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

Percentage Accurate: 96.9% → 96.9%

Time: 8.3s

Alternatives: 17

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

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

FPCore

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

C

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

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 / ((y - z) / (y - x))
end function

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 96.2%

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

   1. *-commutative 96.2%

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

   2. associate-*r/ 82.5%

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

   3. associate-/l* 96.6%

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

   4. sub-neg 96.6%

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

   5. +-commutative 96.6%

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

   6. neg-sub0 96.6%

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

   7. associate-+l- 96.6%

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

   8. sub0-neg 96.6%

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

   9. neg-mul-1 96.6%

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

   10. associate-/r* 96.6%

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

3. Simplified 96.6%

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

4. Final simplification 96.6%

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

Alternative 2: 71.5% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{t}{1 - \frac{z}{y}}\\ \mathbf{if}\;y \leq -1.7 \cdot 10^{+112}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq -1.8 \cdot 10^{+37}:\\ \;\;\;\;t \cdot \frac{x - y}{z}\\ \mathbf{elif}\;y \leq -1.6 \cdot 10^{-102}:\\ \;\;\;\;\frac{t}{\frac{y}{y - x}}\\ \mathbf{elif}\;y \leq 1.9 \cdot 10^{-87}:\\ \;\;\;\;\left(x - y\right) \cdot \frac{t}{z}\\ \mathbf{elif}\;y \leq 9.8 \cdot 10^{+30}:\\ \;\;\;\;\frac{t \cdot x}{z - y}\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (/ t (- 1.0 (/ z y)))))
   (if (<= y -1.7e+112)
     t_1
     (if (<= y -1.8e+37)
       (* t (/ (- x y) z))
       (if (<= y -1.6e-102)
         (/ t (/ y (- y x)))
         (if (<= y 1.9e-87)
           (* (- x y) (/ t z))
           (if (<= y 9.8e+30) (/ (* t x) (- 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 <= -1.7e+112) {
		tmp = t_1;
	} else if (y <= -1.8e+37) {
		tmp = t * ((x - y) / z);
	} else if (y <= -1.6e-102) {
		tmp = t / (y / (y - x));
	} else if (y <= 1.9e-87) {
		tmp = (x - y) * (t / z);
	} else if (y <= 9.8e+30) {
		tmp = (t * x) / (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 <= (-1.7d+112)) then
        tmp = t_1
    else if (y <= (-1.8d+37)) then
        tmp = t * ((x - y) / z)
    else if (y <= (-1.6d-102)) then
        tmp = t / (y / (y - x))
    else if (y <= 1.9d-87) then
        tmp = (x - y) * (t / z)
    else if (y <= 9.8d+30) then
        tmp = (t * x) / (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 <= -1.7e+112) {
		tmp = t_1;
	} else if (y <= -1.8e+37) {
		tmp = t * ((x - y) / z);
	} else if (y <= -1.6e-102) {
		tmp = t / (y / (y - x));
	} else if (y <= 1.9e-87) {
		tmp = (x - y) * (t / z);
	} else if (y <= 9.8e+30) {
		tmp = (t * x) / (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 <= -1.7e+112:
		tmp = t_1
	elif y <= -1.8e+37:
		tmp = t * ((x - y) / z)
	elif y <= -1.6e-102:
		tmp = t / (y / (y - x))
	elif y <= 1.9e-87:
		tmp = (x - y) * (t / z)
	elif y <= 9.8e+30:
		tmp = (t * x) / (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 <= -1.7e+112)
		tmp = t_1;
	elseif (y <= -1.8e+37)
		tmp = Float64(t * Float64(Float64(x - y) / z));
	elseif (y <= -1.6e-102)
		tmp = Float64(t / Float64(y / Float64(y - x)));
	elseif (y <= 1.9e-87)
		tmp = Float64(Float64(x - y) * Float64(t / z));
	elseif (y <= 9.8e+30)
		tmp = Float64(Float64(t * x) / 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 <= -1.7e+112)
		tmp = t_1;
	elseif (y <= -1.8e+37)
		tmp = t * ((x - y) / z);
	elseif (y <= -1.6e-102)
		tmp = t / (y / (y - x));
	elseif (y <= 1.9e-87)
		tmp = (x - y) * (t / z);
	elseif (y <= 9.8e+30)
		tmp = (t * x) / (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, -1.7e+112], t$95$1, If[LessEqual[y, -1.8e+37], N[(t * N[(N[(x - y), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, -1.6e-102], N[(t / N[(y / N[(y - x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 1.9e-87], N[(N[(x - y), $MachinePrecision] * N[(t / z), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 9.8e+30], N[(N[(t * x), $MachinePrecision] / N[(z - y), $MachinePrecision]), $MachinePrecision], t$95$1]]]]]]

Derivation

1. Split input into 5 regimes

2. if y < -1.69999999999999997e112 or 9.79999999999999969e30 < y

   1. Initial program 99.9%

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

      1. *-commutative 99.9%

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

      2. associate-*r/ 71.3%

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

      3. associate-/l* 99.8%

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

      4. sub-neg 99.8%

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

      5. +-commutative 99.8%

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

      6. neg-sub0 99.8%

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

      7. associate-+l- 99.8%

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

      8. sub0-neg 99.8%

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

      9. neg-mul-1 99.8%

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

      10. associate-/r* 99.8%

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

   3. Simplified 99.8%

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

   4. Taylor expanded in x around 0 84.2%

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

      1. div-sub 84.3%

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

      2. *-inverses 84.3%

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

   6. Simplified 84.3%

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

   if -1.69999999999999997e112 < y < -1.79999999999999999e37

   1. Initial program 99.9%

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

   2. Taylor expanded in z around inf 70.0%

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

   if -1.79999999999999999e37 < y < -1.59999999999999993e-102

   1. Initial program 99.7%

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

      1. *-commutative 99.7%

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

      2. associate-*r/ 96.5%

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

      3. associate-/l* 99.8%

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

      4. sub-neg 99.8%

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

      5. +-commutative 99.8%

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

      6. neg-sub0 99.8%

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

      7. associate-+l- 99.8%

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

      8. sub0-neg 99.8%

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

      9. neg-mul-1 99.8%

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

      10. associate-/r* 99.8%

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

   3. Simplified 99.8%

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

   4. Taylor expanded in z around 0 70.1%

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

   if -1.59999999999999993e-102 < y < 1.9e-87

   1. Initial program 89.5%

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

   2. Taylor expanded in z around inf 82.9%

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

      1. associate-/l* 81.3%

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

      2. associate-/r/ 82.4%

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

   4. Simplified 82.4%

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

   if 1.9e-87 < y < 9.79999999999999969e30

   1. Initial program 99.8%

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

   2. Taylor expanded in x around inf 84.4%

      \[\leadsto \color{blue}{\frac{t \cdot x}{z - y}} \]
3. Recombined 5 regimes into one program.

