Numeric.Signal.Multichannel:$cput from hsignal-0.2.7.1

Percentage Accurate: 96.9% → 96.9%

Time: 10.0s

Alternatives: 13

Speedup: 1.0×

Specification

Math

\[\begin{array}{l} \\ \frac{x - y}{z - y} \cdot t \end{array} \]

FPCore

(FPCore (x y z t) :precision binary64 (* (/ (- x y) (- z y)) t))

C

double code(double x, double y, double z, double t) {
	return ((x - y) / (z - y)) * t;
}

Fortran

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

Java

public static double code(double x, double y, double z, double t) {
	return ((x - y) / (z - y)) * t;
}

Python

def code(x, y, z, t):
	return ((x - y) / (z - y)) * t

Julia

function code(x, y, z, t)
	return Float64(Float64(Float64(x - y) / Float64(z - y)) * t)
end

MATLAB

function tmp = code(x, y, z, t)
	tmp = ((x - y) / (z - y)) * t;
end

Wolfram

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

Initial Program: 96.9% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \frac{x - y}{z - y} \cdot t \end{array} \]

FPCore

(FPCore (x y z t) :precision binary64 (* (/ (- x y) (- z y)) t))

C

double code(double x, double y, double z, double t) {
	return ((x - y) / (z - y)) * t;
}

Fortran

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

Java

public static double code(double x, double y, double z, double t) {
	return ((x - y) / (z - y)) * t;
}

Python

def code(x, y, z, t):
	return ((x - y) / (z - y)) * t

Julia

function code(x, y, z, t)
	return Float64(Float64(Float64(x - y) / Float64(z - y)) * t)
end

MATLAB

function tmp = code(x, y, z, t)
	tmp = ((x - y) / (z - y)) * t;
end

Wolfram

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

Alternative 1: 96.9% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \frac{x - y}{z - y} \cdot t \end{array} \]

FPCore

(FPCore (x y z t) :precision binary64 (* (/ (- x y) (- z y)) t))

C

double code(double x, double y, double z, double t) {
	return ((x - y) / (z - y)) * t;
}

Fortran

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

Java

public static double code(double x, double y, double z, double t) {
	return ((x - y) / (z - y)) * t;
}

Python

def code(x, y, z, t):
	return ((x - y) / (z - y)) * t

Julia

function code(x, y, z, t)
	return Float64(Float64(Float64(x - y) / Float64(z - y)) * t)
end

MATLAB

function tmp = code(x, y, z, t)
	tmp = ((x - y) / (z - y)) * t;
end

Wolfram

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

Derivation

1. Initial program 97.3%

   \[\frac{x - y}{z - y} \cdot t \]
2. Add Preprocessing
3. Add Preprocessing

Alternative 2: 70.2% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := y \cdot \frac{t}{y - z}\\ \mathbf{if}\;y \leq -6.5 \cdot 10^{+174}:\\ \;\;\;\;t\\ \mathbf{elif}\;y \leq -1.9 \cdot 10^{-96}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y \leq 2.75 \cdot 10^{-11}:\\ \;\;\;\;x \cdot \frac{t}{z - y}\\ \mathbf{elif}\;y \leq 4.9 \cdot 10^{+92}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;t\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (* y (/ t (- y z)))))
   (if (<= y -6.5e+174)
     t
     (if (<= y -1.9e-96)
       t_1
       (if (<= y 2.75e-11) (* x (/ t (- z y))) (if (<= y 4.9e+92) t_1 t))))))

C

double code(double x, double y, double z, double t) {
	double t_1 = y * (t / (y - z));
	double tmp;
	if (y <= -6.5e+174) {
		tmp = t;
	} else if (y <= -1.9e-96) {
		tmp = t_1;
	} else if (y <= 2.75e-11) {
		tmp = x * (t / (z - y));
	} else if (y <= 4.9e+92) {
		tmp = t_1;
	} else {
		tmp = t;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: t_1
    real(8) :: tmp
    t_1 = y * (t / (y - z))
    if (y <= (-6.5d+174)) then
        tmp = t
    else if (y <= (-1.9d-96)) then
        tmp = t_1
    else if (y <= 2.75d-11) then
        tmp = x * (t / (z - y))
    else if (y <= 4.9d+92) then
        tmp = t_1
    else
        tmp = t
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double t_1 = y * (t / (y - z));
	double tmp;
	if (y <= -6.5e+174) {
		tmp = t;
	} else if (y <= -1.9e-96) {
		tmp = t_1;
	} else if (y <= 2.75e-11) {
		tmp = x * (t / (z - y));
	} else if (y <= 4.9e+92) {
		tmp = t_1;
	} else {
		tmp = t;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = y * (t / (y - z))
	tmp = 0
	if y <= -6.5e+174:
		tmp = t
	elif y <= -1.9e-96:
		tmp = t_1
	elif y <= 2.75e-11:
		tmp = x * (t / (z - y))
	elif y <= 4.9e+92:
		tmp = t_1
	else:
		tmp = t
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(y * Float64(t / Float64(y - z)))
	tmp = 0.0
	if (y <= -6.5e+174)
		tmp = t;
	elseif (y <= -1.9e-96)
		tmp = t_1;
	elseif (y <= 2.75e-11)
		tmp = Float64(x * Float64(t / Float64(z - y)));
	elseif (y <= 4.9e+92)
		tmp = t_1;
	else
		tmp = t;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = y * (t / (y - z));
	tmp = 0.0;
	if (y <= -6.5e+174)
		tmp = t;
	elseif (y <= -1.9e-96)
		tmp = t_1;
	elseif (y <= 2.75e-11)
		tmp = x * (t / (z - y));
	elseif (y <= 4.9e+92)
		tmp = t_1;
	else
		tmp = t;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(y * N[(t / N[(y - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -6.5e+174], t, If[LessEqual[y, -1.9e-96], t$95$1, If[LessEqual[y, 2.75e-11], N[(x * N[(t / N[(z - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 4.9e+92], t$95$1, t]]]]]

Derivation

1. Split input into 3 regimes

2. if y < -6.5000000000000001e174 or 4.9000000000000002e92 < y

   1. Initial program 100.0%

      \[\frac{x - y}{z - y} \cdot t \]
   2. Step-by-step derivation

      1. associate-*l/ 67.4%

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

      2. associate-/l* 59.7%

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

   3. Simplified 59.7%

      \[\leadsto \color{blue}{\left(x - y\right) \cdot \frac{t}{z - y}} \]
   4. Add Preprocessing

   5. Taylor expanded in y around inf 84.1%

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

   if -6.5000000000000001e174 < y < -1.9e-96 or 2.74999999999999987e-11 < y < 4.9000000000000002e92

   1. Initial program 98.6%

      \[\frac{x - y}{z - y} \cdot t \]
   2. Step-by-step derivation

      1. associate-*l/ 92.0%

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

      2. associate-/l* 91.9%

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

   3. Simplified 91.9%

      \[\leadsto \color{blue}{\left(x - y\right) \cdot \frac{t}{z - y}} \]
   4. Add Preprocessing

   5. Taylor expanded in x around 0 60.5%

      \[\leadsto \color{blue}{-1 \cdot \frac{t \cdot y}{z - y}} \]
   6. Step-by-step derivation

      1. associate-*r/ 60.5%

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

      2. mul-1-neg 60.5%

         \[\leadsto \frac{\color{blue}{-t \cdot y}}{z - y} \]

      3. distribute-rgt-neg-out 60.5%

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

      4. associate-*l/ 62.5%

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

      5. *-commutative 62.5%

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

      6. distribute-lft-neg-out 62.5%

         \[\leadsto \color{blue}{-y \cdot \frac{t}{z - y}} \]

      7. distribute-rgt-neg-in 62.5%

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

      8. distribute-frac-neg2 62.5%

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

      9. neg-sub0 62.5%

         \[\leadsto y \cdot \frac{t}{\color{blue}{0 - \left(z - y\right)}} \]

      10. sub-neg 62.5%

          \[\leadsto y \cdot \frac{t}{0 - \color{blue}{\left(z + \left(-y\right)\right)}} \]

      11. +-commutative 62.5%

          \[\leadsto y \cdot \frac{t}{0 - \color{blue}{\left(\left(-y\right) + z\right)}} \]

      12. associate--r+ 62.5%

          \[\leadsto y \cdot \frac{t}{\color{blue}{\left(0 - \left(-y\right)\right) - z}} \]

