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

Percentage Accurate: 97.0% → 97.0%

Time: 8.7s

Alternatives: 14

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: 97.0% 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: 97.0% 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]

Derivation

1. Initial program 96.9%

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

   1. associate-*l/ 83.9%

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

   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. Step-by-step derivation

   1. associate-*r/ 83.9%

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

   2. associate-*l/ 96.9%

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

   3. *-commutative 96.9%

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

   4. clear-num 96.7%

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

   5. un-div-inv 97.0%

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

6. Applied egg-rr 97.0%

   \[\leadsto \color{blue}{\frac{t}{\frac{z - y}{x - y}}} \]
7. Add Preprocessing

Alternative 2: 60.1% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -1950000000000:\\ \;\;\;\;t\\ \mathbf{elif}\;y \leq 7.2 \cdot 10^{-24}:\\ \;\;\;\;\frac{t}{\frac{z}{x}}\\ \mathbf{elif}\;y \leq 3.4 \cdot 10^{+96}:\\ \;\;\;\;\frac{t \cdot \left(-x\right)}{y}\\ \mathbf{else}:\\ \;\;\;\;t\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= y -1950000000000.0)
   t
   (if (<= y 7.2e-24) (/ t (/ z x)) (if (<= y 3.4e+96) (/ (* t (- x)) y) t))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (y <= -1950000000000.0) {
		tmp = t;
	} else if (y <= 7.2e-24) {
		tmp = t / (z / x);
	} else if (y <= 3.4e+96) {
		tmp = (t * -x) / 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 <= (-1950000000000.0d0)) then
        tmp = t
    else if (y <= 7.2d-24) then
        tmp = t / (z / x)
    else if (y <= 3.4d+96) then
        tmp = (t * -x) / 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 <= -1950000000000.0) {
		tmp = t;
	} else if (y <= 7.2e-24) {
		tmp = t / (z / x);
	} else if (y <= 3.4e+96) {
		tmp = (t * -x) / y;
	} else {
		tmp = t;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if y <= -1950000000000.0:
		tmp = t
	elif y <= 7.2e-24:
		tmp = t / (z / x)
	elif y <= 3.4e+96:
		tmp = (t * -x) / y
	else:
		tmp = t
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (y <= -1950000000000.0)
		tmp = t;
	elseif (y <= 7.2e-24)
		tmp = Float64(t / Float64(z / x));
	elseif (y <= 3.4e+96)
		tmp = Float64(Float64(t * Float64(-x)) / y);
	else
		tmp = t;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (y <= -1950000000000.0)
		tmp = t;
	elseif (y <= 7.2e-24)
		tmp = t / (z / x);
	elseif (y <= 3.4e+96)
		tmp = (t * -x) / y;
	else
		tmp = t;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[y, -1950000000000.0], t, If[LessEqual[y, 7.2e-24], N[(t / N[(z / x), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 3.4e+96], N[(N[(t * (-x)), $MachinePrecision] / y), $MachinePrecision], t]]]