4. Final simplification 81.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.7 \cdot 10^{+112}:\\ \;\;\;\;\frac{t}{1 - \frac{z}{y}}\\ \mathbf{elif}\;y \leq -1.8 \cdot 10^{+37}:\\ \;\;\;\;t \cdot \frac{x - y}{z}\\ \mathbf{elif}\;y \leq -1.6 \cdot 10^{-102}:\\ \;\;\;\;\frac{t}{\frac{y}{y - x}}\\ \mathbf{elif}\;y \leq 1.9 \cdot 10^{-87}:\\ \;\;\;\;\left(x - y\right) \cdot \frac{t}{z}\\ \mathbf{elif}\;y \leq 9.8 \cdot 10^{+30}:\\ \;\;\;\;\frac{t \cdot x}{z - y}\\ \mathbf{else}:\\ \;\;\;\;\frac{t}{1 - \frac{z}{y}}\\ \end{array} \]

Alternative 3: 59.6% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -2.2 \cdot 10^{+94}:\\ \;\;\;\;t\\ \mathbf{elif}\;y \leq -1.75 \cdot 10^{+45}:\\ \;\;\;\;t \cdot \frac{x}{z}\\ \mathbf{elif}\;y \leq -7.5 \cdot 10^{+22}:\\ \;\;\;\;\frac{t \cdot \left(-y\right)}{z}\\ \mathbf{elif}\;y \leq -2.6 \cdot 10^{-100}:\\ \;\;\;\;x \cdot \frac{-t}{y}\\ \mathbf{elif}\;y \leq 2.75 \cdot 10^{+31}:\\ \;\;\;\;\frac{t}{\frac{z}{x}}\\ \mathbf{else}:\\ \;\;\;\;t\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= y -2.2e+94)
   t
   (if (<= y -1.75e+45)
     (* t (/ x z))
     (if (<= y -7.5e+22)
       (/ (* t (- y)) z)
       (if (<= y -2.6e-100)
         (* x (/ (- t) y))
         (if (<= y 2.75e+31) (/ t (/ z x)) t))))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (y <= -2.2e+94) {
		tmp = t;
	} else if (y <= -1.75e+45) {
		tmp = t * (x / z);
	} else if (y <= -7.5e+22) {
		tmp = (t * -y) / z;
	} else if (y <= -2.6e-100) {
		tmp = x * (-t / y);
	} else if (y <= 2.75e+31) {
		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 <= (-2.2d+94)) then
        tmp = t
    else if (y <= (-1.75d+45)) then
        tmp = t * (x / z)
    else if (y <= (-7.5d+22)) then
        tmp = (t * -y) / z
    else if (y <= (-2.6d-100)) then
        tmp = x * (-t / y)
    else if (y <= 2.75d+31) 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 <= -2.2e+94) {
		tmp = t;
	} else if (y <= -1.75e+45) {
		tmp = t * (x / z);
	} else if (y <= -7.5e+22) {
		tmp = (t * -y) / z;
	} else if (y <= -2.6e-100) {
		tmp = x * (-t / y);
	} else if (y <= 2.75e+31) {
		tmp = t / (z / x);
	} else {
		tmp = t;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if y <= -2.2e+94:
		tmp = t
	elif y <= -1.75e+45:
		tmp = t * (x / z)
	elif y <= -7.5e+22:
		tmp = (t * -y) / z
	elif y <= -2.6e-100:
		tmp = x * (-t / y)
	elif y <= 2.75e+31:
		tmp = t / (z / x)
	else:
		tmp = t
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (y <= -2.2e+94)
		tmp = t;
	elseif (y <= -1.75e+45)
		tmp = Float64(t * Float64(x / z));
	elseif (y <= -7.5e+22)
		tmp = Float64(Float64(t * Float64(-y)) / z);
	elseif (y <= -2.6e-100)
		tmp = Float64(x * Float64(Float64(-t) / y));
	elseif (y <= 2.75e+31)
		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 <= -2.2e+94)
		tmp = t;
	elseif (y <= -1.75e+45)
		tmp = t * (x / z);
	elseif (y <= -7.5e+22)
		tmp = (t * -y) / z;
	elseif (y <= -2.6e-100)
		tmp = x * (-t / y);
	elseif (y <= 2.75e+31)
		tmp = t / (z / x);
	else
		tmp = t;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[y, -2.2e+94], t, If[LessEqual[y, -1.75e+45], N[(t * N[(x / z), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, -7.5e+22], N[(N[(t * (-y)), $MachinePrecision] / z), $MachinePrecision], If[LessEqual[y, -2.6e-100], N[(x * N[((-t) / y), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 2.75e+31], N[(t / N[(z / x), $MachinePrecision]), $MachinePrecision], t]]]]]