      13. neg-sub0 62.5%

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

      14. remove-double-neg 62.5%

          \[\leadsto y \cdot \frac{t}{\color{blue}{y} - z} \]

   7. Simplified 62.5%

      \[\leadsto \color{blue}{y \cdot \frac{t}{y - z}} \]

   if -1.9e-96 < y < 2.74999999999999987e-11

   1. Initial program 94.7%

      \[\frac{x - y}{z - y} \cdot t \]
   2. Step-by-step derivation

      1. associate-*l/ 93.7%

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

      2. associate-/l* 92.8%

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

   3. Simplified 92.8%

      \[\leadsto \color{blue}{\left(x - y\right) \cdot \frac{t}{z - y}} \]
   4. Add Preprocessing

   5. Taylor expanded in x around inf 80.4%

      \[\leadsto \color{blue}{x} \cdot \frac{t}{z - y} \]
3. Recombined 3 regimes into one program.
4. Add Preprocessing

Alternative 3: 59.0% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -5.6 \cdot 10^{+84}:\\ \;\;\;\;t\\ \mathbf{elif}\;y \leq -1.65 \cdot 10^{-45}:\\ \;\;\;\;t \cdot \frac{-x}{y}\\ \mathbf{elif}\;y \leq -5.8 \cdot 10^{-138}:\\ \;\;\;\;\frac{t}{z} \cdot \left(-y\right)\\ \mathbf{elif}\;y \leq 6.2 \cdot 10^{-32}:\\ \;\;\;\;x \cdot \frac{t}{z}\\ \mathbf{else}:\\ \;\;\;\;t\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= y -5.6e+84)
   t
   (if (<= y -1.65e-45)
     (* t (/ (- x) y))
     (if (<= y -5.8e-138)
       (* (/ t z) (- y))
       (if (<= y 6.2e-32) (* x (/ t z)) t)))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (y <= -5.6e+84) {
		tmp = t;
	} else if (y <= -1.65e-45) {
		tmp = t * (-x / y);
	} else if (y <= -5.8e-138) {
		tmp = (t / z) * -y;
	} else if (y <= 6.2e-32) {
		tmp = x * (t / z);
	} else {
		tmp = t;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if (y <= (-5.6d+84)) then
        tmp = t
    else if (y <= (-1.65d-45)) then
        tmp = t * (-x / y)
    else if (y <= (-5.8d-138)) then
        tmp = (t / z) * -y
    else if (y <= 6.2d-32) then
        tmp = x * (t / z)
    else
        tmp = t
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if (y <= -5.6e+84) {
		tmp = t;
	} else if (y <= -1.65e-45) {
		tmp = t * (-x / y);
	} else if (y <= -5.8e-138) {
		tmp = (t / z) * -y;
	} else if (y <= 6.2e-32) {
		tmp = x * (t / z);
	} else {
		tmp = t;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if y <= -5.6e+84:
		tmp = t
	elif y <= -1.65e-45:
		tmp = t * (-x / y)
	elif y <= -5.8e-138:
		tmp = (t / z) * -y
	elif y <= 6.2e-32:
		tmp = x * (t / z)
	else:
		tmp = t
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (y <= -5.6e+84)
		tmp = t;
	elseif (y <= -1.65e-45)
		tmp = Float64(t * Float64(Float64(-x) / y));
	elseif (y <= -5.8e-138)
		tmp = Float64(Float64(t / z) * Float64(-y));
	elseif (y <= 6.2e-32)
		tmp = Float64(x * Float64(t / z));
	else
		tmp = t;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (y <= -5.6e+84)
		tmp = t;
	elseif (y <= -1.65e-45)
		tmp = t * (-x / y);
	elseif (y <= -5.8e-138)
		tmp = (t / z) * -y;
	elseif (y <= 6.2e-32)
		tmp = x * (t / z);
	else
		tmp = t;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[y, -5.6e+84], t, If[LessEqual[y, -1.65e-45], N[(t * N[((-x) / y), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, -5.8e-138], N[(N[(t / z), $MachinePrecision] * (-y)), $MachinePrecision], If[LessEqual[y, 6.2e-32], N[(x * N[(t / z), $MachinePrecision]), $MachinePrecision], t]]]]

Derivation

1. Split input into 4 regimes

2. if y < -5.59999999999999963e84 or 6.20000000000000021e-32 < y

   1. Initial program 99.9%

      \[\frac{x - y}{z - y} \cdot t \]
   2. Step-by-step derivation

      1. associate-*l/ 75.3%

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

      2. associate-/l* 71.8%

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

   3. Simplified 71.8%

      \[\leadsto \color{blue}{\left(x - y\right) \cdot \frac{t}{z - y}} \]
   4. Add Preprocessing

   5. Taylor expanded in y around inf 67.4%

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

   if -5.59999999999999963e84 < y < -1.65e-45

   1. Initial program 99.7%

      \[\frac{x - y}{z - y} \cdot t \]
   2. Add Preprocessing

   3. Taylor expanded in x around inf 56.8%

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

   4. Taylor expanded in z around 0 45.8%

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

      1. associate-*r/ 45.8%

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

      2. neg-mul-1 45.8%

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

   6. Simplified 45.8%

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

   if -1.65e-45 < y < -5.79999999999999946e-138

   1. Initial program 94.6%

      \[\frac{x - y}{z - y} \cdot t \]
   2. Step-by-step derivation

      1. associate-*l/ 99.4%

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

      2. associate-/l* 99.7%

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

   3. Simplified 99.7%

      \[\leadsto \color{blue}{\left(x - y\right) \cdot \frac{t}{z - y}} \]
   4. Add Preprocessing

   5. Taylor expanded in x around 0 74.4%

      \[\leadsto \color{blue}{-1 \cdot \frac{t \cdot y}{z - y}} \]
   6. Step-by-step derivation

      1. associate-*r/ 74.4%

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

      2. mul-1-neg 74.4%

         \[\leadsto \frac{\color{blue}{-t \cdot y}}{z - y} \]

      3. distribute-rgt-neg-out 74.4%

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

      4. associate-*l/ 74.6%

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

      5. *-commutative 74.6%

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

      6. distribute-lft-neg-out 74.6%

         \[\leadsto \color{blue}{-y \cdot \frac{t}{z - y}} \]

      7. distribute-rgt-neg-in 74.6%

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

      8. distribute-frac-neg2 74.6%

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

      9. neg-sub0 74.6%

         \[\leadsto y \cdot \frac{t}{\color{blue}{0 - \left(z - y\right)}} \]

      10. sub-neg 74.6%

          \[\leadsto y \cdot \frac{t}{0 - \color{blue}{\left(z + \left(-y\right)\right)}} \]

      11. +-commutative 74.6%

          \[\leadsto y \cdot \frac{t}{0 - \color{blue}{\left(\left(-y\right) + z\right)}} \]

      12. associate--r+ 74.6%

          \[\leadsto y \cdot \frac{t}{\color{blue}{\left(0 - \left(-y\right)\right) - z}} \]

      13. neg-sub0 74.6%

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

      14. remove-double-neg 74.6%

          \[\leadsto y \cdot \frac{t}{\color{blue}{y} - z} \]

   7. Simplified 74.6%

      \[\leadsto \color{blue}{y \cdot \frac{t}{y - z}} \]

   8. Taylor expanded in y around 0 77.8%

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

      1. associate-*r/ 77.8%

         \[\leadsto y \cdot \color{blue}{\frac{-1 \cdot t}{z}} \]

      2. neg-mul-1 77.8%

         \[\leadsto y \cdot \frac{\color{blue}{-t}}{z} \]

   10. Simplified 77.8%

       \[\leadsto y \cdot \color{blue}{\frac{-t}{z}} \]

   if -5.79999999999999946e-138 < y < 6.20000000000000021e-32

   1. Initial program 94.0%

      \[\frac{x - y}{z - y} \cdot t \]
   2. Step-by-step derivation

      1. associate-*l/ 93.0%

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

      2. associate-/l* 91.9%

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

   3. Simplified 91.9%

      \[\leadsto \color{blue}{\left(x - y\right) \cdot \frac{t}{z - y}} \]
   4. Add Preprocessing