Derivation

1. Split input into 3 regimes

2. if y < -1.95e12 or 3.4000000000000001e96 < y

   1. Initial program 99.9%

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

      1. associate-*l/ 68.4%

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

      2. associate-/l* 75.0%

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

   3. Simplified 75.0%

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

   5. Taylor expanded in y around inf 76.1%

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

   if -1.95e12 < y < 7.2000000000000002e-24

   1. Initial program 93.9%

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

      1. associate-*l/ 93.1%

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

      2. associate-/l* 90.9%

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

   3. Simplified 90.9%

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

      1. associate-*r/ 93.1%

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

      2. associate-*l/ 93.9%

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

      3. *-commutative 93.9%

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

      4. clear-num 93.7%

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

      5. un-div-inv 94.2%

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

   6. Applied egg-rr 94.2%

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

   7. Taylor expanded in y around 0 69.3%

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

   if 7.2000000000000002e-24 < y < 3.4000000000000001e96

   1. Initial program 99.7%

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

      1. associate-*l/ 95.7%

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

      2. associate-/l* 90.1%

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

   3. Simplified 90.1%

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

   5. Taylor expanded in x around inf 58.4%

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

   6. Taylor expanded in z around 0 51.6%

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

      1. associate-*r/ 51.6%

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

      2. mul-1-neg 51.6%

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

      3. distribute-rgt-neg-out 51.6%

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

   8. Simplified 51.6%

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

Alternative 3: 60.2% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -2300000000000:\\ \;\;\;\;t\\ \mathbf{elif}\;y \leq 1.5 \cdot 10^{-20}:\\ \;\;\;\;\frac{t}{\frac{z}{x}}\\ \mathbf{elif}\;y \leq 2.2 \cdot 10^{+96}:\\ \;\;\;\;t \cdot \frac{x}{-y}\\ \mathbf{else}:\\ \;\;\;\;t\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= y -2300000000000.0)
   t
   (if (<= y 1.5e-20) (/ t (/ z x)) (if (<= y 2.2e+96) (* t (/ x (- y))) t))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (y <= -2300000000000.0) {
		tmp = t;
	} else if (y <= 1.5e-20) {
		tmp = t / (z / x);
	} else if (y <= 2.2e+96) {
		tmp = t * (x / -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 <= (-2300000000000.0d0)) then
        tmp = t
    else if (y <= 1.5d-20) then
        tmp = t / (z / x)
    else if (y <= 2.2d+96) then
        tmp = t * (x / -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 <= -2300000000000.0) {
		tmp = t;
	} else if (y <= 1.5e-20) {
		tmp = t / (z / x);
	} else if (y <= 2.2e+96) {
		tmp = t * (x / -y);
	} else {
		tmp = t;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if y <= -2300000000000.0:
		tmp = t
	elif y <= 1.5e-20:
		tmp = t / (z / x)
	elif y <= 2.2e+96:
		tmp = t * (x / -y)
	else:
		tmp = t
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (y <= -2300000000000.0)
		tmp = t;
	elseif (y <= 1.5e-20)
		tmp = Float64(t / Float64(z / x));
	elseif (y <= 2.2e+96)
		tmp = Float64(t * Float64(x / Float64(-y)));
	else
		tmp = t;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (y <= -2300000000000.0)
		tmp = t;
	elseif (y <= 1.5e-20)
		tmp = t / (z / x);
	elseif (y <= 2.2e+96)
		tmp = t * (x / -y);
	else
		tmp = t;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[y, -2300000000000.0], t, If[LessEqual[y, 1.5e-20], N[(t / N[(z / x), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 2.2e+96], N[(t * N[(x / (-y)), $MachinePrecision]), $MachinePrecision], t]]]