Derivation

1. Split input into 5 regimes

2. if y < -2.20000000000000012e94 or 2.75000000000000001e31 < y

   1. Initial program 99.9%

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

   2. Taylor expanded in y around inf 72.1%

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

   if -2.20000000000000012e94 < y < -1.75000000000000011e45

   1. Initial program 99.8%

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

   2. Taylor expanded in y around 0 67.2%

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

   if -1.75000000000000011e45 < y < -7.5000000000000002e22

   1. Initial program 99.7%

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

      1. *-commutative 99.7%

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

      2. associate-*r/ 99.4%

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

      3. associate-/l* 99.7%

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

      4. sub-neg 99.7%

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

      5. +-commutative 99.7%

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

      6. neg-sub0 99.7%

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

      7. associate-+l- 99.7%

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

      8. sub0-neg 99.7%

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

      9. neg-mul-1 99.7%

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

      10. associate-/r* 99.7%

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

   3. Simplified 99.7%

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

   4. Taylor expanded in x around 0 80.9%

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

      1. div-sub 80.9%

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

      2. *-inverses 80.9%

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

   6. Simplified 80.9%

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

   7. Taylor expanded in z around inf 61.5%

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

      1. mul-1-neg 61.5%

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

      2. associate-/l* 61.2%

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

      3. associate-/r/ 61.2%

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

   9. Simplified 61.2%

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

   10. Taylor expanded in y around 0 61.5%

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

   if -7.5000000000000002e22 < y < -2.5999999999999998e-100

   1. Initial program 99.8%

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

      1. *-commutative 99.8%

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

      2. associate-*r/ 96.0%

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

      3. associate-/l* 99.9%

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

      4. sub-neg 99.9%

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

      5. +-commutative 99.9%

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

      6. neg-sub0 99.9%

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

      7. associate-+l- 99.9%

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

      8. sub0-neg 99.9%

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

      9. neg-mul-1 99.9%

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

      10. associate-/r* 99.9%

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

   3. Simplified 99.9%

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

   4. Taylor expanded in z around 0 72.9%

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

   5. Taylor expanded in y around 0 52.0%

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

      1. *-commutative 52.0%

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

      2. associate-*r/ 55.6%

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

      3. neg-mul-1 55.6%

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

      4. distribute-rgt-neg-in 55.6%

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

   7. Simplified 55.6%

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

   if -2.5999999999999998e-100 < y < 2.75000000000000001e31

   1. Initial program 91.3%

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

      1. *-commutative 91.3%

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

      2. associate-*r/ 90.1%

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

      3. associate-/l* 92.3%

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

      4. sub-neg 92.3%

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

      5. +-commutative 92.3%

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

      6. neg-sub0 92.3%

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

      7. associate-+l- 92.3%

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

      8. sub0-neg 92.3%

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

      9. neg-mul-1 92.3%

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

      10. associate-/r* 92.3%

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

   3. Simplified 92.3%

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

   4. Taylor expanded in y around 0 70.7%

      \[\leadsto \frac{t}{\color{blue}{\frac{z}{x}}} \]
3. Recombined 5 regimes into one program.

4. Final simplification 69.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -2.2 \cdot 10^{+94}:\\ \;\;\;\;t\\ \mathbf{elif}\;y \leq -1.75 \cdot 10^{+45}:\\ \;\;\;\;t \cdot \frac{x}{z}\\ \mathbf{elif}\;y \leq -7.5 \cdot 10^{+22}:\\ \;\;\;\;\frac{t \cdot \left(-y\right)}{z}\\ \mathbf{elif}\;y \leq -2.6 \cdot 10^{-100}:\\ \;\;\;\;x \cdot \frac{-t}{y}\\ \mathbf{elif}\;y \leq 2.75 \cdot 10^{+31}:\\ \;\;\;\;\frac{t}{\frac{z}{x}}\\ \mathbf{else}:\\ \;\;\;\;t\\ \end{array} \]

Alternative 4: 71.5% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -8.6 \cdot 10^{+111} \lor \neg \left(y \leq -3.4 \cdot 10^{+33}\right) \land \left(y \leq -2.4 \cdot 10^{-100} \lor \neg \left(y \leq 78\right)\right):\\ \;\;\;\;t \cdot \frac{y - x}{y}\\ \mathbf{else}:\\ \;\;\;\;t \cdot \frac{x - y}{z}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= y -8.6e+111)
         (and (not (<= y -3.4e+33)) (or (<= y -2.4e-100) (not (<= y 78.0)))))
   (* t (/ (- y x) y))
   (* t (/ (- x y) z))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((y <= -8.6e+111) || (!(y <= -3.4e+33) && ((y <= -2.4e-100) || !(y <= 78.0)))) {
		tmp = t * ((y - x) / y);
	} else {
		tmp = t * ((x - y) / z);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if ((y <= (-8.6d+111)) .or. (.not. (y <= (-3.4d+33))) .and. (y <= (-2.4d-100)) .or. (.not. (y <= 78.0d0))) then
        tmp = t * ((y - x) / y)
    else
        tmp = t * ((x - y) / z)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if ((y <= -8.6e+111) || (!(y <= -3.4e+33) && ((y <= -2.4e-100) || !(y <= 78.0)))) {
		tmp = t * ((y - x) / y);
	} else {
		tmp = t * ((x - y) / z);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (y <= -8.6e+111) or (not (y <= -3.4e+33) and ((y <= -2.4e-100) or not (y <= 78.0))):
		tmp = t * ((y - x) / y)
	else:
		tmp = t * ((x - y) / z)
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((y <= -8.6e+111) || (!(y <= -3.4e+33) && ((y <= -2.4e-100) || !(y <= 78.0))))
		tmp = Float64(t * Float64(Float64(y - x) / y));
	else
		tmp = Float64(t * Float64(Float64(x - y) / z));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((y <= -8.6e+111) || (~((y <= -3.4e+33)) && ((y <= -2.4e-100) || ~((y <= 78.0)))))
		tmp = t * ((y - x) / y);
	else
		tmp = t * ((x - y) / z);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[y, -8.6e+111], And[N[Not[LessEqual[y, -3.4e+33]], $MachinePrecision], Or[LessEqual[y, -2.4e-100], N[Not[LessEqual[y, 78.0]], $MachinePrecision]]]], N[(t * N[(N[(y - x), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision], N[(t * N[(N[(x - y), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -8.59999999999999987e111 or -3.3999999999999999e33 < y < -2.4000000000000003e-100 or 78 < y

   1. Initial program 99.9%

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

   2. Taylor expanded in z around 0 78.4%

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

      1. associate-*r/ 78.4%

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

      2. neg-mul-1 78.4%

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

      3. neg-sub0 78.4%

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

      4. associate--r- 78.4%

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

      5. neg-sub0 78.4%

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

      6. +-commutative 78.4%

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

      7. sub-neg 78.4%

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

   4. Simplified 78.4%

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

   if -8.59999999999999987e111 < y < -3.3999999999999999e33 or -2.4000000000000003e-100 < y < 78

   1. Initial program 92.0%

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

   2. Taylor expanded in z around inf 79.0%

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

4. Final simplification 78.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -8.6 \cdot 10^{+111} \lor \neg \left(y \leq -3.4 \cdot 10^{+33}\right) \land \left(y \leq -2.4 \cdot 10^{-100} \lor \neg \left(y \leq 78\right)\right):\\ \;\;\;\;t \cdot \frac{y - x}{y}\\ \mathbf{else}:\\ \;\;\;\;t \cdot \frac{x - y}{z}\\ \end{array} \]