   5. Taylor expanded in x around inf 80.8%

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

   6. Taylor expanded in z around inf 69.7%

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

4. Final simplification 66.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -5.6 \cdot 10^{+84}:\\ \;\;\;\;t\\ \mathbf{elif}\;y \leq -1.65 \cdot 10^{-45}:\\ \;\;\;\;t \cdot \frac{-x}{y}\\ \mathbf{elif}\;y \leq -5.8 \cdot 10^{-138}:\\ \;\;\;\;\frac{t}{z} \cdot \left(-y\right)\\ \mathbf{elif}\;y \leq 6.2 \cdot 10^{-32}:\\ \;\;\;\;x \cdot \frac{t}{z}\\ \mathbf{else}:\\ \;\;\;\;t\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 59.0% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -1.5 \cdot 10^{+85}:\\ \;\;\;\;t\\ \mathbf{elif}\;y \leq -3.1 \cdot 10^{-46}:\\ \;\;\;\;\left(-x\right) \cdot \frac{t}{y}\\ \mathbf{elif}\;y \leq -5.8 \cdot 10^{-138}:\\ \;\;\;\;\frac{t}{z} \cdot \left(-y\right)\\ \mathbf{elif}\;y \leq 4.3 \cdot 10^{-32}:\\ \;\;\;\;x \cdot \frac{t}{z}\\ \mathbf{else}:\\ \;\;\;\;t\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= y -1.5e+85)
   t
   (if (<= y -3.1e-46)
     (* (- x) (/ t y))
     (if (<= y -5.8e-138)
       (* (/ t z) (- y))
       (if (<= y 4.3e-32) (* x (/ t z)) t)))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (y <= -1.5e+85) {
		tmp = t;
	} else if (y <= -3.1e-46) {
		tmp = -x * (t / y);
	} else if (y <= -5.8e-138) {
		tmp = (t / z) * -y;
	} else if (y <= 4.3e-32) {
		tmp = x * (t / z);
	} else {
		tmp = t;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if (y <= (-1.5d+85)) then
        tmp = t
    else if (y <= (-3.1d-46)) then
        tmp = -x * (t / y)
    else if (y <= (-5.8d-138)) then
        tmp = (t / z) * -y
    else if (y <= 4.3d-32) then
        tmp = x * (t / z)
    else
        tmp = t
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if (y <= -1.5e+85) {
		tmp = t;
	} else if (y <= -3.1e-46) {
		tmp = -x * (t / y);
	} else if (y <= -5.8e-138) {
		tmp = (t / z) * -y;
	} else if (y <= 4.3e-32) {
		tmp = x * (t / z);
	} else {
		tmp = t;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if y <= -1.5e+85:
		tmp = t
	elif y <= -3.1e-46:
		tmp = -x * (t / y)
	elif y <= -5.8e-138:
		tmp = (t / z) * -y
	elif y <= 4.3e-32:
		tmp = x * (t / z)
	else:
		tmp = t
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (y <= -1.5e+85)
		tmp = t;
	elseif (y <= -3.1e-46)
		tmp = Float64(Float64(-x) * Float64(t / y));
	elseif (y <= -5.8e-138)
		tmp = Float64(Float64(t / z) * Float64(-y));
	elseif (y <= 4.3e-32)
		tmp = Float64(x * Float64(t / z));
	else
		tmp = t;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (y <= -1.5e+85)
		tmp = t;
	elseif (y <= -3.1e-46)
		tmp = -x * (t / y);
	elseif (y <= -5.8e-138)
		tmp = (t / z) * -y;
	elseif (y <= 4.3e-32)
		tmp = x * (t / z);
	else
		tmp = t;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[y, -1.5e+85], t, If[LessEqual[y, -3.1e-46], N[((-x) * N[(t / y), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, -5.8e-138], N[(N[(t / z), $MachinePrecision] * (-y)), $MachinePrecision], If[LessEqual[y, 4.3e-32], N[(x * N[(t / z), $MachinePrecision]), $MachinePrecision], t]]]]

Derivation

1. Split input into 4 regimes

2. if y < -1.5e85 or 4.2999999999999999e-32 < y

   1. Initial program 99.9%

      \[\frac{x - y}{z - y} \cdot t \]
   2. Step-by-step derivation

      1. associate-*l/ 75.3%

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

      2. associate-/l* 71.8%

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

   3. Simplified 71.8%

      \[\leadsto \color{blue}{\left(x - y\right) \cdot \frac{t}{z - y}} \]
   4. Add Preprocessing

   5. Taylor expanded in y around inf 67.4%

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

   if -1.5e85 < y < -3.1000000000000001e-46

   1. Initial program 99.7%

      \[\frac{x - y}{z - y} \cdot t \]
   2. Step-by-step derivation

      1. associate-*l/ 97.1%

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

      2. associate-/l* 94.0%

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

   3. Simplified 94.0%

      \[\leadsto \color{blue}{\left(x - y\right) \cdot \frac{t}{z - y}} \]
   4. Add Preprocessing

   5. Taylor expanded in x around inf 54.0%

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

   6. Taylor expanded in z around 0 45.3%

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

      1. associate-*r/ 45.3%

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

      2. neg-mul-1 45.3%

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

   8. Simplified 45.3%

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

   if -3.1000000000000001e-46 < y < -5.79999999999999946e-138

   1. Initial program 94.6%

      \[\frac{x - y}{z - y} \cdot t \]
   2. Step-by-step derivation

      1. associate-*l/ 99.4%

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

      2. associate-/l* 99.7%

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

   3. Simplified 99.7%

      \[\leadsto \color{blue}{\left(x - y\right) \cdot \frac{t}{z - y}} \]
   4. Add Preprocessing

   5. Taylor expanded in x around 0 74.4%

      \[\leadsto \color{blue}{-1 \cdot \frac{t \cdot y}{z - y}} \]
   6. Step-by-step derivation

      1. associate-*r/ 74.4%

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

      2. mul-1-neg 74.4%

         \[\leadsto \frac{\color{blue}{-t \cdot y}}{z - y} \]

      3. distribute-rgt-neg-out 74.4%

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

      4. associate-*l/ 74.6%

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

      5. *-commutative 74.6%

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

      6. distribute-lft-neg-out 74.6%

         \[\leadsto \color{blue}{-y \cdot \frac{t}{z - y}} \]

      7. distribute-rgt-neg-in 74.6%

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

      8. distribute-frac-neg2 74.6%

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

      9. neg-sub0 74.6%

         \[\leadsto y \cdot \frac{t}{\color{blue}{0 - \left(z - y\right)}} \]

      10. sub-neg 74.6%

          \[\leadsto y \cdot \frac{t}{0 - \color{blue}{\left(z + \left(-y\right)\right)}} \]

      11. +-commutative 74.6%

          \[\leadsto y \cdot \frac{t}{0 - \color{blue}{\left(\left(-y\right) + z\right)}} \]

      12. associate--r+ 74.6%

          \[\leadsto y \cdot \frac{t}{\color{blue}{\left(0 - \left(-y\right)\right) - z}} \]

      13. neg-sub0 74.6%

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

      14. remove-double-neg 74.6%

          \[\leadsto y \cdot \frac{t}{\color{blue}{y} - z} \]

   7. Simplified 74.6%

      \[\leadsto \color{blue}{y \cdot \frac{t}{y - z}} \]

   8. Taylor expanded in y around 0 77.8%

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

      1. associate-*r/ 77.8%

         \[\leadsto y \cdot \color{blue}{\frac{-1 \cdot t}{z}} \]

      2. neg-mul-1 77.8%

         \[\leadsto y \cdot \frac{\color{blue}{-t}}{z} \]

   10. Simplified 77.8%

       \[\leadsto y \cdot \color{blue}{\frac{-t}{z}} \]

   if -5.79999999999999946e-138 < y < 4.2999999999999999e-32

   1. Initial program 94.0%

      \[\frac{x - y}{z - y} \cdot t \]
   2. Step-by-step derivation

      1. associate-*l/ 93.0%

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

      2. associate-/l* 91.9%

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

   3. Simplified 91.9%

      \[\leadsto \color{blue}{\left(x - y\right) \cdot \frac{t}{z - y}} \]
   4. Add Preprocessing