Derivation

1. Split input into 3 regimes

2. if y < -2.3e12 or 2.1999999999999999e96 < y

   1. Initial program 99.9%

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

      1. associate-*l/ 68.4%

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

      2. associate-/l* 75.0%

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

   3. Simplified 75.0%

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

   5. Taylor expanded in y around inf 76.1%

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

   if -2.3e12 < y < 1.50000000000000014e-20

   1. Initial program 93.9%

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

      1. associate-*l/ 93.1%

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

      2. associate-/l* 90.9%

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

   3. Simplified 90.9%

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

      1. associate-*r/ 93.1%

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

      2. associate-*l/ 93.9%

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

      3. *-commutative 93.9%

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

      4. clear-num 93.7%

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

      5. un-div-inv 94.2%

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

   6. Applied egg-rr 94.2%

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

   7. Taylor expanded in y around 0 69.3%

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

   if 1.50000000000000014e-20 < y < 2.1999999999999999e96

   1. Initial program 99.7%

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

      1. associate-*l/ 95.7%

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

      2. associate-/l* 90.1%

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

   3. Simplified 90.1%

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

   5. Taylor expanded in x around inf 53.3%

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

   6. Taylor expanded in z around 0 51.6%

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

      1. mul-1-neg 51.6%

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

      2. associate-/l* 51.6%

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

      3. distribute-lft-neg-in 51.6%

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

   8. Simplified 51.6%

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

4. Final simplification 69.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -2300000000000:\\ \;\;\;\;t\\ \mathbf{elif}\;y \leq 1.5 \cdot 10^{-20}:\\ \;\;\;\;\frac{t}{\frac{z}{x}}\\ \mathbf{elif}\;y \leq 2.2 \cdot 10^{+96}:\\ \;\;\;\;t \cdot \frac{x}{-y}\\ \mathbf{else}:\\ \;\;\;\;t\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 60.1% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -3900000000000:\\ \;\;\;\;t\\ \mathbf{elif}\;y \leq 1.7 \cdot 10^{-23}:\\ \;\;\;\;\frac{t}{\frac{z}{x}}\\ \mathbf{elif}\;y \leq 1.85 \cdot 10^{+98}:\\ \;\;\;\;x \cdot \frac{t}{-y}\\ \mathbf{else}:\\ \;\;\;\;t\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= y -3900000000000.0)
   t
   (if (<= y 1.7e-23) (/ t (/ z x)) (if (<= y 1.85e+98) (* x (/ t (- y))) t))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (y <= -3900000000000.0) {
		tmp = t;
	} else if (y <= 1.7e-23) {
		tmp = t / (z / x);
	} else if (y <= 1.85e+98) {
		tmp = x * (t / -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 <= (-3900000000000.0d0)) then
        tmp = t
    else if (y <= 1.7d-23) then
        tmp = t / (z / x)
    else if (y <= 1.85d+98) then
        tmp = x * (t / -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 <= -3900000000000.0) {
		tmp = t;
	} else if (y <= 1.7e-23) {
		tmp = t / (z / x);
	} else if (y <= 1.85e+98) {
		tmp = x * (t / -y);
	} else {
		tmp = t;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if y <= -3900000000000.0:
		tmp = t
	elif y <= 1.7e-23:
		tmp = t / (z / x)
	elif y <= 1.85e+98:
		tmp = x * (t / -y)
	else:
		tmp = t
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (y <= -3900000000000.0)
		tmp = t;
	elseif (y <= 1.7e-23)
		tmp = Float64(t / Float64(z / x));
	elseif (y <= 1.85e+98)
		tmp = Float64(x * Float64(t / Float64(-y)));
	else
		tmp = t;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (y <= -3900000000000.0)
		tmp = t;
	elseif (y <= 1.7e-23)
		tmp = t / (z / x);
	elseif (y <= 1.85e+98)
		tmp = x * (t / -y);
	else
		tmp = t;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[y, -3900000000000.0], t, If[LessEqual[y, 1.7e-23], N[(t / N[(z / x), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 1.85e+98], N[(x * N[(t / (-y)), $MachinePrecision]), $MachinePrecision], t]]]