Alternative 5: 65.1% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(x - y\right) \cdot \frac{t}{z}\\ \mathbf{if}\;y \leq -8 \cdot 10^{+100}:\\ \;\;\;\;t\\ \mathbf{elif}\;y \leq -2.55 \cdot 10^{+22}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq -9.5 \cdot 10^{-59}:\\ \;\;\;\;x \cdot \frac{-t}{y}\\ \mathbf{elif}\;y \leq 1.6 \cdot 10^{+31}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (* (- x y) (/ t z))))
   (if (<= y -8e+100)
     t
     (if (<= y -2.55e+22)
       t_1
       (if (<= y -9.5e-59) (* x (/ (- t) y)) (if (<= y 1.6e+31) t_1 t))))))

C

double code(double x, double y, double z, double t) {
	double t_1 = (x - y) * (t / z);
	double tmp;
	if (y <= -8e+100) {
		tmp = t;
	} else if (y <= -2.55e+22) {
		tmp = t_1;
	} else if (y <= -9.5e-59) {
		tmp = x * (-t / y);
	} else if (y <= 1.6e+31) {
		tmp = t_1;
	} else {
		tmp = t;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: t_1
    real(8) :: tmp
    t_1 = (x - y) * (t / z)
    if (y <= (-8d+100)) then
        tmp = t
    else if (y <= (-2.55d+22)) then
        tmp = t_1
    else if (y <= (-9.5d-59)) then
        tmp = x * (-t / y)
    else if (y <= 1.6d+31) then
        tmp = t_1
    else
        tmp = t
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double t_1 = (x - y) * (t / z);
	double tmp;
	if (y <= -8e+100) {
		tmp = t;
	} else if (y <= -2.55e+22) {
		tmp = t_1;
	} else if (y <= -9.5e-59) {
		tmp = x * (-t / y);
	} else if (y <= 1.6e+31) {
		tmp = t_1;
	} else {
		tmp = t;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = (x - y) * (t / z)
	tmp = 0
	if y <= -8e+100:
		tmp = t
	elif y <= -2.55e+22:
		tmp = t_1
	elif y <= -9.5e-59:
		tmp = x * (-t / y)
	elif y <= 1.6e+31:
		tmp = t_1
	else:
		tmp = t
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(Float64(x - y) * Float64(t / z))
	tmp = 0.0
	if (y <= -8e+100)
		tmp = t;
	elseif (y <= -2.55e+22)
		tmp = t_1;
	elseif (y <= -9.5e-59)
		tmp = Float64(x * Float64(Float64(-t) / y));
	elseif (y <= 1.6e+31)
		tmp = t_1;
	else
		tmp = t;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = (x - y) * (t / z);
	tmp = 0.0;
	if (y <= -8e+100)
		tmp = t;
	elseif (y <= -2.55e+22)
		tmp = t_1;
	elseif (y <= -9.5e-59)
		tmp = x * (-t / y);
	elseif (y <= 1.6e+31)
		tmp = t_1;
	else
		tmp = t;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(N[(x - y), $MachinePrecision] * N[(t / z), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -8e+100], t, If[LessEqual[y, -2.55e+22], t$95$1, If[LessEqual[y, -9.5e-59], N[(x * N[((-t) / y), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 1.6e+31], t$95$1, t]]]]]

Derivation

1. Split input into 3 regimes

2. if y < -8.00000000000000013e100 or 1.6e31 < y

   1. Initial program 99.9%

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

   2. Taylor expanded in y around inf 72.1%

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

   if -8.00000000000000013e100 < y < -2.5500000000000001e22 or -9.4999999999999994e-59 < y < 1.6e31

   1. Initial program 92.6%

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

   2. Taylor expanded in z around inf 75.9%

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

      1. associate-/l* 76.9%

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

      2. associate-/r/ 74.9%

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

   4. Simplified 74.9%

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

   if -2.5500000000000001e22 < y < -9.4999999999999994e-59

   1. Initial program 99.7%

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

      1. *-commutative 99.7%

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

      2. associate-*r/ 95.2%

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

      3. associate-/l* 99.9%

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

      4. sub-neg 99.9%

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

      5. +-commutative 99.9%

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

      6. neg-sub0 99.9%

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

      7. associate-+l- 99.9%

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

      8. sub0-neg 99.9%

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

      9. neg-mul-1 99.9%

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

      10. associate-/r* 99.9%

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

   3. Simplified 99.9%

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

   4. Taylor expanded in z around 0 75.7%

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

   5. Taylor expanded in y around 0 57.8%

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

      1. *-commutative 57.8%

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

      2. associate-*r/ 62.3%

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

      3. neg-mul-1 62.3%

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

      4. distribute-rgt-neg-in 62.3%

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

   7. Simplified 62.3%

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

4. Final simplification 72.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -8 \cdot 10^{+100}:\\ \;\;\;\;t\\ \mathbf{elif}\;y \leq -2.55 \cdot 10^{+22}:\\ \;\;\;\;\left(x - y\right) \cdot \frac{t}{z}\\ \mathbf{elif}\;y \leq -9.5 \cdot 10^{-59}:\\ \;\;\;\;x \cdot \frac{-t}{y}\\ \mathbf{elif}\;y \leq 1.6 \cdot 10^{+31}:\\ \;\;\;\;\left(x - y\right) \cdot \frac{t}{z}\\ \mathbf{else}:\\ \;\;\;\;t\\ \end{array} \]

Alternative 6: 66.0% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := t \cdot \frac{x - y}{z}\\ \mathbf{if}\;y \leq -4 \cdot 10^{+94}:\\ \;\;\;\;t\\ \mathbf{elif}\;y \leq -2.75 \cdot 10^{+23}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq -9.5 \cdot 10^{-59}:\\ \;\;\;\;x \cdot \frac{-t}{y}\\ \mathbf{elif}\;y \leq 2.6 \cdot 10^{+30}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (* t (/ (- x y) z))))
   (if (<= y -4e+94)
     t
     (if (<= y -2.75e+23)
       t_1
       (if (<= y -9.5e-59) (* x (/ (- t) y)) (if (<= y 2.6e+30) t_1 t))))))