   5. Taylor expanded in x around inf 80.8%

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

   6. Taylor expanded in z around inf 69.7%

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

4. Final simplification 65.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.5 \cdot 10^{+85}:\\ \;\;\;\;t\\ \mathbf{elif}\;y \leq -3.1 \cdot 10^{-46}:\\ \;\;\;\;\left(-x\right) \cdot \frac{t}{y}\\ \mathbf{elif}\;y \leq -5.8 \cdot 10^{-138}:\\ \;\;\;\;\frac{t}{z} \cdot \left(-y\right)\\ \mathbf{elif}\;y \leq 4.3 \cdot 10^{-32}:\\ \;\;\;\;x \cdot \frac{t}{z}\\ \mathbf{else}:\\ \;\;\;\;t\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 74.9% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -4.8 \cdot 10^{-45}:\\ \;\;\;\;t \cdot \frac{y - x}{y}\\ \mathbf{elif}\;y \leq -1.9 \cdot 10^{-238}:\\ \;\;\;\;\left(x - y\right) \cdot \frac{t}{z}\\ \mathbf{elif}\;y \leq 1.18 \cdot 10^{-11}:\\ \;\;\;\;\frac{x \cdot t}{z - y}\\ \mathbf{else}:\\ \;\;\;\;t \cdot \frac{y}{y - z}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= y -4.8e-45)
   (* t (/ (- y x) y))
   (if (<= y -1.9e-238)
     (* (- x y) (/ t z))
     (if (<= y 1.18e-11) (/ (* x t) (- z y)) (* t (/ y (- y z)))))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (y <= -4.8e-45) {
		tmp = t * ((y - x) / y);
	} else if (y <= -1.9e-238) {
		tmp = (x - y) * (t / z);
	} else if (y <= 1.18e-11) {
		tmp = (x * t) / (z - y);
	} else {
		tmp = t * (y / (y - z));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if (y <= (-4.8d-45)) then
        tmp = t * ((y - x) / y)
    else if (y <= (-1.9d-238)) then
        tmp = (x - y) * (t / z)
    else if (y <= 1.18d-11) then
        tmp = (x * t) / (z - y)
    else
        tmp = t * (y / (y - z))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if (y <= -4.8e-45) {
		tmp = t * ((y - x) / y);
	} else if (y <= -1.9e-238) {
		tmp = (x - y) * (t / z);
	} else if (y <= 1.18e-11) {
		tmp = (x * t) / (z - y);
	} else {
		tmp = t * (y / (y - z));
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if y <= -4.8e-45:
		tmp = t * ((y - x) / y)
	elif y <= -1.9e-238:
		tmp = (x - y) * (t / z)
	elif y <= 1.18e-11:
		tmp = (x * t) / (z - y)
	else:
		tmp = t * (y / (y - z))
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (y <= -4.8e-45)
		tmp = Float64(t * Float64(Float64(y - x) / y));
	elseif (y <= -1.9e-238)
		tmp = Float64(Float64(x - y) * Float64(t / z));
	elseif (y <= 1.18e-11)
		tmp = Float64(Float64(x * t) / Float64(z - y));
	else
		tmp = Float64(t * Float64(y / Float64(y - z)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (y <= -4.8e-45)
		tmp = t * ((y - x) / y);
	elseif (y <= -1.9e-238)
		tmp = (x - y) * (t / z);
	elseif (y <= 1.18e-11)
		tmp = (x * t) / (z - y);
	else
		tmp = t * (y / (y - z));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[y, -4.8e-45], N[(t * N[(N[(y - x), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, -1.9e-238], N[(N[(x - y), $MachinePrecision] * N[(t / z), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 1.18e-11], N[(N[(x * t), $MachinePrecision] / N[(z - y), $MachinePrecision]), $MachinePrecision], N[(t * N[(y / N[(y - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 4 regimes

2. if y < -4.7999999999999998e-45

   1. Initial program 99.8%

      \[\frac{x - y}{z - y} \cdot t \]
   2. Add Preprocessing

   3. Taylor expanded in z around 0 78.3%

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

      1. associate-*r/ 78.3%

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

      2. neg-mul-1 78.3%

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

      3. neg-sub0 78.3%

         \[\leadsto \frac{\color{blue}{0 - \left(x - y\right)}}{y} \cdot t \]

      4. sub-neg 78.3%

         \[\leadsto \frac{0 - \color{blue}{\left(x + \left(-y\right)\right)}}{y} \cdot t \]

      5. +-commutative 78.3%

         \[\leadsto \frac{0 - \color{blue}{\left(\left(-y\right) + x\right)}}{y} \cdot t \]

      6. associate--r+ 78.3%

         \[\leadsto \frac{\color{blue}{\left(0 - \left(-y\right)\right) - x}}{y} \cdot t \]

      7. neg-sub0 78.3%

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

      8. remove-double-neg 78.3%

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

   5. Simplified 78.3%

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

   if -4.7999999999999998e-45 < y < -1.8999999999999998e-238

   1. Initial program 95.1%

      \[\frac{x - y}{z - y} \cdot t \]
   2. Step-by-step derivation

      1. associate-*l/ 90.6%

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

      2. associate-/l* 95.1%

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

   3. Simplified 95.1%

      \[\leadsto \color{blue}{\left(x - y\right) \cdot \frac{t}{z - y}} \]
   4. Add Preprocessing

   5. Taylor expanded in z around inf 84.8%

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

   if -1.8999999999999998e-238 < y < 1.18e-11

   1. Initial program 93.9%

      \[\frac{x - y}{z - y} \cdot t \]
   2. Step-by-step derivation

      1. associate-*l/ 96.0%

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

      2. associate-/l* 92.5%

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

   3. Simplified 92.5%

      \[\leadsto \color{blue}{\left(x - y\right) \cdot \frac{t}{z - y}} \]
   4. Add Preprocessing

   5. Taylor expanded in x around inf 85.2%

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

   if 1.18e-11 < y

   1. Initial program 99.9%

      \[\frac{x - y}{z - y} \cdot t \]
   2. Add Preprocessing

   3. Taylor expanded in x around 0 86.2%

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

      1. neg-mul-1 86.2%

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

      2. distribute-neg-frac2 86.2%

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

      3. neg-sub0 86.2%

         \[\leadsto \frac{y}{\color{blue}{0 - \left(z - y\right)}} \cdot t \]

      4. sub-neg 86.2%

         \[\leadsto \frac{y}{0 - \color{blue}{\left(z + \left(-y\right)\right)}} \cdot t \]

      5. +-commutative 86.2%

         \[\leadsto \frac{y}{0 - \color{blue}{\left(\left(-y\right) + z\right)}} \cdot t \]

      6. associate--r+ 86.2%

         \[\leadsto \frac{y}{\color{blue}{\left(0 - \left(-y\right)\right) - z}} \cdot t \]

      7. neg-sub0 86.2%

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

      8. remove-double-neg 86.2%

         \[\leadsto \frac{y}{\color{blue}{y} - z} \cdot t \]

   5. Simplified 86.2%

      \[\leadsto \color{blue}{\frac{y}{y - z}} \cdot t \]
3. Recombined 4 regimes into one program.

