = abs(y);
double code(double x, double y, double z) {
	double tmp;
	if (x <= 4.4e+15) {
		tmp = fabs((((x + 4.0) - (x * z)) / y));
	} else {
		tmp = fabs(((z + -1.0) * (x / y)));
	}
	return tmp;
}

Fortran

NOTE: y should be positive before calling this function
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 <= 4.4d+15) then
        tmp = abs((((x + 4.0d0) - (x * z)) / y))
    else
        tmp = abs(((z + (-1.0d0)) * (x / y)))
    end if
    code = tmp
end function

Java

y = Math.abs(y);
public static double code(double x, double y, double z) {
	double tmp;
	if (x <= 4.4e+15) {
		tmp = Math.abs((((x + 4.0) - (x * z)) / y));
	} else {
		tmp = Math.abs(((z + -1.0) * (x / y)));
	}
	return tmp;
}

Python

y = abs(y)
def code(x, y, z):
	tmp = 0
	if x <= 4.4e+15:
		tmp = math.fabs((((x + 4.0) - (x * z)) / y))
	else:
		tmp = math.fabs(((z + -1.0) * (x / y)))
	return tmp

Julia

y = abs(y)
function code(x, y, z)
	tmp = 0.0
	if (x <= 4.4e+15)
		tmp = abs(Float64(Float64(Float64(x + 4.0) - Float64(x * z)) / y));
	else
		tmp = abs(Float64(Float64(z + -1.0) * Float64(x / y)));
	end
	return tmp
end

MATLAB

y = abs(y)
function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (x <= 4.4e+15)
		tmp = abs((((x + 4.0) - (x * z)) / y));
	else
		tmp = abs(((z + -1.0) * (x / y)));
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: y should be positive before calling this function
code[x_, y_, z_] := If[LessEqual[x, 4.4e+15], N[Abs[N[(N[(N[(x + 4.0), $MachinePrecision] - N[(x * z), $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision]], $MachinePrecision], N[Abs[N[(N[(z + -1.0), $MachinePrecision] * N[(x / y), $MachinePrecision]), $MachinePrecision]], $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < 4.4e15

   1. Initial program 92.1%

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

      1. associate-*l/ 95.2%

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

      2. sub-div 98.9%

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

   3. Applied egg-rr 98.9%

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

   if 4.4e15 < x

   1. Initial program 86.2%

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

   3. Simplified 89.7%

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

   4. Taylor expanded in x around inf 89.8%

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

      1. associate-/l* 99.8%

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

      2. div-inv 99.7%

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

      3. sub-neg 99.7%

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

      4. metadata-eval 99.7%

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

      5. clear-num 99.9%

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

   6. Applied egg-rr 99.9%

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

4. Final simplification 99.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq 4.4 \cdot 10^{+15}:\\ \;\;\;\;\left|\frac{\left(x + 4\right) - x \cdot z}{y}\right|\\ \mathbf{else}:\\ \;\;\;\;\left|\left(z + -1\right) \cdot \frac{x}{y}\right|\\ \end{array} \]

Alternative 11: 84.7% accurate, 1.0× speedup

Math

\[\begin{array}{l} y = |y|\\ \\ \begin{array}{l} \mathbf{if}\;z \leq -3.5 \cdot 10^{+127}:\\ \;\;\;\;\left|\frac{x \cdot z}{y}\right|\\ \mathbf{elif}\;z \leq 10^{+30}:\\ \;\;\;\;\left|\frac{-4 - x}{y}\right|\\ \mathbf{else}:\\ \;\;\;\;\left|\frac{z}{\frac{y}{x}}\right|\\ \end{array} \end{array} \]

FPCore

NOTE: y should be positive before calling this function
(FPCore (x y z)
 :precision binary64
 (if (<= z -3.5e+127)
   (fabs (/ (* x z) y))
   (if (<= z 1e+30) (fabs (/ (- -4.0 x) y)) (fabs (/ z (/ y x))))))