C

double code(double x, double y, double z, double t) {
	double t_1 = t * ((x - y) / z);
	double tmp;
	if (y <= -4e+94) {
		tmp = t;
	} else if (y <= -2.75e+23) {
		tmp = t_1;
	} else if (y <= -9.5e-59) {
		tmp = x * (-t / y);
	} else if (y <= 2.6e+30) {
		tmp = t_1;
	} else {
		tmp = t;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: t_1
    real(8) :: tmp
    t_1 = t * ((x - y) / z)
    if (y <= (-4d+94)) then
        tmp = t
    else if (y <= (-2.75d+23)) then
        tmp = t_1
    else if (y <= (-9.5d-59)) then
        tmp = x * (-t / y)
    else if (y <= 2.6d+30) then
        tmp = t_1
    else
        tmp = t
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double t_1 = t * ((x - y) / z);
	double tmp;
	if (y <= -4e+94) {
		tmp = t;
	} else if (y <= -2.75e+23) {
		tmp = t_1;
	} else if (y <= -9.5e-59) {
		tmp = x * (-t / y);
	} else if (y <= 2.6e+30) {
		tmp = t_1;
	} else {
		tmp = t;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = t * ((x - y) / z)
	tmp = 0
	if y <= -4e+94:
		tmp = t
	elif y <= -2.75e+23:
		tmp = t_1
	elif y <= -9.5e-59:
		tmp = x * (-t / y)
	elif y <= 2.6e+30:
		tmp = t_1
	else:
		tmp = t
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(t * Float64(Float64(x - y) / z))
	tmp = 0.0
	if (y <= -4e+94)
		tmp = t;
	elseif (y <= -2.75e+23)
		tmp = t_1;
	elseif (y <= -9.5e-59)
		tmp = Float64(x * Float64(Float64(-t) / y));
	elseif (y <= 2.6e+30)
		tmp = t_1;
	else
		tmp = t;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = t * ((x - y) / z);
	tmp = 0.0;
	if (y <= -4e+94)
		tmp = t;
	elseif (y <= -2.75e+23)
		tmp = t_1;
	elseif (y <= -9.5e-59)
		tmp = x * (-t / y);
	elseif (y <= 2.6e+30)
		tmp = t_1;
	else
		tmp = t;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(t * N[(N[(x - y), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -4e+94], t, If[LessEqual[y, -2.75e+23], t$95$1, If[LessEqual[y, -9.5e-59], N[(x * N[((-t) / y), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 2.6e+30], t$95$1, t]]]]]

Derivation

1. Split input into 3 regimes

2. if y < -4.0000000000000001e94 or 2.59999999999999988e30 < y

   1. Initial program 99.9%

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

   2. Taylor expanded in y around inf 72.1%

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

   if -4.0000000000000001e94 < y < -2.75000000000000002e23 or -9.4999999999999994e-59 < y < 2.59999999999999988e30

   1. Initial program 92.6%

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

   2. Taylor expanded in z around inf 76.1%

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

   if -2.75000000000000002e23 < y < -9.4999999999999994e-59

   1. Initial program 99.7%

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

      1. *-commutative 99.7%

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

      2. associate-*r/ 95.2%

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

      3. associate-/l* 99.9%

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

      4. sub-neg 99.9%

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

      5. +-commutative 99.9%

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

      6. neg-sub0 99.9%

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

      7. associate-+l- 99.9%

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

      8. sub0-neg 99.9%

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

      9. neg-mul-1 99.9%

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

      10. associate-/r* 99.9%

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

   3. Simplified 99.9%

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

   4. Taylor expanded in z around 0 75.7%

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

   5. Taylor expanded in y around 0 57.8%

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

      1. *-commutative 57.8%

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

      2. associate-*r/ 62.3%

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

      3. neg-mul-1 62.3%

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

      4. distribute-rgt-neg-in 62.3%

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

   7. Simplified 62.3%

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

4. Final simplification 73.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -4 \cdot 10^{+94}:\\ \;\;\;\;t\\ \mathbf{elif}\;y \leq -2.75 \cdot 10^{+23}:\\ \;\;\;\;t \cdot \frac{x - y}{z}\\ \mathbf{elif}\;y \leq -9.5 \cdot 10^{-59}:\\ \;\;\;\;x \cdot \frac{-t}{y}\\ \mathbf{elif}\;y \leq 2.6 \cdot 10^{+30}:\\ \;\;\;\;t \cdot \frac{x - y}{z}\\ \mathbf{else}:\\ \;\;\;\;t\\ \end{array} \]

Alternative 7: 72.1% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := t \cdot \frac{x - y}{z}\\ t_2 := \frac{t}{1 - \frac{z}{y}}\\ \mathbf{if}\;y \leq -1.7 \cdot 10^{+112}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;y \leq -1.35 \cdot 10^{+42}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq -2.6 \cdot 10^{-100}:\\ \;\;\;\;t \cdot \frac{y - x}{y}\\ \mathbf{elif}\;y \leq 7 \cdot 10^{+28}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (* t (/ (- x y) z))) (t_2 (/ t (- 1.0 (/ z y)))))
   (if (<= y -1.7e+112)
     t_2
     (if (<= y -1.35e+42)
       t_1
       (if (<= y -2.6e-100) (* t (/ (- y x) y)) (if (<= y 7e+28) t_1 t_2))))))