4. Final simplification 83.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -4.8 \cdot 10^{-45}:\\ \;\;\;\;t \cdot \frac{y - x}{y}\\ \mathbf{elif}\;y \leq -1.9 \cdot 10^{-238}:\\ \;\;\;\;\left(x - y\right) \cdot \frac{t}{z}\\ \mathbf{elif}\;y \leq 1.18 \cdot 10^{-11}:\\ \;\;\;\;\frac{x \cdot t}{z - y}\\ \mathbf{else}:\\ \;\;\;\;t \cdot \frac{y}{y - z}\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 75.3% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -6 \cdot 10^{-43}:\\ \;\;\;\;t \cdot \frac{y - x}{y}\\ \mathbf{elif}\;y \leq -7.4 \cdot 10^{-240}:\\ \;\;\;\;\left(x - y\right) \cdot \frac{t}{z}\\ \mathbf{elif}\;y \leq 1.22 \cdot 10^{-9}:\\ \;\;\;\;\frac{t}{\frac{z - y}{x}}\\ \mathbf{else}:\\ \;\;\;\;t \cdot \frac{y}{y - z}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= y -6e-43)
   (* t (/ (- y x) y))
   (if (<= y -7.4e-240)
     (* (- x y) (/ t z))
     (if (<= y 1.22e-9) (/ t (/ (- z y) x)) (* t (/ y (- y z)))))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (y <= -6e-43) {
		tmp = t * ((y - x) / y);
	} else if (y <= -7.4e-240) {
		tmp = (x - y) * (t / z);
	} else if (y <= 1.22e-9) {
		tmp = t / ((z - y) / x);
	} else {
		tmp = t * (y / (y - z));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if (y <= (-6d-43)) then
        tmp = t * ((y - x) / y)
    else if (y <= (-7.4d-240)) then
        tmp = (x - y) * (t / z)
    else if (y <= 1.22d-9) then
        tmp = t / ((z - y) / x)
    else
        tmp = t * (y / (y - z))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if (y <= -6e-43) {
		tmp = t * ((y - x) / y);
	} else if (y <= -7.4e-240) {
		tmp = (x - y) * (t / z);
	} else if (y <= 1.22e-9) {
		tmp = t / ((z - y) / x);
	} else {
		tmp = t * (y / (y - z));
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if y <= -6e-43:
		tmp = t * ((y - x) / y)
	elif y <= -7.4e-240:
		tmp = (x - y) * (t / z)
	elif y <= 1.22e-9:
		tmp = t / ((z - y) / x)
	else:
		tmp = t * (y / (y - z))
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (y <= -6e-43)
		tmp = Float64(t * Float64(Float64(y - x) / y));
	elseif (y <= -7.4e-240)
		tmp = Float64(Float64(x - y) * Float64(t / z));
	elseif (y <= 1.22e-9)
		tmp = Float64(t / Float64(Float64(z - y) / x));
	else
		tmp = Float64(t * Float64(y / Float64(y - z)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (y <= -6e-43)
		tmp = t * ((y - x) / y);
	elseif (y <= -7.4e-240)
		tmp = (x - y) * (t / z);
	elseif (y <= 1.22e-9)
		tmp = t / ((z - y) / x);
	else
		tmp = t * (y / (y - z));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[y, -6e-43], N[(t * N[(N[(y - x), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, -7.4e-240], N[(N[(x - y), $MachinePrecision] * N[(t / z), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 1.22e-9], N[(t / N[(N[(z - y), $MachinePrecision] / x), $MachinePrecision]), $MachinePrecision], N[(t * N[(y / N[(y - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 4 regimes

2. if y < -6.00000000000000007e-43

   1. Initial program 99.8%

      \[\frac{x - y}{z - y} \cdot t \]
   2. Add Preprocessing

   3. Taylor expanded in z around 0 78.3%

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

      1. associate-*r/ 78.3%

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

      2. neg-mul-1 78.3%

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

      3. neg-sub0 78.3%

         \[\leadsto \frac{\color{blue}{0 - \left(x - y\right)}}{y} \cdot t \]

      4. sub-neg 78.3%

         \[\leadsto \frac{0 - \color{blue}{\left(x + \left(-y\right)\right)}}{y} \cdot t \]

      5. +-commutative 78.3%

         \[\leadsto \frac{0 - \color{blue}{\left(\left(-y\right) + x\right)}}{y} \cdot t \]

      6. associate--r+ 78.3%

         \[\leadsto \frac{\color{blue}{\left(0 - \left(-y\right)\right) - x}}{y} \cdot t \]

      7. neg-sub0 78.3%

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

      8. remove-double-neg 78.3%

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

   5. Simplified 78.3%

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

   if -6.00000000000000007e-43 < y < -7.4000000000000003e-240

   1. Initial program 95.1%

      \[\frac{x - y}{z - y} \cdot t \]
   2. Step-by-step derivation

      1. associate-*l/ 90.6%

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

      2. associate-/l* 95.1%

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

   3. Simplified 95.1%

      \[\leadsto \color{blue}{\left(x - y\right) \cdot \frac{t}{z - y}} \]
   4. Add Preprocessing

   5. Taylor expanded in z around inf 84.8%

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

   if -7.4000000000000003e-240 < y < 1.2199999999999999e-9

   1. Initial program 93.9%

      \[\frac{x - y}{z - y} \cdot t \]
   2. Add Preprocessing

   3. Taylor expanded in x around inf 83.0%

      \[\leadsto \frac{\color{blue}{x}}{z - y} \cdot t \]
   4. Step-by-step derivation

      1. *-commutative 83.0%

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

      2. clear-num 82.9%

         \[\leadsto t \cdot \color{blue}{\frac{1}{\frac{z - y}{x}}} \]

      3. un-div-inv 83.9%

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

   5. Applied egg-rr 83.9%

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

   if 1.2199999999999999e-9 < y

   1. Initial program 99.9%

      \[\frac{x - y}{z - y} \cdot t \]
   2. Add Preprocessing

   3. Taylor expanded in x around 0 86.2%

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

      1. neg-mul-1 86.2%

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

      2. distribute-neg-frac2 86.2%

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

      3. neg-sub0 86.2%

         \[\leadsto \frac{y}{\color{blue}{0 - \left(z - y\right)}} \cdot t \]

      4. sub-neg 86.2%

         \[\leadsto \frac{y}{0 - \color{blue}{\left(z + \left(-y\right)\right)}} \cdot t \]

      5. +-commutative 86.2%

         \[\leadsto \frac{y}{0 - \color{blue}{\left(\left(-y\right) + z\right)}} \cdot t \]

      6. associate--r+ 86.2%

         \[\leadsto \frac{y}{\color{blue}{\left(0 - \left(-y\right)\right) - z}} \cdot t \]

      7. neg-sub0 86.2%

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

      8. remove-double-neg 86.2%

         \[\leadsto \frac{y}{\color{blue}{y} - z} \cdot t \]

   5. Simplified 86.2%

      \[\leadsto \color{blue}{\frac{y}{y - z}} \cdot t \]
3. Recombined 4 regimes into one program.

4. Final simplification 82.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -6 \cdot 10^{-43}:\\ \;\;\;\;t \cdot \frac{y - x}{y}\\ \mathbf{elif}\;y \leq -7.4 \cdot 10^{-240}:\\ \;\;\;\;\left(x - y\right) \cdot \frac{t}{z}\\ \mathbf{elif}\;y \leq 1.22 \cdot 10^{-9}:\\ \;\;\;\;\frac{t}{\frac{z - y}{x}}\\ \mathbf{else}:\\ \;\;\;\;t \cdot \frac{y}{y - z}\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 74.9% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -1.6 \cdot 10^{-45}:\\ \;\;\;\;t \cdot \frac{y - x}{y}\\ \mathbf{elif}\;y \leq -2.9 \cdot 10^{-241}:\\ \;\;\;\;\left(x - y\right) \cdot \frac{t}{z}\\ \mathbf{elif}\;y \leq 8.5 \cdot 10^{-15}:\\ \;\;\;\;x \cdot \frac{t}{z - y}\\ \mathbf{else}:\\ \;\;\;\;t \cdot \frac{y}{y - z}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= y -1.6e-45)
   (* t (/ (- y x) y))
   (if (<= y -2.9e-241)
     (* (- x y) (/ t z))
     (if (<= y 8.5e-15) (* x (/ t (- z y))) (* t (/ y (- y z)))))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (y <= -1.6e-45) {
		tmp = t * ((y - x) / y);
	} else if (y <= -2.9e-241) {
		tmp = (x - y) * (t / z);
	} else if (y <= 8.5e-15) {
		tmp = x * (t / (z - y));
	} else {
		tmp = t * (y / (y - z));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if (y <= (-1.6d-45)) then
        tmp = t * ((y - x) / y)
    else if (y <= (-2.9d-241)) then
        tmp = (x - y) * (t / z)
    else if (y <= 8.5d-15) then
        tmp = x * (t / (z - y))
    else
        tmp = t * (y / (y - z))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if (y <= -1.6e-45) {
		tmp = t * ((y - x) / y);
	} else if (y <= -2.9e-241) {
		tmp = (x - y) * (t / z);
	} else if (y <= 8.5e-15) {
		tmp = x * (t / (z - y));
	} else {
		tmp = t * (y / (y - z));
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if y <= -1.6e-45:
		tmp = t * ((y - x) / y)
	elif y <= -2.9e-241:
		tmp = (x - y) * (t / z)
	elif y <= 8.5e-15:
		tmp = x * (t / (z - y))
	else:
		tmp = t * (y / (y - z))
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (y <= -1.6e-45)
		tmp = Float64(t * Float64(Float64(y - x) / y));
	elseif (y <= -2.9e-241)
		tmp = Float64(Float64(x - y) * Float64(t / z));
	elseif (y <= 8.5e-15)
		tmp = Float64(x * Float64(t / Float64(z - y)));
	else
		tmp = Float64(t * Float64(y / Float64(y - z)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (y <= -1.6e-45)
		tmp = t * ((y - x) / y);
	elseif (y <= -2.9e-241)
		tmp = (x - y) * (t / z);
	elseif (y <= 8.5e-15)
		tmp = x * (t / (z - y));
	else
		tmp = t * (y / (y - z));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[y, -1.6e-45], N[(t * N[(N[(y - x), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, -2.9e-241], N[(N[(x - y), $MachinePrecision] * N[(t / z), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 8.5e-15], N[(x * N[(t / N[(z - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(t * N[(y / N[(y - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 4 regimes

