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

Percentage Accurate: 96.9% → 96.9%

Time: 8.2s

Alternatives: 11

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 96.3%

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

2. Final simplification 96.3%

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

Alternative 2: 74.9% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{t}{1 - \frac{z}{y}}\\ \mathbf{if}\;y \leq -1 \cdot 10^{+113}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq -1.55 \cdot 10^{+87}:\\ \;\;\;\;t \cdot \frac{-x}{y}\\ \mathbf{elif}\;y \leq -8.8 \cdot 10^{-60} \lor \neg \left(y \leq 4.1 \cdot 10^{+24}\right):\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;x \cdot \frac{t}{z - y}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (/ t (- 1.0 (/ z y)))))
   (if (<= y -1e+113)
     t_1
     (if (<= y -1.55e+87)
       (* t (/ (- x) y))
       (if (or (<= y -8.8e-60) (not (<= y 4.1e+24)))
         t_1
         (* x (/ t (- z y))))))))

C

double code(double x, double y, double z, double t) {
	double t_1 = t / (1.0 - (z / y));
	double tmp;
	if (y <= -1e+113) {
		tmp = t_1;
	} else if (y <= -1.55e+87) {
		tmp = t * (-x / y);
	} else if ((y <= -8.8e-60) || !(y <= 4.1e+24)) {
		tmp = t_1;
	} else {
		tmp = x * (t / (z - 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) :: t_1
    real(8) :: tmp
    t_1 = t / (1.0d0 - (z / y))
    if (y <= (-1d+113)) then
        tmp = t_1
    else if (y <= (-1.55d+87)) then
        tmp = t * (-x / y)
    else if ((y <= (-8.8d-60)) .or. (.not. (y <= 4.1d+24))) then
        tmp = t_1
    else
        tmp = x * (t / (z - y))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double t_1 = t / (1.0 - (z / y));
	double tmp;
	if (y <= -1e+113) {
		tmp = t_1;
	} else if (y <= -1.55e+87) {
		tmp = t * (-x / y);
	} else if ((y <= -8.8e-60) || !(y <= 4.1e+24)) {
		tmp = t_1;
	} else {
		tmp = x * (t / (z - y));
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = t / (1.0 - (z / y))
	tmp = 0
	if y <= -1e+113:
		tmp = t_1
	elif y <= -1.55e+87:
		tmp = t * (-x / y)
	elif (y <= -8.8e-60) or not (y <= 4.1e+24):
		tmp = t_1
	else:
		tmp = x * (t / (z - y))
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(t / Float64(1.0 - Float64(z / y)))
	tmp = 0.0
	if (y <= -1e+113)
		tmp = t_1;
	elseif (y <= -1.55e+87)
		tmp = Float64(t * Float64(Float64(-x) / y));
	elseif ((y <= -8.8e-60) || !(y <= 4.1e+24))
		tmp = t_1;
	else
		tmp = Float64(x * Float64(t / Float64(z - y)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = t / (1.0 - (z / y));
	tmp = 0.0;
	if (y <= -1e+113)
		tmp = t_1;
	elseif (y <= -1.55e+87)
		tmp = t * (-x / y);
	elseif ((y <= -8.8e-60) || ~((y <= 4.1e+24)))
		tmp = t_1;
	else
		tmp = x * (t / (z - y));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(t / N[(1.0 - N[(z / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -1e+113], t$95$1, If[LessEqual[y, -1.55e+87], N[(t * N[((-x) / y), $MachinePrecision]), $MachinePrecision], If[Or[LessEqual[y, -8.8e-60], N[Not[LessEqual[y, 4.1e+24]], $MachinePrecision]], t$95$1, N[(x * N[(t / N[(z - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]

Derivation

1. Split input into 3 regimes

2. if y < -1e113 or -1.55e87 < y < -8.7999999999999995e-60 or 4.1000000000000001e24 < y