C

double code(double x, double y, double z, double t) {
	double t_1 = t * ((x - y) / z);
	double t_2 = t / (1.0 - (z / y));
	double tmp;
	if (y <= -1.7e+112) {
		tmp = t_2;
	} else if (y <= -1.35e+42) {
		tmp = t_1;
	} else if (y <= -2.6e-100) {
		tmp = t * ((y - x) / y);
	} else if (y <= 7e+28) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	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) :: t_2
    real(8) :: tmp
    t_1 = t * ((x - y) / z)
    t_2 = t / (1.0d0 - (z / y))
    if (y <= (-1.7d+112)) then
        tmp = t_2
    else if (y <= (-1.35d+42)) then
        tmp = t_1
    else if (y <= (-2.6d-100)) then
        tmp = t * ((y - x) / y)
    else if (y <= 7d+28) then
        tmp = t_1
    else
        tmp = t_2
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double t_1 = t * ((x - y) / z);
	double t_2 = t / (1.0 - (z / y));
	double tmp;
	if (y <= -1.7e+112) {
		tmp = t_2;
	} else if (y <= -1.35e+42) {
		tmp = t_1;
	} else if (y <= -2.6e-100) {
		tmp = t * ((y - x) / y);
	} else if (y <= 7e+28) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = t * ((x - y) / z)
	t_2 = t / (1.0 - (z / y))
	tmp = 0
	if y <= -1.7e+112:
		tmp = t_2
	elif y <= -1.35e+42:
		tmp = t_1
	elif y <= -2.6e-100:
		tmp = t * ((y - x) / y)
	elif y <= 7e+28:
		tmp = t_1
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(t * Float64(Float64(x - y) / z))
	t_2 = Float64(t / Float64(1.0 - Float64(z / y)))
	tmp = 0.0
	if (y <= -1.7e+112)
		tmp = t_2;
	elseif (y <= -1.35e+42)
		tmp = t_1;
	elseif (y <= -2.6e-100)
		tmp = Float64(t * Float64(Float64(y - x) / y));
	elseif (y <= 7e+28)
		tmp = t_1;
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = t * ((x - y) / z);
	t_2 = t / (1.0 - (z / y));
	tmp = 0.0;
	if (y <= -1.7e+112)
		tmp = t_2;
	elseif (y <= -1.35e+42)
		tmp = t_1;
	elseif (y <= -2.6e-100)
		tmp = t * ((y - x) / y);
	elseif (y <= 7e+28)
		tmp = t_1;
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(t * N[(N[(x - y), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(t / N[(1.0 - N[(z / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -1.7e+112], t$95$2, If[LessEqual[y, -1.35e+42], t$95$1, If[LessEqual[y, -2.6e-100], N[(t * N[(N[(y - x), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 7e+28], t$95$1, t$95$2]]]]]]

Derivation

1. Split input into 3 regimes

2. if y < -1.69999999999999997e112 or 6.9999999999999999e28 < y

   1. Initial program 99.9%

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

      1. *-commutative 99.9%

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

      2. associate-*r/ 71.3%

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

      3. associate-/l* 99.8%

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

      4. sub-neg 99.8%

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

      5. +-commutative 99.8%

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

      6. neg-sub0 99.8%

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

      7. associate-+l- 99.8%

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

      8. sub0-neg 99.8%

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

      9. neg-mul-1 99.8%

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

      10. associate-/r* 99.8%

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

   3. Simplified 99.8%

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

   4. Taylor expanded in x around 0 84.2%

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

      1. div-sub 84.3%

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

      2. *-inverses 84.3%

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

   6. Simplified 84.3%

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

   if -1.69999999999999997e112 < y < -1.35e42 or -2.5999999999999998e-100 < y < 6.9999999999999999e28

   1. Initial program 92.2%

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

   2. Taylor expanded in z around inf 77.3%

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

   if -1.35e42 < y < -2.5999999999999998e-100

   1. Initial program 99.7%

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

   2. Taylor expanded in z around 0 70.1%

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

      1. associate-*r/ 70.1%

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

      2. neg-mul-1 70.1%

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

      3. neg-sub0 70.1%

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

      4. associate--r- 70.1%

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

      5. neg-sub0 70.1%

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

      6. +-commutative 70.1%

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

      7. sub-neg 70.1%

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

   4. Simplified 70.1%

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

4. Final simplification 79.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.7 \cdot 10^{+112}:\\ \;\;\;\;\frac{t}{1 - \frac{z}{y}}\\ \mathbf{elif}\;y \leq -1.35 \cdot 10^{+42}:\\ \;\;\;\;t \cdot \frac{x - y}{z}\\ \mathbf{elif}\;y \leq -2.6 \cdot 10^{-100}:\\ \;\;\;\;t \cdot \frac{y - x}{y}\\ \mathbf{elif}\;y \leq 7 \cdot 10^{+28}:\\ \;\;\;\;t \cdot \frac{x - y}{z}\\ \mathbf{else}:\\ \;\;\;\;\frac{t}{1 - \frac{z}{y}}\\ \end{array} \]

Alternative 8: 72.0% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := t \cdot \frac{x - y}{z}\\ t_2 := \frac{t}{1 - \frac{z}{y}}\\ \mathbf{if}\;y \leq -1.7 \cdot 10^{+112}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;y \leq -2.45 \cdot 10^{+39}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq -2.5 \cdot 10^{-100}:\\ \;\;\;\;\frac{t}{\frac{y}{y - x}}\\ \mathbf{elif}\;y \leq 1.3 \cdot 10^{+30}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (* t (/ (- x y) z))) (t_2 (/ t (- 1.0 (/ z y)))))
   (if (<= y -1.7e+112)
     t_2
     (if (<= y -2.45e+39)
       t_1
       (if (<= y -2.5e-100)
         (/ t (/ y (- y x)))
         (if (<= y 1.3e+30) t_1 t_2))))))

C

double code(double x, double y, double z, double t) {
	double t_1 = t * ((x - y) / z);
	double t_2 = t / (1.0 - (z / y));
	double tmp;
	if (y <= -1.7e+112) {
		tmp = t_2;
	} else if (y <= -2.45e+39) {
		tmp = t_1;
	} else if (y <= -2.5e-100) {
		tmp = t / (y / (y - x));
	} else if (y <= 1.3e+30) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	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) :: t_2
    real(8) :: tmp
    t_1 = t * ((x - y) / z)
    t_2 = t / (1.0d0 - (z / y))
    if (y <= (-1.7d+112)) then
        tmp = t_2
    else if (y <= (-2.45d+39)) then
        tmp = t_1
    else if (y <= (-2.5d-100)) then
        tmp = t / (y / (y - x))
    else if (y <= 1.3d+30) then
        tmp = t_1
    else
        tmp = t_2
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double t_1 = t * ((x - y) / z);
	double t_2 = t / (1.0 - (z / y));
	double tmp;
	if (y <= -1.7e+112) {
		tmp = t_2;
	} else if (y <= -2.45e+39) {
		tmp = t_1;
	} else if (y <= -2.5e-100) {
		tmp = t / (y / (y - x));
	} else if (y <= 1.3e+30) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = t * ((x - y) / z)
	t_2 = t / (1.0 - (z / y))
	tmp = 0
	if y <= -1.7e+112:
		tmp = t_2
	elif y <= -2.45e+39:
		tmp = t_1
	elif y <= -2.5e-100:
		tmp = t / (y / (y - x))
	elif y <= 1.3e+30:
		tmp = t_1
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(t * Float64(Float64(x - y) / z))
	t_2 = Float64(t / Float64(1.0 - Float64(z / y)))
	tmp = 0.0
	if (y <= -1.7e+112)
		tmp = t_2;
	elseif (y <= -2.45e+39)
		tmp = t_1;
	elseif (y <= -2.5e-100)
		tmp = Float64(t / Float64(y / Float64(y - x)));
	elseif (y <= 1.3e+30)
		tmp = t_1;
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = t * ((x - y) / z);
	t_2 = t / (1.0 - (z / y));
	tmp = 0.0;
	if (y <= -1.7e+112)
		tmp = t_2;
	elseif (y <= -2.45e+39)
		tmp = t_1;
	elseif (y <= -2.5e-100)
		tmp = t / (y / (y - x));
	elseif (y <= 1.3e+30)
		tmp = t_1;
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(t * N[(N[(x - y), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(t / N[(1.0 - N[(z / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -1.7e+112], t$95$2, If[LessEqual[y, -2.45e+39], t$95$1, If[LessEqual[y, -2.5e-100], N[(t / N[(y / N[(y - x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 1.3e+30], t$95$1, t$95$2]]]]]]