2. if y < -1.60000000000000004e-45

   1. Initial program 99.8%

      \[\frac{x - y}{z - y} \cdot t \]
   2. Add Preprocessing

   3. Taylor expanded in z around 0 78.3%

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

      1. associate-*r/ 78.3%

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

      2. neg-mul-1 78.3%

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

      3. neg-sub0 78.3%

         \[\leadsto \frac{\color{blue}{0 - \left(x - y\right)}}{y} \cdot t \]

      4. sub-neg 78.3%

         \[\leadsto \frac{0 - \color{blue}{\left(x + \left(-y\right)\right)}}{y} \cdot t \]

      5. +-commutative 78.3%

         \[\leadsto \frac{0 - \color{blue}{\left(\left(-y\right) + x\right)}}{y} \cdot t \]

      6. associate--r+ 78.3%

         \[\leadsto \frac{\color{blue}{\left(0 - \left(-y\right)\right) - x}}{y} \cdot t \]

      7. neg-sub0 78.3%

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

      8. remove-double-neg 78.3%

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

   5. Simplified 78.3%

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

   if -1.60000000000000004e-45 < y < -2.8999999999999999e-241

   1. Initial program 95.1%

      \[\frac{x - y}{z - y} \cdot t \]
   2. Step-by-step derivation

      1. associate-*l/ 90.6%

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

      2. associate-/l* 95.1%

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

   3. Simplified 95.1%

      \[\leadsto \color{blue}{\left(x - y\right) \cdot \frac{t}{z - y}} \]
   4. Add Preprocessing

   5. Taylor expanded in z around inf 84.8%

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

   if -2.8999999999999999e-241 < y < 8.50000000000000007e-15

   1. Initial program 93.9%

      \[\frac{x - y}{z - y} \cdot t \]
   2. Step-by-step derivation

      1. associate-*l/ 96.0%

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

      2. associate-/l* 92.5%

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

   3. Simplified 92.5%

      \[\leadsto \color{blue}{\left(x - y\right) \cdot \frac{t}{z - y}} \]
   4. Add Preprocessing

   5. Taylor expanded in x around inf 83.8%

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

   if 8.50000000000000007e-15 < y

   1. Initial program 99.9%

      \[\frac{x - y}{z - y} \cdot t \]
   2. Add Preprocessing

   3. Taylor expanded in x around 0 86.2%

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

      1. neg-mul-1 86.2%

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

      2. distribute-neg-frac2 86.2%

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

      3. neg-sub0 86.2%

         \[\leadsto \frac{y}{\color{blue}{0 - \left(z - y\right)}} \cdot t \]

      4. sub-neg 86.2%

         \[\leadsto \frac{y}{0 - \color{blue}{\left(z + \left(-y\right)\right)}} \cdot t \]

      5. +-commutative 86.2%

         \[\leadsto \frac{y}{0 - \color{blue}{\left(\left(-y\right) + z\right)}} \cdot t \]

      6. associate--r+ 86.2%

         \[\leadsto \frac{y}{\color{blue}{\left(0 - \left(-y\right)\right) - z}} \cdot t \]

      7. neg-sub0 86.2%

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

      8. remove-double-neg 86.2%

         \[\leadsto \frac{y}{\color{blue}{y} - z} \cdot t \]

   5. Simplified 86.2%

      \[\leadsto \color{blue}{\frac{y}{y - z}} \cdot t \]
3. Recombined 4 regimes into one program.

4. Final simplification 82.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.6 \cdot 10^{-45}:\\ \;\;\;\;t \cdot \frac{y - x}{y}\\ \mathbf{elif}\;y \leq -2.9 \cdot 10^{-241}:\\ \;\;\;\;\left(x - y\right) \cdot \frac{t}{z}\\ \mathbf{elif}\;y \leq 8.5 \cdot 10^{-15}:\\ \;\;\;\;x \cdot \frac{t}{z - y}\\ \mathbf{else}:\\ \;\;\;\;t \cdot \frac{y}{y - z}\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 60.2% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -5.5 \cdot 10^{+84}:\\ \;\;\;\;t\\ \mathbf{elif}\;y \leq -3.2 \cdot 10^{-52}:\\ \;\;\;\;\left(-x\right) \cdot \frac{t}{y}\\ \mathbf{elif}\;y \leq 5.6 \cdot 10^{-36}:\\ \;\;\;\;x \cdot \frac{t}{z}\\ \mathbf{else}:\\ \;\;\;\;t\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= y -5.5e+84)
   t
   (if (<= y -3.2e-52) (* (- x) (/ t y)) (if (<= y 5.6e-36) (* x (/ t z)) t))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (y <= -5.5e+84) {
		tmp = t;
	} else if (y <= -3.2e-52) {
		tmp = -x * (t / y);
	} else if (y <= 5.6e-36) {
		tmp = x * (t / z);
	} else {
		tmp = t;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if (y <= (-5.5d+84)) then
        tmp = t
    else if (y <= (-3.2d-52)) then
        tmp = -x * (t / y)
    else if (y <= 5.6d-36) then
        tmp = x * (t / z)
    else
        tmp = t
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if (y <= -5.5e+84) {
		tmp = t;
	} else if (y <= -3.2e-52) {
		tmp = -x * (t / y);
	} else if (y <= 5.6e-36) {
		tmp = x * (t / z);
	} else {
		tmp = t;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if y <= -5.5e+84:
		tmp = t
	elif y <= -3.2e-52:
		tmp = -x * (t / y)
	elif y <= 5.6e-36:
		tmp = x * (t / z)
	else:
		tmp = t
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (y <= -5.5e+84)
		tmp = t;
	elseif (y <= -3.2e-52)
		tmp = Float64(Float64(-x) * Float64(t / y));
	elseif (y <= 5.6e-36)
		tmp = Float64(x * Float64(t / z));
	else
		tmp = t;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (y <= -5.5e+84)
		tmp = t;
	elseif (y <= -3.2e-52)
		tmp = -x * (t / y);
	elseif (y <= 5.6e-36)
		tmp = x * (t / z);
	else
		tmp = t;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[y, -5.5e+84], t, If[LessEqual[y, -3.2e-52], N[((-x) * N[(t / y), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 5.6e-36], N[(x * N[(t / z), $MachinePrecision]), $MachinePrecision], t]]]

Derivation

1. Split input into 3 regimes

2. if y < -5.5000000000000004e84 or 5.6000000000000002e-36 < y

   1. Initial program 99.9%

      \[\frac{x - y}{z - y} \cdot t \]
   2. Step-by-step derivation

      1. associate-*l/ 75.3%

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

      2. associate-/l* 71.8%

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

   3. Simplified 71.8%

      \[\leadsto \color{blue}{\left(x - y\right) \cdot \frac{t}{z - y}} \]
   4. Add Preprocessing

   5. Taylor expanded in y around inf 67.4%

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

   if -5.5000000000000004e84 < y < -3.2000000000000001e-52

   1. Initial program 99.7%

      \[\frac{x - y}{z - y} \cdot t \]
   2. Step-by-step derivation

      1. associate-*l/ 97.1%

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

      2. associate-/l* 94.2%

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

   3. Simplified 94.2%

      \[\leadsto \color{blue}{\left(x - y\right) \cdot \frac{t}{z - y}} \]
   4. Add Preprocessing

   5. Taylor expanded in x around inf 52.6%

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

   6. Taylor expanded in z around 0 44.2%

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

      1. associate-*r/ 44.2%

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

      2. neg-mul-1 44.2%

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

   8. Simplified 44.2%

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

   if -3.2000000000000001e-52 < y < 5.6000000000000002e-36

   1. Initial program 94.1%

      \[\frac{x - y}{z - y} \cdot t \]
   2. Step-by-step derivation

      1. associate-*l/ 94.0%

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

      2. associate-/l* 93.1%

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

   3. Simplified 93.1%

      \[\leadsto \color{blue}{\left(x - y\right) \cdot \frac{t}{z - y}} \]
   4. Add Preprocessing

   5. Taylor expanded in x around inf 76.4%

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

   6. Taylor expanded in z around inf 65.4%

      \[\leadsto x \cdot \color{blue}{\frac{t}{z}} \]
3. Recombined 3 regimes into one program.