   1. Initial program 99.8%

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

      1. associate-*l/ 72.7%

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

      2. associate-*r/ 77.3%

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

   3. Simplified 77.3%

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

      1. associate-*r/ 72.7%

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

      2. associate-*l/ 99.8%

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

      3. *-commutative 99.8%

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

      4. clear-num 99.8%

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

      5. un-div-inv 99.9%

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

   5. Applied egg-rr 99.9%

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

   6. Taylor expanded in x around 0 79.2%

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

      1. associate-*r/ 79.2%

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

      2. neg-mul-1 79.2%

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

      3. neg-sub0 79.2%

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

      4. associate--r- 79.2%

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

      5. neg-sub0 79.2%

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

   8. Simplified 79.2%

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

   9. Taylor expanded in z around 0 79.2%

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

       1. mul-1-neg 79.2%

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

       2. unsub-neg 79.2%

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

   11. Simplified 79.2%

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

   if -1e113 < y < -1.55e87

   1. Initial program 100.0%

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

   2. Taylor expanded in x around inf 97.2%

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

   3. Taylor expanded in z around 0 97.2%

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

      1. associate-*r/ 97.2%

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

      2. neg-mul-1 97.2%

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

   5. Simplified 97.2%

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

   if -8.7999999999999995e-60 < y < 4.1000000000000001e24

   1. Initial program 92.9%

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

      1. associate-*l/ 89.0%

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

      2. associate-*r/ 96.1%

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

   3. Simplified 96.1%

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

   4. Taylor expanded in x around inf 77.6%

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

      1. associate-*l/ 84.0%

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

      2. *-commutative 84.0%

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

   6. Simplified 84.0%

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

4. Final simplification 82.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1 \cdot 10^{+113}:\\ \;\;\;\;\frac{t}{1 - \frac{z}{y}}\\ \mathbf{elif}\;y \leq -1.55 \cdot 10^{+87}:\\ \;\;\;\;t \cdot \frac{-x}{y}\\ \mathbf{elif}\;y \leq -8.8 \cdot 10^{-60} \lor \neg \left(y \leq 4.1 \cdot 10^{+24}\right):\\ \;\;\;\;\frac{t}{1 - \frac{z}{y}}\\ \mathbf{else}:\\ \;\;\;\;x \cdot \frac{t}{z - y}\\ \end{array} \]

Alternative 3: 65.5% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -5.6 \cdot 10^{+169}:\\ \;\;\;\;t\\ \mathbf{elif}\;y \leq -1.6 \cdot 10^{+87}:\\ \;\;\;\;t \cdot \frac{-x}{y}\\ \mathbf{elif}\;y \leq -3.5 \cdot 10^{-37}:\\ \;\;\;\;t\\ \mathbf{elif}\;y \leq 1.1 \cdot 10^{+97}:\\ \;\;\;\;x \cdot \frac{t}{z - y}\\ \mathbf{else}:\\ \;\;\;\;t\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= y -5.6e+169)
   t
   (if (<= y -1.6e+87)
     (* t (/ (- x) y))
     (if (<= y -3.5e-37) t (if (<= y 1.1e+97) (* x (/ t (- z y))) t)))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (y <= -5.6e+169) {
		tmp = t;
	} else if (y <= -1.6e+87) {
		tmp = t * (-x / y);
	} else if (y <= -3.5e-37) {
		tmp = t;
	} else if (y <= 1.1e+97) {
		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 <= (-5.6d+169)) then
        tmp = t
    else if (y <= (-1.6d+87)) then
        tmp = t * (-x / y)
    else if (y <= (-3.5d-37)) then
        tmp = t
    else if (y <= 1.1d+97) 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 <= -5.6e+169) {
		tmp = t;
	} else if (y <= -1.6e+87) {
		tmp = t * (-x / y);
	} else if (y <= -3.5e-37) {
		tmp = t;
	} else if (y <= 1.1e+97) {
		tmp = x * (t / (z - y));
	} else {
		tmp = t;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if y <= -5.6e+169:
		tmp = t
	elif y <= -1.6e+87:
		tmp = t * (-x / y)
	elif y <= -3.5e-37:
		tmp = t
	elif y <= 1.1e+97:
		tmp = x * (t / (z - y))
	else:
		tmp = t
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (y <= -5.6e+169)
		tmp = t;
	elseif (y <= -1.6e+87)
		tmp = Float64(t * Float64(Float64(-x) / y));
	elseif (y <= -3.5e-37)
		tmp = t;
	elseif (y <= 1.1e+97)
		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 <= -5.6e+169)
		tmp = t;
	elseif (y <= -1.6e+87)
		tmp = t * (-x / y);
	elseif (y <= -3.5e-37)
		tmp = t;
	elseif (y <= 1.1e+97)
		tmp = x * (t / (z - y));
	else
		tmp = t;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[y, -5.6e+169], t, If[LessEqual[y, -1.6e+87], N[(t * N[((-x) / y), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, -3.5e-37], t, If[LessEqual[y, 1.1e+97], N[(x * N[(t / N[(z - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t]]]]

Derivation

1. Split input into 3 regimes

2. if y < -5.6000000000000003e169 or -1.6e87 < y < -3.5000000000000001e-37 or 1.1e97 < y

   1. Initial program 99.8%

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

      1. associate-*l/ 68.9%

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

      2. associate-*r/ 72.7%

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

   3. Simplified 72.7%

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

   4. Taylor expanded in y around inf 68.8%

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

   if -5.6000000000000003e169 < y < -1.6e87

   1. Initial program 100.0%

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

   2. Taylor expanded in x around inf 69.5%

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

   3. Taylor expanded in z around 0 69.7%

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

      1. associate-*r/ 69.7%

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

      2. neg-mul-1 69.7%

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

   5. Simplified 69.7%

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

   if -3.5000000000000001e-37 < y < 1.1e97

   1. Initial program 93.8%

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

      1. associate-*l/ 89.1%

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

      2. associate-*r/ 96.6%

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

   3. Simplified 96.6%

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

   4. Taylor expanded in x around inf 72.7%

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

      1. associate-*l/ 79.0%

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

      2. *-commutative 79.0%

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

   6. Simplified 79.0%

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

4. Final simplification 74.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -5.6 \cdot 10^{+169}:\\ \;\;\;\;t\\ \mathbf{elif}\;y \leq -1.6 \cdot 10^{+87}:\\ \;\;\;\;t \cdot \frac{-x}{y}\\ \mathbf{elif}\;y \leq -3.5 \cdot 10^{-37}:\\ \;\;\;\;t\\ \mathbf{elif}\;y \leq 1.1 \cdot 10^{+97}:\\ \;\;\;\;x \cdot \frac{t}{z - y}\\ \mathbf{else}:\\ \;\;\;\;t\\ \end{array} \]