Derivation

1. Split input into 3 regimes

2. if y < -1.69999999999999997e112 or 1.29999999999999994e30 < y

   1. Initial program 99.9%

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

      1. *-commutative 99.9%

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

      2. associate-*r/ 71.3%

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

      3. associate-/l* 99.8%

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

      4. sub-neg 99.8%

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

      5. +-commutative 99.8%

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

      6. neg-sub0 99.8%

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

      7. associate-+l- 99.8%

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

      8. sub0-neg 99.8%

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

      9. neg-mul-1 99.8%

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

      10. associate-/r* 99.8%

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

   3. Simplified 99.8%

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

   4. Taylor expanded in x around 0 84.2%

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

      1. div-sub 84.3%

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

      2. *-inverses 84.3%

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

   6. Simplified 84.3%

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

   if -1.69999999999999997e112 < y < -2.44999999999999994e39 or -2.5e-100 < y < 1.29999999999999994e30

   1. Initial program 92.2%

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

   2. Taylor expanded in z around inf 77.3%

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

   if -2.44999999999999994e39 < y < -2.5e-100

   1. Initial program 99.7%

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

      1. *-commutative 99.7%

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

      2. associate-*r/ 96.5%

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

      3. associate-/l* 99.8%

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

      4. sub-neg 99.8%

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

      5. +-commutative 99.8%

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

      6. neg-sub0 99.8%

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

      7. associate-+l- 99.8%

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

      8. sub0-neg 99.8%

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

      9. neg-mul-1 99.8%

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

      10. associate-/r* 99.8%

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

   3. Simplified 99.8%

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

   4. Taylor expanded in z around 0 70.1%

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

4. Final simplification 79.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.7 \cdot 10^{+112}:\\ \;\;\;\;\frac{t}{1 - \frac{z}{y}}\\ \mathbf{elif}\;y \leq -2.45 \cdot 10^{+39}:\\ \;\;\;\;t \cdot \frac{x - y}{z}\\ \mathbf{elif}\;y \leq -2.5 \cdot 10^{-100}:\\ \;\;\;\;\frac{t}{\frac{y}{y - x}}\\ \mathbf{elif}\;y \leq 1.3 \cdot 10^{+30}:\\ \;\;\;\;t \cdot \frac{x - y}{z}\\ \mathbf{else}:\\ \;\;\;\;\frac{t}{1 - \frac{z}{y}}\\ \end{array} \]

Alternative 9: 71.5% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{t}{1 - \frac{z}{y}}\\ \mathbf{if}\;y \leq -1.7 \cdot 10^{+112}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq -1 \cdot 10^{+39}:\\ \;\;\;\;t \cdot \frac{x - y}{z}\\ \mathbf{elif}\;y \leq -2.6 \cdot 10^{-100}:\\ \;\;\;\;\frac{t}{\frac{y}{y - x}}\\ \mathbf{elif}\;y \leq 3 \cdot 10^{+28}:\\ \;\;\;\;\frac{t \cdot \left(x - y\right)}{z}\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (/ t (- 1.0 (/ z y)))))
   (if (<= y -1.7e+112)
     t_1
     (if (<= y -1e+39)
       (* t (/ (- x y) z))
       (if (<= y -2.6e-100)
         (/ t (/ y (- y x)))
         (if (<= y 3e+28) (/ (* t (- x y)) z) 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 <= -1.7e+112) {
		tmp = t_1;
	} else if (y <= -1e+39) {
		tmp = t * ((x - y) / z);
	} else if (y <= -2.6e-100) {
		tmp = t / (y / (y - x));
	} else if (y <= 3e+28) {
		tmp = (t * (x - y)) / z;
	} 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 <= (-1.7d+112)) then
        tmp = t_1
    else if (y <= (-1d+39)) then
        tmp = t * ((x - y) / z)
    else if (y <= (-2.6d-100)) then
        tmp = t / (y / (y - x))
    else if (y <= 3d+28) then
        tmp = (t * (x - y)) / z
    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 <= -1.7e+112) {
		tmp = t_1;
	} else if (y <= -1e+39) {
		tmp = t * ((x - y) / z);
	} else if (y <= -2.6e-100) {
		tmp = t / (y / (y - x));
	} else if (y <= 3e+28) {
		tmp = (t * (x - y)) / z;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = t / (1.0 - (z / y))
	tmp = 0
	if y <= -1.7e+112:
		tmp = t_1
	elif y <= -1e+39:
		tmp = t * ((x - y) / z)
	elif y <= -2.6e-100:
		tmp = t / (y / (y - x))
	elif y <= 3e+28:
		tmp = (t * (x - y)) / z
	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 <= -1.7e+112)
		tmp = t_1;
	elseif (y <= -1e+39)
		tmp = Float64(t * Float64(Float64(x - y) / z));
	elseif (y <= -2.6e-100)
		tmp = Float64(t / Float64(y / Float64(y - x)));
	elseif (y <= 3e+28)
		tmp = Float64(Float64(t * Float64(x - y)) / z);
	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 <= -1.7e+112)
		tmp = t_1;
	elseif (y <= -1e+39)
		tmp = t * ((x - y) / z);
	elseif (y <= -2.6e-100)
		tmp = t / (y / (y - x));
	elseif (y <= 3e+28)
		tmp = (t * (x - y)) / z;
	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, -1.7e+112], t$95$1, If[LessEqual[y, -1e+39], N[(t * N[(N[(x - y), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, -2.6e-100], N[(t / N[(y / N[(y - x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 3e+28], N[(N[(t * N[(x - y), $MachinePrecision]), $MachinePrecision] / z), $MachinePrecision], t$95$1]]]]]