Derivation

1. Split input into 3 regimes

2. if y < -3.9e12 or 1.8499999999999999e98 < y

   1. Initial program 99.9%

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

      1. associate-*l/ 68.4%

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

      2. associate-/l* 75.0%

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

   3. Simplified 75.0%

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

   5. Taylor expanded in y around inf 76.1%

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

   if -3.9e12 < y < 1.7e-23

   1. Initial program 93.9%

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

      1. associate-*l/ 93.1%

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

      2. associate-/l* 90.9%

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

   3. Simplified 90.9%

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

      1. associate-*r/ 93.1%

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

      2. associate-*l/ 93.9%

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

      3. *-commutative 93.9%

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

      4. clear-num 93.7%

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

      5. un-div-inv 94.2%

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

   6. Applied egg-rr 94.2%

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

   7. Taylor expanded in y around 0 69.3%

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

   if 1.7e-23 < y < 1.8499999999999999e98

   1. Initial program 99.7%

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

      1. associate-*l/ 95.7%

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

      2. associate-/l* 90.1%

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

   3. Simplified 90.1%

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

   5. Taylor expanded in x around inf 53.3%

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

   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%

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

4. Final simplification 69.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -3900000000000:\\ \;\;\;\;t\\ \mathbf{elif}\;y \leq 1.7 \cdot 10^{-23}:\\ \;\;\;\;\frac{t}{\frac{z}{x}}\\ \mathbf{elif}\;y \leq 1.85 \cdot 10^{+98}:\\ \;\;\;\;x \cdot \frac{t}{-y}\\ \mathbf{else}:\\ \;\;\;\;t\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 90.1% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -1.02 \cdot 10^{+183} \lor \neg \left(y \leq 1.06 \cdot 10^{+130}\right):\\ \;\;\;\;t \cdot \frac{y - x}{y}\\ \mathbf{else}:\\ \;\;\;\;\left(x - y\right) \cdot \frac{t}{z - y}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= y -1.02e+183) (not (<= y 1.06e+130)))
   (* t (/ (- y x) y))
   (* (- x y) (/ t (- z y)))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((y <= -1.02e+183) || !(y <= 1.06e+130)) {
		tmp = t * ((y - x) / y);
	} else {
		tmp = (x - y) * (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) :: tmp
    if ((y <= (-1.02d+183)) .or. (.not. (y <= 1.06d+130))) then
        tmp = t * ((y - x) / y)
    else
        tmp = (x - y) * (t / (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 <= -1.02e+183) || !(y <= 1.06e+130)) {
		tmp = t * ((y - x) / y);
	} else {
		tmp = (x - y) * (t / (z - y));
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (y <= -1.02e+183) or not (y <= 1.06e+130):
		tmp = t * ((y - x) / y)
	else:
		tmp = (x - y) * (t / (z - y))
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((y <= -1.02e+183) || !(y <= 1.06e+130))
		tmp = Float64(t * Float64(Float64(y - x) / y));
	else
		tmp = Float64(Float64(x - y) * Float64(t / Float64(z - y)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((y <= -1.02e+183) || ~((y <= 1.06e+130)))
		tmp = t * ((y - x) / y);
	else
		tmp = (x - y) * (t / (z - y));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[y, -1.02e+183], N[Not[LessEqual[y, 1.06e+130]], $MachinePrecision]], N[(t * N[(N[(y - x), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision], N[(N[(x - y), $MachinePrecision] * N[(t / N[(z - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -1.02000000000000002e183 or 1.06e130 < y