Alternative 4: 65.5% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -1.12 \cdot 10^{+192}:\\ \;\;\;\;t\\ \mathbf{elif}\;y \leq -9.7 \cdot 10^{+39}:\\ \;\;\;\;t \cdot \frac{x}{z - y}\\ \mathbf{elif}\;y \leq -3.8 \cdot 10^{-37}:\\ \;\;\;\;t\\ \mathbf{elif}\;y \leq 5.5 \cdot 10^{+96}:\\ \;\;\;\;x \cdot \frac{t}{z - y}\\ \mathbf{else}:\\ \;\;\;\;t\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= y -1.12e+192)
   t
   (if (<= y -9.7e+39)
     (* t (/ x (- z y)))
     (if (<= y -3.8e-37) t (if (<= y 5.5e+96) (* x (/ t (- z y))) t)))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (y <= -1.12e+192) {
		tmp = t;
	} else if (y <= -9.7e+39) {
		tmp = t * (x / (z - y));
	} else if (y <= -3.8e-37) {
		tmp = t;
	} else if (y <= 5.5e+96) {
		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 <= (-1.12d+192)) then
        tmp = t
    else if (y <= (-9.7d+39)) then
        tmp = t * (x / (z - y))
    else if (y <= (-3.8d-37)) then
        tmp = t
    else if (y <= 5.5d+96) 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 <= -1.12e+192) {
		tmp = t;
	} else if (y <= -9.7e+39) {
		tmp = t * (x / (z - y));
	} else if (y <= -3.8e-37) {
		tmp = t;
	} else if (y <= 5.5e+96) {
		tmp = x * (t / (z - y));
	} else {
		tmp = t;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if y <= -1.12e+192:
		tmp = t
	elif y <= -9.7e+39:
		tmp = t * (x / (z - y))
	elif y <= -3.8e-37:
		tmp = t
	elif y <= 5.5e+96:
		tmp = x * (t / (z - y))
	else:
		tmp = t
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (y <= -1.12e+192)
		tmp = t;
	elseif (y <= -9.7e+39)
		tmp = Float64(t * Float64(x / Float64(z - y)));
	elseif (y <= -3.8e-37)
		tmp = t;
	elseif (y <= 5.5e+96)
		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 <= -1.12e+192)
		tmp = t;
	elseif (y <= -9.7e+39)
		tmp = t * (x / (z - y));
	elseif (y <= -3.8e-37)
		tmp = t;
	elseif (y <= 5.5e+96)
		tmp = x * (t / (z - y));
	else
		tmp = t;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[y, -1.12e+192], t, If[LessEqual[y, -9.7e+39], N[(t * N[(x / N[(z - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, -3.8e-37], t, If[LessEqual[y, 5.5e+96], N[(x * N[(t / N[(z - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t]]]]

Derivation

1. Split input into 3 regimes

2. if y < -1.12e192 or -9.6999999999999995e39 < y < -3.8000000000000004e-37 or 5.5000000000000002e96 < y

   1. Initial program 99.8%

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

      1. associate-*l/ 65.1%

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

      2. associate-*r/ 67.3%

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

   3. Simplified 67.3%

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

   4. Taylor expanded in y around inf 74.3%

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

   if -1.12e192 < y < -9.6999999999999995e39

   1. Initial program 99.8%

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

   2. Taylor expanded in x around inf 54.7%

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

   if -3.8000000000000004e-37 < y < 5.5000000000000002e96

   1. Initial program 93.8%

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

      1. associate-*l/ 89.1%

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

      2. associate-*r/ 96.6%

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

   3. Simplified 96.6%

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

   4. Taylor expanded in x around inf 72.7%

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

      1. associate-*l/ 79.0%

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

      2. *-commutative 79.0%

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

   6. Simplified 79.0%

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

4. Final simplification 75.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.12 \cdot 10^{+192}:\\ \;\;\;\;t\\ \mathbf{elif}\;y \leq -9.7 \cdot 10^{+39}:\\ \;\;\;\;t \cdot \frac{x}{z - y}\\ \mathbf{elif}\;y \leq -3.8 \cdot 10^{-37}:\\ \;\;\;\;t\\ \mathbf{elif}\;y \leq 5.5 \cdot 10^{+96}:\\ \;\;\;\;x \cdot \frac{t}{z - y}\\ \mathbf{else}:\\ \;\;\;\;t\\ \end{array} \]