4. Final simplification 63.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -5.5 \cdot 10^{+84}:\\ \;\;\;\;t\\ \mathbf{elif}\;y \leq -3.2 \cdot 10^{-52}:\\ \;\;\;\;\left(-x\right) \cdot \frac{t}{y}\\ \mathbf{elif}\;y \leq 5.6 \cdot 10^{-36}:\\ \;\;\;\;x \cdot \frac{t}{z}\\ \mathbf{else}:\\ \;\;\;\;t\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 90.4% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -6.8 \cdot 10^{+156}:\\ \;\;\;\;t - t \cdot \frac{x}{y}\\ \mathbf{elif}\;y \leq 2.4 \cdot 10^{+129}:\\ \;\;\;\;\left(x - y\right) \cdot \frac{t}{z - y}\\ \mathbf{else}:\\ \;\;\;\;t \cdot \frac{y - x}{y}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= y -6.8e+156)
   (- t (* t (/ x y)))
   (if (<= y 2.4e+129) (* (- x y) (/ t (- z y))) (* t (/ (- y x) y)))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (y <= -6.8e+156) {
		tmp = t - (t * (x / y));
	} else if (y <= 2.4e+129) {
		tmp = (x - y) * (t / (z - y));
	} else {
		tmp = t * ((y - x) / y);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if (y <= (-6.8d+156)) then
        tmp = t - (t * (x / y))
    else if (y <= 2.4d+129) then
        tmp = (x - y) * (t / (z - y))
    else
        tmp = t * ((y - x) / y)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if (y <= -6.8e+156) {
		tmp = t - (t * (x / y));
	} else if (y <= 2.4e+129) {
		tmp = (x - y) * (t / (z - y));
	} else {
		tmp = t * ((y - x) / y);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if y <= -6.8e+156:
		tmp = t - (t * (x / y))
	elif y <= 2.4e+129:
		tmp = (x - y) * (t / (z - y))
	else:
		tmp = t * ((y - x) / y)
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (y <= -6.8e+156)
		tmp = Float64(t - Float64(t * Float64(x / y)));
	elseif (y <= 2.4e+129)
		tmp = Float64(Float64(x - y) * Float64(t / Float64(z - y)));
	else
		tmp = Float64(t * Float64(Float64(y - x) / y));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (y <= -6.8e+156)
		tmp = t - (t * (x / y));
	elseif (y <= 2.4e+129)
		tmp = (x - y) * (t / (z - y));
	else
		tmp = t * ((y - x) / y);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[y, -6.8e+156], N[(t - N[(t * N[(x / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 2.4e+129], N[(N[(x - y), $MachinePrecision] * N[(t / N[(z - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(t * N[(N[(y - x), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if y < -6.8000000000000002e156

   1. Initial program 99.9%

      \[\frac{x - y}{z - y} \cdot t \]
   2. Step-by-step derivation

      1. associate-*l/ 70.0%

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

      2. associate-/l* 50.3%

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

   3. Simplified 50.3%

      \[\leadsto \color{blue}{\left(x - y\right) \cdot \frac{t}{z - y}} \]
   4. Add Preprocessing

   5. Taylor expanded in y around inf 84.2%

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

      1. associate--l+ 84.2%

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

      2. distribute-lft-out-- 84.2%

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

      3. div-sub 84.2%

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

      4. mul-1-neg 84.2%

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

      5. unsub-neg 84.2%

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

      6. div-sub 84.2%

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

      7. associate-/l* 84.2%

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

      8. associate-/l* 92.2%

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

      9. distribute-lft-out-- 92.2%

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

      10. div-sub 92.2%

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

   7. Simplified 92.2%

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

   8. Taylor expanded in x around inf 92.2%

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

   if -6.8000000000000002e156 < y < 2.3999999999999999e129

   1. Initial program 96.5%

      \[\frac{x - y}{z - y} \cdot t \]
   2. Step-by-step derivation

      1. associate-*l/ 92.6%

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

      2. associate-/l* 93.5%

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

   3. Simplified 93.5%

      \[\leadsto \color{blue}{\left(x - y\right) \cdot \frac{t}{z - y}} \]
   4. Add Preprocessing

   if 2.3999999999999999e129 < y

   1. Initial program 100.0%

      \[\frac{x - y}{z - y} \cdot t \]
   2. Add Preprocessing

   3. Taylor expanded in z around 0 96.8%

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

      1. associate-*r/ 96.8%

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

      2. neg-mul-1 96.8%

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

      3. neg-sub0 96.8%

         \[\leadsto \frac{\color{blue}{0 - \left(x - y\right)}}{y} \cdot t \]

      4. sub-neg 96.8%

         \[\leadsto \frac{0 - \color{blue}{\left(x + \left(-y\right)\right)}}{y} \cdot t \]

      5. +-commutative 96.8%

         \[\leadsto \frac{0 - \color{blue}{\left(\left(-y\right) + x\right)}}{y} \cdot t \]

      6. associate--r+ 96.8%

         \[\leadsto \frac{\color{blue}{\left(0 - \left(-y\right)\right) - x}}{y} \cdot t \]

      7. neg-sub0 96.8%

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

      8. remove-double-neg 96.8%

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

   5. Simplified 96.8%

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

4. Final simplification 93.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -6.8 \cdot 10^{+156}:\\ \;\;\;\;t - t \cdot \frac{x}{y}\\ \mathbf{elif}\;y \leq 2.4 \cdot 10^{+129}:\\ \;\;\;\;\left(x - y\right) \cdot \frac{t}{z - y}\\ \mathbf{else}:\\ \;\;\;\;t \cdot \frac{y - x}{y}\\ \end{array} \]
5. Add Preprocessing

Alternative 10: 73.1% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -1.6 \cdot 10^{+27} \lor \neg \left(x \leq 3.2 \cdot 10^{+143}\right):\\ \;\;\;\;t \cdot \frac{x}{z - y}\\ \mathbf{else}:\\ \;\;\;\;t \cdot \frac{y}{y - z}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= x -1.6e+27) (not (<= x 3.2e+143)))
   (* t (/ x (- z y)))
   (* t (/ y (- y z)))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((x <= -1.6e+27) || !(x <= 3.2e+143)) {
		tmp = t * (x / (z - y));
	} else {
		tmp = t * (y / (y - z));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if ((x <= (-1.6d+27)) .or. (.not. (x <= 3.2d+143))) then
        tmp = t * (x / (z - y))
    else
        tmp = t * (y / (y - z))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if ((x <= -1.6e+27) || !(x <= 3.2e+143)) {
		tmp = t * (x / (z - y));
	} else {
		tmp = t * (y / (y - z));
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (x <= -1.6e+27) or not (x <= 3.2e+143):
		tmp = t * (x / (z - y))
	else:
		tmp = t * (y / (y - z))
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((x <= -1.6e+27) || !(x <= 3.2e+143))
		tmp = Float64(t * Float64(x / Float64(z - y)));
	else
		tmp = Float64(t * Float64(y / Float64(y - z)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((x <= -1.6e+27) || ~((x <= 3.2e+143)))
		tmp = t * (x / (z - y));
	else
		tmp = t * (y / (y - z));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[x, -1.6e+27], N[Not[LessEqual[x, 3.2e+143]], $MachinePrecision]], N[(t * N[(x / N[(z - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(t * N[(y / N[(y - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < -1.60000000000000008e27 or 3.20000000000000016e143 < x

   1. Initial program 94.8%

      \[\frac{x - y}{z - y} \cdot t \]
   2. Add Preprocessing

   3. Taylor expanded in x around inf 77.5%

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

   if -1.60000000000000008e27 < x < 3.20000000000000016e143

   1. Initial program 98.7%

      \[\frac{x - y}{z - y} \cdot t \]
   2. Add Preprocessing

   3. Taylor expanded in x around 0 76.7%

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

      1. neg-mul-1 76.7%

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

      2. distribute-neg-frac2 76.7%

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

      3. neg-sub0 76.7%

         \[\leadsto \frac{y}{\color{blue}{0 - \left(z - y\right)}} \cdot t \]

      4. sub-neg 76.7%

         \[\leadsto \frac{y}{0 - \color{blue}{\left(z + \left(-y\right)\right)}} \cdot t \]

      5. +-commutative 76.7%

         \[\leadsto \frac{y}{0 - \color{blue}{\left(\left(-y\right) + z\right)}} \cdot t \]

      6. associate--r+ 76.7%

         \[\leadsto \frac{y}{\color{blue}{\left(0 - \left(-y\right)\right) - z}} \cdot t \]

      7. neg-sub0 76.7%

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

      8. remove-double-neg 76.7%

         \[\leadsto \frac{y}{\color{blue}{y} - z} \cdot t \]

   5. Simplified 76.7%

      \[\leadsto \color{blue}{\frac{y}{y - z}} \cdot t \]
3. Recombined 2 regimes into one program.