   1. Initial program 99.9%

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

   3. Taylor expanded in z around 0 94.8%

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

      1. associate-*r/ 94.8%

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

      2. neg-mul-1 94.8%

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

      3. neg-sub0 94.8%

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

      4. sub-neg 94.8%

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

      5. +-commutative 94.8%

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

      6. associate--r+ 94.8%

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

      7. neg-sub0 94.8%

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

      8. remove-double-neg 94.8%

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

   5. Simplified 94.8%

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

   if -1.02000000000000002e183 < y < 1.06e130

   1. Initial program 95.8%

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

      1. associate-*l/ 93.1%

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

      2. associate-/l* 89.2%

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

   3. Simplified 89.2%

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

4. Final simplification 90.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.02 \cdot 10^{+183} \lor \neg \left(y \leq 1.06 \cdot 10^{+130}\right):\\ \;\;\;\;t \cdot \frac{y - x}{y}\\ \mathbf{else}:\\ \;\;\;\;\left(x - y\right) \cdot \frac{t}{z - y}\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 75.1% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -9.6 \cdot 10^{+22} \lor \neg \left(y \leq 3.4 \cdot 10^{-40}\right):\\ \;\;\;\;t \cdot \frac{y - x}{y}\\ \mathbf{else}:\\ \;\;\;\;t \cdot \frac{x}{z - y}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= y -9.6e+22) (not (<= y 3.4e-40)))
   (* t (/ (- y x) y))
   (* t (/ x (- z y)))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((y <= -9.6e+22) || !(y <= 3.4e-40)) {
		tmp = t * ((y - x) / y);
	} else {
		tmp = t * (x / (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 <= (-9.6d+22)) .or. (.not. (y <= 3.4d-40))) then
        tmp = t * ((y - x) / y)
    else
        tmp = t * (x / (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 <= -9.6e+22) || !(y <= 3.4e-40)) {
		tmp = t * ((y - x) / y);
	} else {
		tmp = t * (x / (z - y));
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (y <= -9.6e+22) or not (y <= 3.4e-40):
		tmp = t * ((y - x) / y)
	else:
		tmp = t * (x / (z - y))
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((y <= -9.6e+22) || !(y <= 3.4e-40))
		tmp = Float64(t * Float64(Float64(y - x) / y));
	else
		tmp = Float64(t * Float64(x / Float64(z - y)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((y <= -9.6e+22) || ~((y <= 3.4e-40)))
		tmp = t * ((y - x) / y);
	else
		tmp = t * (x / (z - y));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[y, -9.6e+22], N[Not[LessEqual[y, 3.4e-40]], $MachinePrecision]], N[(t * N[(N[(y - x), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision], N[(t * N[(x / N[(z - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -9.6e22 or 3.39999999999999984e-40 < y

   1. Initial program 99.8%

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

   3. Taylor expanded in z around 0 83.4%

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

      1. associate-*r/ 83.4%

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

      2. neg-mul-1 83.4%

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

      3. neg-sub0 83.4%

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

      4. sub-neg 83.4%

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

      5. +-commutative 83.4%

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

      6. associate--r+ 83.4%

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

      7. neg-sub0 83.4%

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

      8. remove-double-neg 83.4%

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

   5. Simplified 83.4%

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

   if -9.6e22 < y < 3.39999999999999984e-40

   1. Initial program 93.8%

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

   3. Taylor expanded in x around inf 79.4%

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

4. Final simplification 81.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -9.6 \cdot 10^{+22} \lor \neg \left(y \leq 3.4 \cdot 10^{-40}\right):\\ \;\;\;\;t \cdot \frac{y - x}{y}\\ \mathbf{else}:\\ \;\;\;\;t \cdot \frac{x}{z - y}\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 74.6% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -4.5 \cdot 10^{+23} \lor \neg \left(y \leq 6.5 \cdot 10^{+89}\right):\\ \;\;\;\;t \cdot \frac{y}{y - z}\\ \mathbf{else}:\\ \;\;\;\;t \cdot \frac{x}{z - y}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= y -4.5e+23) (not (<= y 6.5e+89)))
   (* t (/ y (- y z)))
   (* t (/ x (- z y)))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((y <= -4.5e+23) || !(y <= 6.5e+89)) {
		tmp = t * (y / (y - z));
	} else {
		tmp = t * (x / (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 <= (-4.5d+23)) .or. (.not. (y <= 6.5d+89))) then
        tmp = t * (y / (y - z))
    else
        tmp = t * (x / (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 <= -4.5e+23) || !(y <= 6.5e+89)) {
		tmp = t * (y / (y - z));
	} else {
		tmp = t * (x / (z - y));
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (y <= -4.5e+23) or not (y <= 6.5e+89):
		tmp = t * (y / (y - z))
	else:
		tmp = t * (x / (z - y))
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((y <= -4.5e+23) || !(y <= 6.5e+89))
		tmp = Float64(t * Float64(y / Float64(y - z)));
	else
		tmp = Float64(t * Float64(x / Float64(z - y)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((y <= -4.5e+23) || ~((y <= 6.5e+89)))
		tmp = t * (y / (y - z));
	else
		tmp = t * (x / (z - y));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[y, -4.5e+23], N[Not[LessEqual[y, 6.5e+89]], $MachinePrecision]], N[(t * N[(y / N[(y - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(t * N[(x / N[(z - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -4.49999999999999979e23 or 6.4999999999999996e89 < y