Alternative 5: 57.7% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -1.12 \cdot 10^{+192}:\\ \;\;\;\;t\\ \mathbf{elif}\;y \leq -8 \cdot 10^{+60}:\\ \;\;\;\;x \cdot \frac{-t}{y}\\ \mathbf{elif}\;y \leq -3.8 \cdot 10^{-37}:\\ \;\;\;\;t\\ \mathbf{elif}\;y \leq 4.1 \cdot 10^{+20}:\\ \;\;\;\;x \cdot \frac{t}{z}\\ \mathbf{else}:\\ \;\;\;\;t\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= y -1.12e+192)
   t
   (if (<= y -8e+60)
     (* x (/ (- t) y))
     (if (<= y -3.8e-37) t (if (<= y 4.1e+20) (* x (/ t z)) t)))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (y <= -1.12e+192) {
		tmp = t;
	} else if (y <= -8e+60) {
		tmp = x * (-t / y);
	} else if (y <= -3.8e-37) {
		tmp = t;
	} else if (y <= 4.1e+20) {
		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 <= (-1.12d+192)) then
        tmp = t
    else if (y <= (-8d+60)) then
        tmp = x * (-t / y)
    else if (y <= (-3.8d-37)) then
        tmp = t
    else if (y <= 4.1d+20) 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 <= -1.12e+192) {
		tmp = t;
	} else if (y <= -8e+60) {
		tmp = x * (-t / y);
	} else if (y <= -3.8e-37) {
		tmp = t;
	} else if (y <= 4.1e+20) {
		tmp = x * (t / z);
	} else {
		tmp = t;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if y <= -1.12e+192:
		tmp = t
	elif y <= -8e+60:
		tmp = x * (-t / y)
	elif y <= -3.8e-37:
		tmp = t
	elif y <= 4.1e+20:
		tmp = x * (t / z)
	else:
		tmp = t
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (y <= -1.12e+192)
		tmp = t;
	elseif (y <= -8e+60)
		tmp = Float64(x * Float64(Float64(-t) / y));
	elseif (y <= -3.8e-37)
		tmp = t;
	elseif (y <= 4.1e+20)
		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 <= -1.12e+192)
		tmp = t;
	elseif (y <= -8e+60)
		tmp = x * (-t / y);
	elseif (y <= -3.8e-37)
		tmp = t;
	elseif (y <= 4.1e+20)
		tmp = x * (t / z);
	else
		tmp = t;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[y, -1.12e+192], t, If[LessEqual[y, -8e+60], N[(x * N[((-t) / y), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, -3.8e-37], t, If[LessEqual[y, 4.1e+20], N[(x * N[(t / z), $MachinePrecision]), $MachinePrecision], t]]]]

Derivation

1. Split input into 3 regimes

2. if y < -1.12e192 or -7.9999999999999996e60 < y < -3.8000000000000004e-37 or 4.1e20 < y

   1. Initial program 99.8%

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

      1. associate-*l/ 69.2%

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

      2. associate-*r/ 73.8%

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

   3. Simplified 73.8%

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

   4. Taylor expanded in y around inf 66.1%

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

   if -1.12e192 < y < -7.9999999999999996e60

   1. Initial program 99.9%

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

      1. associate-*l/ 86.4%

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

      2. associate-*r/ 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. Taylor expanded in x around inf 48.8%

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

      1. associate-*l/ 53.1%

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

      2. *-commutative 53.1%

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

   6. Simplified 53.1%

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

   7. Taylor expanded in z around 0 53.2%

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

      1. associate-*r/ 53.2%

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

      2. neg-mul-1 53.2%

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

   9. Simplified 53.2%

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

   if -3.8000000000000004e-37 < y < 4.1e20

   1. Initial program 93.1%

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

      1. associate-*l/ 89.3%

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

      2. associate-*r/ 96.2%

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

   3. Simplified 96.2%

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

   4. Taylor expanded in x around inf 76.1%

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

      1. associate-*l/ 82.4%

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

      2. *-commutative 82.4%

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

   6. Simplified 82.4%

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

   7. Taylor expanded in z around inf 70.0%

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

4. Final simplification 67.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.12 \cdot 10^{+192}:\\ \;\;\;\;t\\ \mathbf{elif}\;y \leq -8 \cdot 10^{+60}:\\ \;\;\;\;x \cdot \frac{-t}{y}\\ \mathbf{elif}\;y \leq -3.8 \cdot 10^{-37}:\\ \;\;\;\;t\\ \mathbf{elif}\;y \leq 4.1 \cdot 10^{+20}:\\ \;\;\;\;x \cdot \frac{t}{z}\\ \mathbf{else}:\\ \;\;\;\;t\\ \end{array} \]