4. Final simplification 77.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -1.6 \cdot 10^{+27} \lor \neg \left(x \leq 3.2 \cdot 10^{+143}\right):\\ \;\;\;\;t \cdot \frac{x}{z - y}\\ \mathbf{else}:\\ \;\;\;\;t \cdot \frac{y}{y - z}\\ \end{array} \]
5. Add Preprocessing

Alternative 11: 68.6% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -4 \cdot 10^{+85}:\\ \;\;\;\;t\\ \mathbf{elif}\;y \leq 0.075:\\ \;\;\;\;x \cdot \frac{t}{z - y}\\ \mathbf{else}:\\ \;\;\;\;t\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= y -4e+85) t (if (<= y 0.075) (* x (/ t (- z y))) t)))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (y <= -4e+85) {
		tmp = t;
	} else if (y <= 0.075) {
		tmp = x * (t / (z - y));
	} else {
		tmp = t;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if (y <= (-4d+85)) then
        tmp = t
    else if (y <= 0.075d0) then
        tmp = x * (t / (z - y))
    else
        tmp = t
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if (y <= -4e+85) {
		tmp = t;
	} else if (y <= 0.075) {
		tmp = x * (t / (z - y));
	} else {
		tmp = t;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if y <= -4e+85:
		tmp = t
	elif y <= 0.075:
		tmp = x * (t / (z - y))
	else:
		tmp = t
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (y <= -4e+85)
		tmp = t;
	elseif (y <= 0.075)
		tmp = Float64(x * Float64(t / Float64(z - y)));
	else
		tmp = t;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (y <= -4e+85)
		tmp = t;
	elseif (y <= 0.075)
		tmp = x * (t / (z - y));
	else
		tmp = t;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[y, -4e+85], t, If[LessEqual[y, 0.075], N[(x * N[(t / N[(z - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t]]

Derivation

1. Split input into 2 regimes

2. if y < -4.0000000000000001e85 or 0.0749999999999999972 < y

   1. Initial program 99.9%

      \[\frac{x - y}{z - y} \cdot t \]
   2. Step-by-step derivation

      1. associate-*l/ 74.6%

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

      2. associate-/l* 70.9%

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

   3. Simplified 70.9%

      \[\leadsto \color{blue}{\left(x - y\right) \cdot \frac{t}{z - y}} \]
   4. Add Preprocessing

   5. Taylor expanded in y around inf 68.3%

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

   if -4.0000000000000001e85 < y < 0.0749999999999999972

   1. Initial program 95.5%

      \[\frac{x - y}{z - y} \cdot t \]
   2. Step-by-step derivation

      1. associate-*l/ 94.8%

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

      2. associate-/l* 93.5%

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

   3. Simplified 93.5%

      \[\leadsto \color{blue}{\left(x - y\right) \cdot \frac{t}{z - y}} \]
   4. Add Preprocessing

   5. Taylor expanded in x around inf 70.6%

      \[\leadsto \color{blue}{x} \cdot \frac{t}{z - y} \]
3. Recombined 2 regimes into one program.
4. Add Preprocessing

Alternative 12: 60.2% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -4.6 \cdot 10^{-43}:\\ \;\;\;\;t\\ \mathbf{elif}\;y \leq 3.2 \cdot 10^{-32}:\\ \;\;\;\;x \cdot \frac{t}{z}\\ \mathbf{else}:\\ \;\;\;\;t\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= y -4.6e-43) t (if (<= y 3.2e-32) (* x (/ t z)) t)))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (y <= -4.6e-43) {
		tmp = t;
	} else if (y <= 3.2e-32) {
		tmp = x * (t / z);
	} else {
		tmp = t;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if (y <= (-4.6d-43)) then
        tmp = t
    else if (y <= 3.2d-32) then
        tmp = x * (t / z)
    else
        tmp = t
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if (y <= -4.6e-43) {
		tmp = t;
	} else if (y <= 3.2e-32) {
		tmp = x * (t / z);
	} else {
		tmp = t;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if y <= -4.6e-43:
		tmp = t
	elif y <= 3.2e-32:
		tmp = x * (t / z)
	else:
		tmp = t
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (y <= -4.6e-43)
		tmp = t;
	elseif (y <= 3.2e-32)
		tmp = Float64(x * Float64(t / z));
	else
		tmp = t;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (y <= -4.6e-43)
		tmp = t;
	elseif (y <= 3.2e-32)
		tmp = x * (t / z);
	else
		tmp = t;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[y, -4.6e-43], t, If[LessEqual[y, 3.2e-32], N[(x * N[(t / z), $MachinePrecision]), $MachinePrecision], t]]

Derivation

1. Split input into 2 regimes

2. if y < -4.5999999999999998e-43 or 3.2000000000000002e-32 < y

   1. Initial program 99.9%

      \[\frac{x - y}{z - y} \cdot t \]
   2. Step-by-step derivation

      1. associate-*l/ 80.9%

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

      2. associate-/l* 77.5%

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

   3. Simplified 77.5%

      \[\leadsto \color{blue}{\left(x - y\right) \cdot \frac{t}{z - y}} \]
   4. Add Preprocessing

   5. Taylor expanded in y around inf 57.4%

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

   if -4.5999999999999998e-43 < y < 3.2000000000000002e-32

   1. Initial program 94.1%

      \[\frac{x - y}{z - y} \cdot t \]
   2. Step-by-step derivation

      1. associate-*l/ 94.0%

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

      2. associate-/l* 93.2%

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

   3. Simplified 93.2%

      \[\leadsto \color{blue}{\left(x - y\right) \cdot \frac{t}{z - y}} \]
   4. Add Preprocessing

   5. Taylor expanded in x around inf 75.8%

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

   6. Taylor expanded in z around inf 64.8%

      \[\leadsto x \cdot \color{blue}{\frac{t}{z}} \]
3. Recombined 2 regimes into one program.
4. Add Preprocessing

Alternative 13: 35.2% accurate, 9.0× speedup

Math

\[\begin{array}{l} \\ t \end{array} \]

FPCore

(FPCore (x y z t) :precision binary64 t)

C

double code(double x, double y, double z, double t) {
	return t;
}

Fortran

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

Java

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

Python

def code(x, y, z, t):
	return t

Julia

function code(x, y, z, t)
	return t
end

MATLAB

function tmp = code(x, y, z, t)
	tmp = t;
end

Wolfram

code[x_, y_, z_, t_] := t

Derivation

1. Initial program 97.3%

   \[\frac{x - y}{z - y} \cdot t \]
2. Step-by-step derivation

   1. associate-*l/ 86.9%

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

   2. associate-/l* 84.6%

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

3. Simplified 84.6%

   \[\leadsto \color{blue}{\left(x - y\right) \cdot \frac{t}{z - y}} \]
4. Add Preprocessing

5. Taylor expanded in y around inf 34.4%

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

Developer Target 1: 97.1% accurate, 1.0× speedup

Math

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

FPCore

(FPCore (x y z t) :precision binary64 (/ t (/ (- z y) (- x y))))

C

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

Fortran

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

Java

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

Python

def code(x, y, z, t):
	return t / ((z - y) / (x - y))

Julia

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

MATLAB

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

Wolfram

code[x_, y_, z_, t_] := N[(t / N[(N[(z - y), $MachinePrecision] / N[(x - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]

Reproduce

herbie shell --seed 2024146 
(FPCore (x y z t)
  :name "Numeric.Signal.Multichannel:$cput from hsignal-0.2.7.1"
  :precision binary64

  :alt
  (! :herbie-platform default (/ t (/ (- z y) (- x y))))

  (* (/ (- x y) (- z y)) t))