   1. Initial program 99.9%

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

   3. Taylor expanded in x around 0 85.9%

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

      1. neg-mul-1 85.9%

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

      2. distribute-neg-frac2 85.9%

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

      3. neg-sub0 85.9%

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

      4. sub-neg 85.9%

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

      5. +-commutative 85.9%

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

      6. associate--r+ 85.9%

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

      7. neg-sub0 85.9%

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

      8. remove-double-neg 85.9%

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

   5. Simplified 85.9%

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

   if -4.49999999999999979e23 < y < 6.4999999999999996e89

   1. Initial program 95.0%

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

   3. Taylor expanded in x around inf 75.6%

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

4. Final simplification 79.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -4.5 \cdot 10^{+23} \lor \neg \left(y \leq 6.5 \cdot 10^{+89}\right):\\ \;\;\;\;t \cdot \frac{y}{y - z}\\ \mathbf{else}:\\ \;\;\;\;t \cdot \frac{x}{z - y}\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 68.6% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -7.6 \cdot 10^{+28}:\\ \;\;\;\;t\\ \mathbf{elif}\;y \leq 2.6 \cdot 10^{+100}:\\ \;\;\;\;t \cdot \frac{x}{z - y}\\ \mathbf{else}:\\ \;\;\;\;t\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= y -7.6e+28) t (if (<= y 2.6e+100) (* t (/ x (- z y))) t)))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (y <= -7.6e+28) {
		tmp = t;
	} else if (y <= 2.6e+100) {
		tmp = t * (x / (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 <= (-7.6d+28)) then
        tmp = t
    else if (y <= 2.6d+100) then
        tmp = t * (x / (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 <= -7.6e+28) {
		tmp = t;
	} else if (y <= 2.6e+100) {
		tmp = t * (x / (z - y));
	} else {
		tmp = t;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if y <= -7.6e+28:
		tmp = t
	elif y <= 2.6e+100:
		tmp = t * (x / (z - y))
	else:
		tmp = t
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (y <= -7.6e+28)
		tmp = t;
	elseif (y <= 2.6e+100)
		tmp = Float64(t * Float64(x / Float64(z - y)));
	else
		tmp = t;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (y <= -7.6e+28)
		tmp = t;
	elseif (y <= 2.6e+100)
		tmp = t * (x / (z - y));
	else
		tmp = t;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[y, -7.6e+28], t, If[LessEqual[y, 2.6e+100], N[(t * N[(x / N[(z - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t]]

Derivation

1. Split input into 2 regimes

2. if y < -7.5999999999999998e28 or 2.6000000000000002e100 < y

   1. Initial program 99.9%

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

      1. associate-*l/ 67.8%

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

      2. associate-/l* 74.4%

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

   3. Simplified 74.4%

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

   5. Taylor expanded in y around inf 77.7%

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

   if -7.5999999999999998e28 < y < 2.6000000000000002e100

   1. Initial program 95.0%

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

   3. Taylor expanded in x around inf 75.8%

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

4. Final simplification 76.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -7.6 \cdot 10^{+28}:\\ \;\;\;\;t\\ \mathbf{elif}\;y \leq 2.6 \cdot 10^{+100}:\\ \;\;\;\;t \cdot \frac{x}{z - y}\\ \mathbf{else}:\\ \;\;\;\;t\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 67.6% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -1.05 \cdot 10^{+26}:\\ \;\;\;\;t\\ \mathbf{elif}\;y \leq 7.5 \cdot 10^{+96}:\\ \;\;\;\;x \cdot \frac{t}{z - y}\\ \mathbf{else}:\\ \;\;\;\;t\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= y -1.05e+26) t (if (<= y 7.5e+96) (* x (/ t (- z y))) t)))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (y <= -1.05e+26) {
		tmp = t;
	} else if (y <= 7.5e+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 <= (-1.05d+26)) then
        tmp = t
    else if (y <= 7.5d+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 <= -1.05e+26) {
		tmp = t;
	} else if (y <= 7.5e+96) {
		tmp = x * (t / (z - y));
	} else {
		tmp = t;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if y <= -1.05e+26:
		tmp = t
	elif y <= 7.5e+96:
		tmp = x * (t / (z - y))
	else:
		tmp = t
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (y <= -1.05e+26)
		tmp = t;
	elseif (y <= 7.5e+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 <= -1.05e+26)
		tmp = t;
	elseif (y <= 7.5e+96)
		tmp = x * (t / (z - y));
	else
		tmp = t;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[y, -1.05e+26], t, If[LessEqual[y, 7.5e+96], N[(x * N[(t / N[(z - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t]]