Alternative 6: 59.1% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -5.6 \cdot 10^{+169}:\\ \;\;\;\;t\\ \mathbf{elif}\;y \leq -1.6 \cdot 10^{+87}:\\ \;\;\;\;t \cdot \frac{-x}{y}\\ \mathbf{elif}\;y \leq -3.8 \cdot 10^{-37}:\\ \;\;\;\;t\\ \mathbf{elif}\;y \leq 7.5 \cdot 10^{+19}:\\ \;\;\;\;x \cdot \frac{t}{z}\\ \mathbf{else}:\\ \;\;\;\;t\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= y -5.6e+169)
   t
   (if (<= y -1.6e+87)
     (* t (/ (- x) y))
     (if (<= y -3.8e-37) t (if (<= y 7.5e+19) (* x (/ t z)) t)))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (y <= -5.6e+169) {
		tmp = t;
	} else if (y <= -1.6e+87) {
		tmp = t * (-x / y);
	} else if (y <= -3.8e-37) {
		tmp = t;
	} else if (y <= 7.5e+19) {
		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+169)) then
        tmp = t
    else if (y <= (-1.6d+87)) then
        tmp = t * (-x / y)
    else if (y <= (-3.8d-37)) then
        tmp = t
    else if (y <= 7.5d+19) 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+169) {
		tmp = t;
	} else if (y <= -1.6e+87) {
		tmp = t * (-x / y);
	} else if (y <= -3.8e-37) {
		tmp = t;
	} else if (y <= 7.5e+19) {
		tmp = x * (t / z);
	} else {
		tmp = t;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if y <= -5.6e+169:
		tmp = t
	elif y <= -1.6e+87:
		tmp = t * (-x / y)
	elif y <= -3.8e-37:
		tmp = t
	elif y <= 7.5e+19:
		tmp = x * (t / z)
	else:
		tmp = t
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (y <= -5.6e+169)
		tmp = t;
	elseif (y <= -1.6e+87)
		tmp = Float64(t * Float64(Float64(-x) / y));
	elseif (y <= -3.8e-37)
		tmp = t;
	elseif (y <= 7.5e+19)
		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+169)
		tmp = t;
	elseif (y <= -1.6e+87)
		tmp = t * (-x / y);
	elseif (y <= -3.8e-37)
		tmp = t;
	elseif (y <= 7.5e+19)
		tmp = x * (t / z);
	else
		tmp = t;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[y, -5.6e+169], t, If[LessEqual[y, -1.6e+87], N[(t * N[((-x) / y), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, -3.8e-37], t, If[LessEqual[y, 7.5e+19], N[(x * N[(t / z), $MachinePrecision]), $MachinePrecision], t]]]]

Derivation

1. Split input into 3 regimes

2. if y < -5.6000000000000003e169 or -1.6e87 < y < -3.8000000000000004e-37 or 7.5e19 < y

   1. Initial program 99.8%

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

      1. associate-*l/ 71.4%

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

      2. associate-*r/ 76.3%

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

   3. Simplified 76.3%

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

   4. Taylor expanded in y around inf 63.7%

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

   if -5.6000000000000003e169 < y < -1.6e87

   1. Initial program 100.0%

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

   2. Taylor expanded in x around inf 69.5%

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

   3. Taylor expanded in z around 0 69.7%

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

      1. associate-*r/ 69.7%

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

      2. neg-mul-1 69.7%

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

   5. Simplified 69.7%

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

   if -3.8000000000000004e-37 < y < 7.5e19

   1. Initial program 93.1%

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

      1. associate-*l/ 89.3%

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

      2. associate-*r/ 96.2%

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

   3. Simplified 96.2%

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

   4. Taylor expanded in x around inf 76.1%

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

      1. associate-*l/ 82.4%

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

      2. *-commutative 82.4%

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

   6. Simplified 82.4%

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

   7. Taylor expanded in z around inf 70.0%

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

4. Final simplification 67.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -5.6 \cdot 10^{+169}:\\ \;\;\;\;t\\ \mathbf{elif}\;y \leq -1.6 \cdot 10^{+87}:\\ \;\;\;\;t \cdot \frac{-x}{y}\\ \mathbf{elif}\;y \leq -3.8 \cdot 10^{-37}:\\ \;\;\;\;t\\ \mathbf{elif}\;y \leq 7.5 \cdot 10^{+19}:\\ \;\;\;\;x \cdot \frac{t}{z}\\ \mathbf{else}:\\ \;\;\;\;t\\ \end{array} \]

Alternative 7: 73.8% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{t}{1 - \frac{z}{y}}\\ \mathbf{if}\;y \leq -1.6 \cdot 10^{+218}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq -3.45 \cdot 10^{-37}:\\ \;\;\;\;\frac{t}{y} \cdot \left(y - x\right)\\ \mathbf{elif}\;y \leq 3.6 \cdot 10^{+24}:\\ \;\;\;\;x \cdot \frac{t}{z - y}\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (/ t (- 1.0 (/ z y)))))
   (if (<= y -1.6e+218)
     t_1
     (if (<= y -3.45e-37)
       (* (/ t y) (- y x))
       (if (<= y 3.6e+24) (* x (/ t (- z y))) t_1)))))