C

y = abs(y);
double code(double x, double y, double z) {
	double tmp;
	if (z <= -3.5e+127) {
		tmp = fabs(((x * z) / y));
	} else if (z <= 1e+30) {
		tmp = fabs(((-4.0 - x) / y));
	} else {
		tmp = fabs((z / (y / x)));
	}
	return tmp;
}

Fortran

NOTE: y should be positive before calling this function
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 <= (-3.5d+127)) then
        tmp = abs(((x * z) / y))
    else if (z <= 1d+30) then
        tmp = abs((((-4.0d0) - x) / y))
    else
        tmp = abs((z / (y / x)))
    end if
    code = tmp
end function

Java

y = Math.abs(y);
public static double code(double x, double y, double z) {
	double tmp;
	if (z <= -3.5e+127) {
		tmp = Math.abs(((x * z) / y));
	} else if (z <= 1e+30) {
		tmp = Math.abs(((-4.0 - x) / y));
	} else {
		tmp = Math.abs((z / (y / x)));
	}
	return tmp;
}

Python

y = abs(y)
def code(x, y, z):
	tmp = 0
	if z <= -3.5e+127:
		tmp = math.fabs(((x * z) / y))
	elif z <= 1e+30:
		tmp = math.fabs(((-4.0 - x) / y))
	else:
		tmp = math.fabs((z / (y / x)))
	return tmp

Julia

y = abs(y)
function code(x, y, z)
	tmp = 0.0
	if (z <= -3.5e+127)
		tmp = abs(Float64(Float64(x * z) / y));
	elseif (z <= 1e+30)
		tmp = abs(Float64(Float64(-4.0 - x) / y));
	else
		tmp = abs(Float64(z / Float64(y / x)));
	end
	return tmp
end

MATLAB

y = abs(y)
function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (z <= -3.5e+127)
		tmp = abs(((x * z) / y));
	elseif (z <= 1e+30)
		tmp = abs(((-4.0 - x) / y));
	else
		tmp = abs((z / (y / x)));
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: y should be positive before calling this function
code[x_, y_, z_] := If[LessEqual[z, -3.5e+127], N[Abs[N[(N[(x * z), $MachinePrecision] / y), $MachinePrecision]], $MachinePrecision], If[LessEqual[z, 1e+30], N[Abs[N[(N[(-4.0 - x), $MachinePrecision] / y), $MachinePrecision]], $MachinePrecision], N[Abs[N[(z / N[(y / x), $MachinePrecision]), $MachinePrecision]], $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if z < -3.49999999999999978e127

   1. Initial program 93.3%

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

   3. Simplified 95.4%

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

   4. Taylor expanded in z around inf 81.8%

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

   if -3.49999999999999978e127 < z < 1e30

   1. Initial program 94.3%

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

   3. Simplified 98.1%

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

   4. Taylor expanded in z around 0 94.9%

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

      1. associate-*r/ 94.9%

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

      2. distribute-lft-in 94.9%

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

      3. metadata-eval 94.9%

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

      4. neg-mul-1 94.9%

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

      5. sub-neg 94.9%

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

   6. Simplified 94.9%

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

   if 1e30 < z

   1. Initial program 77.5%

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

   3. Simplified 92.8%

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

      1. associate-*l/ 92.8%

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

      2. associate-/l* 92.7%

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

      3. fma-udef 92.7%

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

      4. associate-+r- 92.7%

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

      5. fma-udef 92.7%

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

   5. Applied egg-rr 92.7%

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

   6. Taylor expanded in z around inf 74.1%

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

      1. associate-/l* 79.1%

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

   8. Simplified 79.1%

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

4. Final simplification 89.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -3.5 \cdot 10^{+127}:\\ \;\;\;\;\left|\frac{x \cdot z}{y}\right|\\ \mathbf{elif}\;z \leq 10^{+30}:\\ \;\;\;\;\left|\frac{-4 - x}{y}\right|\\ \mathbf{else}:\\ \;\;\;\;\left|\frac{z}{\frac{y}{x}}\right|\\ \end{array} \]