Derivation

1. Split input into 2 regimes

2. if y < -1.05e26 or 7.4999999999999996e96 < y

   1. Initial program 99.9%

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

      1. associate-*l/ 67.8%

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

      2. associate-/l* 74.4%

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

   3. Simplified 74.4%

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

   5. Taylor expanded in y around inf 77.7%

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

   if -1.05e26 < y < 7.4999999999999996e96

   1. Initial program 95.0%

      \[\frac{x - y}{z - y} \cdot t \]
   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* 90.8%

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

   3. Simplified 90.8%

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

   5. Taylor expanded in x around inf 70.7%

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

Alternative 10: 60.1% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -2600000000000:\\ \;\;\;\;t\\ \mathbf{elif}\;y \leq 4.2 \cdot 10^{-36}:\\ \;\;\;\;\frac{t}{\frac{z}{x}}\\ \mathbf{else}:\\ \;\;\;\;t\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= y -2600000000000.0) t (if (<= y 4.2e-36) (/ t (/ z x)) t)))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (y <= -2600000000000.0) {
		tmp = t;
	} else if (y <= 4.2e-36) {
		tmp = t / (z / x);
	} 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 <= (-2600000000000.0d0)) then
        tmp = t
    else if (y <= 4.2d-36) then
        tmp = t / (z / x)
    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 <= -2600000000000.0) {
		tmp = t;
	} else if (y <= 4.2e-36) {
		tmp = t / (z / x);
	} else {
		tmp = t;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if y <= -2600000000000.0:
		tmp = t
	elif y <= 4.2e-36:
		tmp = t / (z / x)
	else:
		tmp = t
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (y <= -2600000000000.0)
		tmp = t;
	elseif (y <= 4.2e-36)
		tmp = Float64(t / Float64(z / x));
	else
		tmp = t;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (y <= -2600000000000.0)
		tmp = t;
	elseif (y <= 4.2e-36)
		tmp = t / (z / x);
	else
		tmp = t;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[y, -2600000000000.0], t, If[LessEqual[y, 4.2e-36], N[(t / N[(z / x), $MachinePrecision]), $MachinePrecision], t]]

Derivation

1. Split input into 2 regimes

2. if y < -2.6e12 or 4.19999999999999982e-36 < y

   1. Initial program 99.8%

      \[\frac{x - y}{z - y} \cdot t \]
   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* 78.2%