C

double code(double x, double y, double z, double t) {
	double t_1 = t / (1.0 - (z / y));
	double tmp;
	if (y <= -1.6e+218) {
		tmp = t_1;
	} else if (y <= -3.45e-37) {
		tmp = (t / y) * (y - x);
	} else if (y <= 3.6e+24) {
		tmp = x * (t / (z - y));
	} else {
		tmp = t_1;
	}
	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 = t / (1.0d0 - (z / y))
    if (y <= (-1.6d+218)) then
        tmp = t_1
    else if (y <= (-3.45d-37)) then
        tmp = (t / y) * (y - x)
    else if (y <= 3.6d+24) then
        tmp = x * (t / (z - y))
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double t_1 = t / (1.0 - (z / y));
	double tmp;
	if (y <= -1.6e+218) {
		tmp = t_1;
	} else if (y <= -3.45e-37) {
		tmp = (t / y) * (y - x);
	} else if (y <= 3.6e+24) {
		tmp = x * (t / (z - y));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = t / (1.0 - (z / y))
	tmp = 0
	if y <= -1.6e+218:
		tmp = t_1
	elif y <= -3.45e-37:
		tmp = (t / y) * (y - x)
	elif y <= 3.6e+24:
		tmp = x * (t / (z - y))
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(t / Float64(1.0 - Float64(z / y)))
	tmp = 0.0
	if (y <= -1.6e+218)
		tmp = t_1;
	elseif (y <= -3.45e-37)
		tmp = Float64(Float64(t / y) * Float64(y - x));
	elseif (y <= 3.6e+24)
		tmp = Float64(x * Float64(t / Float64(z - y)));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = t / (1.0 - (z / y));
	tmp = 0.0;
	if (y <= -1.6e+218)
		tmp = t_1;
	elseif (y <= -3.45e-37)
		tmp = (t / y) * (y - x);
	elseif (y <= 3.6e+24)
		tmp = x * (t / (z - y));
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(t / N[(1.0 - N[(z / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -1.6e+218], t$95$1, If[LessEqual[y, -3.45e-37], N[(N[(t / y), $MachinePrecision] * N[(y - x), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 3.6e+24], N[(x * N[(t / N[(z - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if y < -1.59999999999999994e218 or 3.59999999999999983e24 < y

   1. Initial program 99.9%

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

      1. associate-*l/ 66.8%

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

      2. associate-*r/ 69.6%

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

   3. Simplified 69.6%

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

      1. associate-*r/ 66.8%

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

      2. associate-*l/ 99.9%

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

      3. *-commutative 99.9%

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

      4. clear-num 99.9%

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

      5. un-div-inv 99.9%

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

   5. Applied egg-rr 99.9%

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

   6. Taylor expanded in x around 0 83.0%

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

      1. associate-*r/ 83.0%

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

      2. neg-mul-1 83.0%

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

      3. neg-sub0 83.0%

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

      4. associate--r- 83.0%

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

      5. neg-sub0 83.0%

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

   8. Simplified 83.0%

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

   9. Taylor expanded in z around 0 83.0%

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

       1. mul-1-neg 83.0%

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

       2. unsub-neg 83.0%

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

   11. Simplified 83.0%

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

   if -1.59999999999999994e218 < y < -3.4499999999999999e-37

   1. Initial program 99.8%

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

      1. associate-*l/ 82.3%

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

      2. associate-*r/ 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. Taylor expanded in z around 0 79.7%

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

      1. associate-*r/ 39.1%

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

      2. neg-mul-1 39.1%

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

   6. Simplified 79.7%

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

   if -3.4499999999999999e-37 < y < 3.59999999999999983e24

   1. Initial program 93.1%

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

      1. associate-*l/ 89.4%

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

      2. associate-*r/ 96.3%

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

   3. Simplified 96.3%

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

   4. Taylor expanded in x around inf 76.3%

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

      1. associate-*l/ 82.5%

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

      2. *-commutative 82.5%

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

   6. Simplified 82.5%

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

4. Final simplification 82.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.6 \cdot 10^{+218}:\\ \;\;\;\;\frac{t}{1 - \frac{z}{y}}\\ \mathbf{elif}\;y \leq -3.45 \cdot 10^{-37}:\\ \;\;\;\;\frac{t}{y} \cdot \left(y - x\right)\\ \mathbf{elif}\;y \leq 3.6 \cdot 10^{+24}:\\ \;\;\;\;x \cdot \frac{t}{z - y}\\ \mathbf{else}:\\ \;\;\;\;\frac{t}{1 - \frac{z}{y}}\\ \end{array} \]

Alternative 8: 89.8% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -1.7 \cdot 10^{+218}:\\ \;\;\;\;\frac{t}{1 - \frac{z}{y}}\\ \mathbf{elif}\;y \leq 4.8 \cdot 10^{+212}:\\ \;\;\;\;\left(x - y\right) \cdot \frac{t}{z - y}\\ \mathbf{else}:\\ \;\;\;\;\frac{-t}{\frac{y}{x - y}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= y -1.7e+218)
   (/ t (- 1.0 (/ z y)))
   (if (<= y 4.8e+212) (* (- x y) (/ t (- z y))) (/ (- t) (/ y (- x y))))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (y <= -1.7e+218) {
		tmp = t / (1.0 - (z / y));
	} else if (y <= 4.8e+212) {
		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 <= (-1.7d+218)) then
        tmp = t / (1.0d0 - (z / y))
    else if (y <= 4.8d+212) 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 <= -1.7e+218) {
		tmp = t / (1.0 - (z / y));
	} else if (y <= 4.8e+212) {
		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 <= -1.7e+218:
		tmp = t / (1.0 - (z / y))
	elif y <= 4.8e+212:
		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 <= -1.7e+218)
		tmp = Float64(t / Float64(1.0 - Float64(z / y)));
	elseif (y <= 4.8e+212)
		tmp = Float64(Float64(x - y) * Float64(t / Float64(z - y)));
	else
		tmp = Float64(Float64(-t) / Float64(y / Float64(x - y)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (y <= -1.7e+218)
		tmp = t / (1.0 - (z / y));
	elseif (y <= 4.8e+212)
		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, -1.7e+218], N[(t / N[(1.0 - N[(z / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 4.8e+212], N[(N[(x - y), $MachinePrecision] * N[(t / N[(z - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[((-t) / N[(y / N[(x - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if y < -1.70000000000000004e218