Alternative 12: 68.2% accurate, 1.0× speedup

Math

\[\begin{array}{l} y = |y|\\ \\ \begin{array}{l} \mathbf{if}\;x \leq -10.5 \lor \neg \left(x \leq 4\right):\\ \;\;\;\;\left|\frac{x}{y}\right|\\ \mathbf{else}:\\ \;\;\;\;\left|\frac{4}{y}\right|\\ \end{array} \end{array} \]

FPCore

NOTE: y should be positive before calling this function
(FPCore (x y z)
 :precision binary64
 (if (or (<= x -10.5) (not (<= x 4.0))) (fabs (/ x y)) (fabs (/ 4.0 y))))

C

y = abs(y);
double code(double x, double y, double z) {
	double tmp;
	if ((x <= -10.5) || !(x <= 4.0)) {
		tmp = fabs((x / y));
	} else {
		tmp = fabs((4.0 / y));
	}
	return tmp;
}

Fortran

NOTE: y should be positive before calling this function
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 <= (-10.5d0)) .or. (.not. (x <= 4.0d0))) then
        tmp = abs((x / y))
    else
        tmp = abs((4.0d0 / y))
    end if
    code = tmp
end function

Java

y = Math.abs(y);
public static double code(double x, double y, double z) {
	double tmp;
	if ((x <= -10.5) || !(x <= 4.0)) {
		tmp = Math.abs((x / y));
	} else {
		tmp = Math.abs((4.0 / y));
	}
	return tmp;
}

Python

y = abs(y)
def code(x, y, z):
	tmp = 0
	if (x <= -10.5) or not (x <= 4.0):
		tmp = math.fabs((x / y))
	else:
		tmp = math.fabs((4.0 / y))
	return tmp

Julia

y = abs(y)
function code(x, y, z)
	tmp = 0.0
	if ((x <= -10.5) || !(x <= 4.0))
		tmp = abs(Float64(x / y));
	else
		tmp = abs(Float64(4.0 / y));
	end
	return tmp
end

MATLAB

y = abs(y)
function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if ((x <= -10.5) || ~((x <= 4.0)))
		tmp = abs((x / y));
	else
		tmp = abs((4.0 / y));
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: y should be positive before calling this function
code[x_, y_, z_] := If[Or[LessEqual[x, -10.5], 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 < -10.5 or 4 < x

   1. Initial program 84.0%

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

      1. associate-*l/ 81.9%

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

      2. sub-div 92.8%

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

   3. Applied egg-rr 92.8%

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

   4. Taylor expanded in x around inf 91.9%

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

      1. associate-/l* 98.8%

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

   6. Simplified 98.8%

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

   7. Taylor expanded in z around 0 65.5%

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

   if -10.5 < x < 4

   1. Initial program 96.4%

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

   2. Taylor expanded in x around 0 77.9%

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

4. Final simplification 72.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -10.5 \lor \neg \left(x \leq 4\right):\\ \;\;\;\;\left|\frac{x}{y}\right|\\ \mathbf{else}:\\ \;\;\;\;\left|\frac{4}{y}\right|\\ \end{array} \]

Alternative 13: 39.2% accurate, 1.1× speedup

Math

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

FPCore

NOTE: y should be positive before calling this function
(FPCore (x y z) :precision binary64 (fabs (/ 4.0 y)))

C

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

Fortran

NOTE: y should be positive before calling this function
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

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

Python

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

Julia

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

MATLAB

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

Wolfram

NOTE: y should be positive before calling this function
code[x_, y_, z_] := N[Abs[N[(4.0 / y), $MachinePrecision]], $MachinePrecision]

Derivation

1. Initial program 90.6%

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

2. Taylor expanded in x around 0 44.1%

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

3. Final simplification 44.1%

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

Reproduce

herbie shell --seed 2023189 
(FPCore (x y z)
  :name "fabs fraction 1"
  :precision binary64
  (fabs (- (/ (+ x 4.0) y) (* (/ x y) z))))