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

   3. Simplified 78.2%

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

   5. Taylor expanded in y around inf 64.4%

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

   if -2.6e12 < y < 4.19999999999999982e-36

   1. Initial program 93.7%

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

      1. associate-*l/ 92.9%

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

      2. associate-/l* 91.4%

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

   3. Simplified 91.4%

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

      1. associate-*r/ 92.9%

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

      2. associate-*l/ 93.7%

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

      3. *-commutative 93.7%

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

      4. clear-num 93.6%

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

      5. un-div-inv 94.1%

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

   6. Applied egg-rr 94.1%

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

   7. Taylor expanded in y around 0 70.1%

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

Alternative 11: 60.0% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -1100000000000:\\ \;\;\;\;t\\ \mathbf{elif}\;y \leq 4.5 \cdot 10^{-38}:\\ \;\;\;\;t \cdot \frac{x}{z}\\ \mathbf{else}:\\ \;\;\;\;t\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= y -1100000000000.0) t (if (<= y 4.5e-38) (* t (/ x z)) t)))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (y <= -1100000000000.0) {
		tmp = t;
	} else if (y <= 4.5e-38) {
		tmp = t * (x / 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 <= (-1100000000000.0d0)) then
        tmp = t
    else if (y <= 4.5d-38) then
        tmp = t * (x / 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 <= -1100000000000.0) {
		tmp = t;
	} else if (y <= 4.5e-38) {
		tmp = t * (x / z);
	} else {
		tmp = t;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if y <= -1100000000000.0:
		tmp = t
	elif y <= 4.5e-38:
		tmp = t * (x / z)
	else:
		tmp = t
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (y <= -1100000000000.0)
		tmp = t;
	elseif (y <= 4.5e-38)
		tmp = Float64(t * Float64(x / z));
	else
		tmp = t;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (y <= -1100000000000.0)
		tmp = t;
	elseif (y <= 4.5e-38)
		tmp = t * (x / z);
	else
		tmp = t;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[y, -1100000000000.0], t, If[LessEqual[y, 4.5e-38], N[(t * N[(x / z), $MachinePrecision]), $MachinePrecision], t]]

Derivation

1. Split input into 2 regimes

2. if y < -1.1e12 or 4.50000000000000009e-38 < y

   1. Initial program 99.8%

      \[\frac{x - y}{z - y} \cdot t \]
   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* 78.2%

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

   3. Simplified 78.2%

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

   5. Taylor expanded in y around inf 64.4%

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

   if -1.1e12 < y < 4.50000000000000009e-38

   1. Initial program 93.7%

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

   3. Taylor expanded in y around 0 70.0%

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

4. Final simplification 67.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1100000000000:\\ \;\;\;\;t\\ \mathbf{elif}\;y \leq 4.5 \cdot 10^{-38}:\\ \;\;\;\;t \cdot \frac{x}{z}\\ \mathbf{else}:\\ \;\;\;\;t\\ \end{array} \]
5. Add Preprocessing

Alternative 12: 59.3% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -3000000000000:\\ \;\;\;\;t\\ \mathbf{elif}\;y \leq 4.2 \cdot 10^{-36}:\\ \;\;\;\;x \cdot \frac{t}{z}\\ \mathbf{else}:\\ \;\;\;\;t\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= y -3000000000000.0) t (if (<= y 4.2e-36) (* x (/ t z)) t)))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (y <= -3000000000000.0) {
		tmp = t;
	} else if (y <= 4.2e-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 <= (-3000000000000.0d0)) then
        tmp = t
    else if (y <= 4.2d-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 <= -3000000000000.0) {
		tmp = t;
	} else if (y <= 4.2e-36) {
		tmp = x * (t / z);
	} else {
		tmp = t;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if y <= -3000000000000.0:
		tmp = t
	elif y <= 4.2e-36:
		tmp = x * (t / z)
	else:
		tmp = t
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (y <= -3000000000000.0)
		tmp = t;
	elseif (y <= 4.2e-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 <= -3000000000000.0)
		tmp = t;
	elseif (y <= 4.2e-36)
		tmp = x * (t / z);
	else
		tmp = t;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[y, -3000000000000.0], t, If[LessEqual[y, 4.2e-36], N[(x * N[(t / z), $MachinePrecision]), $MachinePrecision], t]]

Derivation

1. Split input into 2 regimes

2. if y < -3e12 or 4.19999999999999982e-36 < y

   1. Initial program 99.8%

      \[\frac{x - y}{z - y} \cdot t \]
   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* 78.2%

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

   3. Simplified 78.2%

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

   5. Taylor expanded in y around inf 64.4%

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

   if -3e12 < y < 4.19999999999999982e-36

   1. Initial program 93.7%

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

      1. associate-*l/ 92.9%

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

      2. associate-/l* 91.4%

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

   3. Simplified 91.4%

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

   5. Taylor expanded in x around inf 75.3%

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

   6. Taylor expanded in z around inf 64.8%

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

Alternative 13: 97.0% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 96.9%

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

3. Final simplification 96.9%

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

Alternative 14: 35.3% 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 96.9%

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

   1. associate-*l/ 83.9%

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

   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 37.8%

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

Developer Target 1: 97.0% 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 2024170 
(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))