   1. Initial program 99.9%

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

      1. associate-*l/ 67.9%

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

      2. associate-*r/ 52.8%

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

   3. Simplified 52.8%

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

      1. associate-*r/ 67.9%

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

      2. associate-*l/ 99.9%

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

      3. *-commutative 99.9%

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

      4. clear-num 100.0%

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

      5. un-div-inv 100.0%

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

   5. Applied egg-rr 100.0%

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

   6. Taylor expanded in x around 0 95.0%

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

      1. associate-*r/ 95.0%

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

      2. neg-mul-1 95.0%

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

      3. neg-sub0 95.0%

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

      4. associate--r- 95.0%

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

      5. neg-sub0 95.0%

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

   8. Simplified 95.0%

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

   9. Taylor expanded in z around 0 95.0%

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

       1. mul-1-neg 95.0%

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

       2. unsub-neg 95.0%

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

   11. Simplified 95.0%

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

   if -1.70000000000000004e218 < y < 4.8e212

   1. Initial program 95.6%

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

      1. associate-*l/ 85.3%

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

      2. associate-*r/ 93.4%

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

   3. Simplified 93.4%

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

   if 4.8e212 < y

   1. Initial program 100.0%

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

      1. associate-*l/ 52.5%

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

      2. associate-*r/ 56.5%

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

   3. Simplified 56.5%

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

      1. associate-*r/ 52.5%

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

      2. associate-*l/ 100.0%

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

      3. *-commutative 100.0%

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

      4. clear-num 100.0%

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

      5. un-div-inv 100.0%

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

   5. Applied egg-rr 100.0%

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

   6. Taylor expanded in z around 0 52.5%

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

      1. mul-1-neg 52.5%

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

      2. associate-/l* 100.0%

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

      3. distribute-neg-frac 100.0%

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

   8. Simplified 100.0%

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

4. Final simplification 94.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.7 \cdot 10^{+218}:\\ \;\;\;\;\frac{t}{1 - \frac{z}{y}}\\ \mathbf{elif}\;y \leq 4.8 \cdot 10^{+212}:\\ \;\;\;\;\left(x - y\right) \cdot \frac{t}{z - y}\\ \mathbf{else}:\\ \;\;\;\;\frac{-t}{\frac{y}{x - y}}\\ \end{array} \]

Alternative 9: 75.8% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -3.8 \cdot 10^{-37}:\\ \;\;\;\;\frac{-t}{\frac{y}{x - y}}\\ \mathbf{elif}\;y \leq 4.5 \cdot 10^{+24}:\\ \;\;\;\;x \cdot \frac{t}{z - y}\\ \mathbf{else}:\\ \;\;\;\;\frac{t}{1 - \frac{z}{y}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= y -3.8e-37)
   (/ (- t) (/ y (- x y)))
   (if (<= y 4.5e+24) (* x (/ t (- z y))) (/ t (- 1.0 (/ z y))))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (y <= -3.8e-37) {
		tmp = -t / (y / (x - y));
	} else if (y <= 4.5e+24) {
		tmp = x * (t / (z - y));
	} else {
		tmp = t / (1.0 - (z / 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 <= (-3.8d-37)) then
        tmp = -t / (y / (x - y))
    else if (y <= 4.5d+24) then
        tmp = x * (t / (z - y))
    else
        tmp = t / (1.0d0 - (z / y))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if (y <= -3.8e-37) {
		tmp = -t / (y / (x - y));
	} else if (y <= 4.5e+24) {
		tmp = x * (t / (z - y));
	} else {
		tmp = t / (1.0 - (z / y));
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if y <= -3.8e-37:
		tmp = -t / (y / (x - y))
	elif y <= 4.5e+24:
		tmp = x * (t / (z - y))
	else:
		tmp = t / (1.0 - (z / y))
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (y <= -3.8e-37)
		tmp = Float64(Float64(-t) / Float64(y / Float64(x - y)));
	elseif (y <= 4.5e+24)
		tmp = Float64(x * Float64(t / Float64(z - y)));
	else
		tmp = Float64(t / Float64(1.0 - Float64(z / y)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (y <= -3.8e-37)
		tmp = -t / (y / (x - y));
	elseif (y <= 4.5e+24)
		tmp = x * (t / (z - y));
	else
		tmp = t / (1.0 - (z / y));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[y, -3.8e-37], N[((-t) / N[(y / N[(x - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 4.5e+24], N[(x * N[(t / N[(z - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(t / N[(1.0 - N[(z / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if y < -3.8000000000000004e-37

   1. Initial program 99.8%

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

      1. associate-*l/ 77.8%

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

      2. associate-*r/ 80.2%

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

   3. Simplified 80.2%

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

      1. associate-*r/ 77.8%

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

      2. associate-*l/ 99.8%

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

      3. *-commutative 99.8%

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

      4. clear-num 99.8%

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

      5. un-div-inv 99.8%

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

   5. Applied egg-rr 99.8%

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

   6. Taylor expanded in z around 0 64.5%

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

      1. mul-1-neg 64.5%

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

      2. associate-/l* 81.7%

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

      3. distribute-neg-frac 81.7%

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

   8. Simplified 81.7%

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

   if -3.8000000000000004e-37 < y < 4.50000000000000019e24

   1. Initial program 93.1%

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

      1. associate-*l/ 89.4%

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

      2. associate-*r/ 96.3%

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

   3. Simplified 96.3%

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

   4. Taylor expanded in x around inf 76.3%

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

      1. associate-*l/ 82.5%

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

      2. *-commutative 82.5%

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

   6. Simplified 82.5%

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

   if 4.50000000000000019e24 < y

   1. Initial program 99.8%

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

      1. associate-*l/ 66.5%

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

      2. associate-*r/ 74.5%

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

   3. Simplified 74.5%

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

      1. associate-*r/ 66.5%

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

      2. associate-*l/ 99.8%

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

      3. *-commutative 99.8%

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

      4. clear-num 99.8%

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

      5. un-div-inv 99.9%

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

   5. Applied egg-rr 99.9%

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

   6. Taylor expanded in x around 0 79.5%

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

      1. associate-*r/ 79.5%

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

      2. neg-mul-1 79.5%

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

      3. neg-sub0 79.5%

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

      4. associate--r- 79.5%

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

      5. neg-sub0 79.5%

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

   8. Simplified 79.5%

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

   9. Taylor expanded in z around 0 79.5%

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

       1. mul-1-neg 79.5%

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

       2. unsub-neg 79.5%

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

   11. Simplified 79.5%

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

4. Final simplification 81.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -3.8 \cdot 10^{-37}:\\ \;\;\;\;\frac{-t}{\frac{y}{x - y}}\\ \mathbf{elif}\;y \leq 4.5 \cdot 10^{+24}:\\ \;\;\;\;x \cdot \frac{t}{z - y}\\ \mathbf{else}:\\ \;\;\;\;\frac{t}{1 - \frac{z}{y}}\\ \end{array} \]

Alternative 10: 61.4% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -3.5 \cdot 10^{-37}:\\ \;\;\;\;t\\ \mathbf{elif}\;y \leq 4.3 \cdot 10^{+19}:\\ \;\;\;\;x \cdot \frac{t}{z}\\ \mathbf{else}:\\ \;\;\;\;t\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= y -3.5e-37) t (if (<= y 4.3e+19) (* x (/ t z)) t)))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (y <= -3.5e-37) {
		tmp = t;
	} else if (y <= 4.3e+19) {
		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 <= (-3.5d-37)) then
        tmp = t
    else if (y <= 4.3d+19) 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 <= -3.5e-37) {
		tmp = t;
	} else if (y <= 4.3e+19) {
		tmp = x * (t / z);
	} else {
		tmp = t;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if y <= -3.5e-37:
		tmp = t
	elif y <= 4.3e+19:
		tmp = x * (t / z)
	else:
		tmp = t
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (y <= -3.5e-37)
		tmp = t;
	elseif (y <= 4.3e+19)
		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 <= -3.5e-37)
		tmp = t;
	elseif (y <= 4.3e+19)
		tmp = x * (t / z);
	else
		tmp = t;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[y, -3.5e-37], t, If[LessEqual[y, 4.3e+19], N[(x * N[(t / z), $MachinePrecision]), $MachinePrecision], t]]

Derivation

1. Split input into 2 regimes

2. if y < -3.5000000000000001e-37 or 4.3e19 < y

   1. Initial program 99.8%

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

      1. associate-*l/ 72.2%

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

      2. associate-*r/ 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. Taylor expanded in y around inf 59.7%

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

   if -3.5000000000000001e-37 < y < 4.3e19

   1. Initial program 93.1%

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

      1. associate-*l/ 89.3%

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

      2. associate-*r/ 96.2%

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

   3. Simplified 96.2%

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

   4. Taylor expanded in x around inf 76.1%

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

      1. associate-*l/ 82.4%

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

      2. *-commutative 82.4%

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

   6. Simplified 82.4%

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

   7. Taylor expanded in z around inf 70.0%

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

4. Final simplification 65.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -3.5 \cdot 10^{-37}:\\ \;\;\;\;t\\ \mathbf{elif}\;y \leq 4.3 \cdot 10^{+19}:\\ \;\;\;\;x \cdot \frac{t}{z}\\ \mathbf{else}:\\ \;\;\;\;t\\ \end{array} \]

Alternative 11: 35.4% 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 96.3%

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

   1. associate-*l/ 81.2%

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

   2. associate-*r/ 87.4%

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

3. Simplified 87.4%

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

4. Taylor expanded in y around inf 33.1%

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

5. Final simplification 33.1%

   \[\leadsto t \]

Developer target: 96.8% 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 2023192 
(FPCore (x y z t)
  :name "Numeric.Signal.Multichannel:$cput from hsignal-0.2.7.1"
  :precision binary64

  :herbie-target
  (/ t (/ (- z y) (- x y)))

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