Derivation

1. Split input into 4 regimes

2. if y < -1.69999999999999997e112 or 3.0000000000000001e28 < y

   1. Initial program 99.9%

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

      1. *-commutative 99.9%

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

      2. associate-*r/ 71.3%

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

      3. associate-/l* 99.8%

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

      4. sub-neg 99.8%

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

      5. +-commutative 99.8%

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

      6. neg-sub0 99.8%

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

      7. associate-+l- 99.8%

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

      8. sub0-neg 99.8%

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

      9. neg-mul-1 99.8%

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

      10. associate-/r* 99.8%

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

   3. Simplified 99.8%

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

   4. Taylor expanded in x around 0 84.2%

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

      1. div-sub 84.3%

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

      2. *-inverses 84.3%

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

   6. Simplified 84.3%

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

   if -1.69999999999999997e112 < y < -9.9999999999999994e38

   1. Initial program 99.9%

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

   2. Taylor expanded in z around inf 70.0%

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

   if -9.9999999999999994e38 < y < -2.5999999999999998e-100

   1. Initial program 99.7%

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

      1. *-commutative 99.7%

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

      2. associate-*r/ 96.5%

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

      3. associate-/l* 99.8%

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

      4. sub-neg 99.8%

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

      5. +-commutative 99.8%

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

      6. neg-sub0 99.8%

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

      7. associate-+l- 99.8%

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

      8. sub0-neg 99.8%

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

      9. neg-mul-1 99.8%

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

      10. associate-/r* 99.8%

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

   3. Simplified 99.8%

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

   4. Taylor expanded in z around 0 70.1%

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

   if -2.5999999999999998e-100 < y < 3.0000000000000001e28

   1. Initial program 91.3%

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

   2. Taylor expanded in z around inf 79.6%

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

4. Final simplification 80.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.7 \cdot 10^{+112}:\\ \;\;\;\;\frac{t}{1 - \frac{z}{y}}\\ \mathbf{elif}\;y \leq -1 \cdot 10^{+39}:\\ \;\;\;\;t \cdot \frac{x - y}{z}\\ \mathbf{elif}\;y \leq -2.6 \cdot 10^{-100}:\\ \;\;\;\;\frac{t}{\frac{y}{y - x}}\\ \mathbf{elif}\;y \leq 3 \cdot 10^{+28}:\\ \;\;\;\;\frac{t \cdot \left(x - y\right)}{z}\\ \mathbf{else}:\\ \;\;\;\;\frac{t}{1 - \frac{z}{y}}\\ \end{array} \]

Alternative 10: 60.1% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -2 \cdot 10^{+94}:\\ \;\;\;\;t\\ \mathbf{elif}\;y \leq -5.4 \cdot 10^{+48}:\\ \;\;\;\;t \cdot \frac{x}{z}\\ \mathbf{elif}\;y \leq -2.75 \cdot 10^{-67}:\\ \;\;\;\;t \cdot \frac{-y}{z}\\ \mathbf{elif}\;y \leq 4.8 \cdot 10^{+28}:\\ \;\;\;\;\frac{t}{\frac{z}{x}}\\ \mathbf{else}:\\ \;\;\;\;t\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= y -2e+94)
   t
   (if (<= y -5.4e+48)
     (* t (/ x z))
     (if (<= y -2.75e-67)
       (* t (/ (- y) z))
       (if (<= y 4.8e+28) (/ t (/ z x)) t)))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (y <= -2e+94) {
		tmp = t;
	} else if (y <= -5.4e+48) {
		tmp = t * (x / z);
	} else if (y <= -2.75e-67) {
		tmp = t * (-y / z);
	} else if (y <= 4.8e+28) {
		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 <= (-2d+94)) then
        tmp = t
    else if (y <= (-5.4d+48)) then
        tmp = t * (x / z)
    else if (y <= (-2.75d-67)) then
        tmp = t * (-y / z)
    else if (y <= 4.8d+28) 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 <= -2e+94) {
		tmp = t;
	} else if (y <= -5.4e+48) {
		tmp = t * (x / z);
	} else if (y <= -2.75e-67) {
		tmp = t * (-y / z);
	} else if (y <= 4.8e+28) {
		tmp = t / (z / x);
	} else {
		tmp = t;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if y <= -2e+94:
		tmp = t
	elif y <= -5.4e+48:
		tmp = t * (x / z)
	elif y <= -2.75e-67:
		tmp = t * (-y / z)
	elif y <= 4.8e+28:
		tmp = t / (z / x)
	else:
		tmp = t
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (y <= -2e+94)
		tmp = t;
	elseif (y <= -5.4e+48)
		tmp = Float64(t * Float64(x / z));
	elseif (y <= -2.75e-67)
		tmp = Float64(t * Float64(Float64(-y) / z));
	elseif (y <= 4.8e+28)
		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 <= -2e+94)
		tmp = t;
	elseif (y <= -5.4e+48)
		tmp = t * (x / z);
	elseif (y <= -2.75e-67)
		tmp = t * (-y / z);
	elseif (y <= 4.8e+28)
		tmp = t / (z / x);
	else
		tmp = t;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[y, -2e+94], t, If[LessEqual[y, -5.4e+48], N[(t * N[(x / z), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, -2.75e-67], N[(t * N[((-y) / z), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 4.8e+28], N[(t / N[(z / x), $MachinePrecision]), $MachinePrecision], t]]]]

Derivation

1. Split input into 4 regimes

2. if y < -2e94 or 4.79999999999999962e28 < y

   1. Initial program 99.9%

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

   2. Taylor expanded in y around inf 72.1%

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

   if -2e94 < y < -5.40000000000000007e48

   1. Initial program 99.8%

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

   2. Taylor expanded in y around 0 67.2%

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

   if -5.40000000000000007e48 < y < -2.7500000000000001e-67

   1. Initial program 99.7%

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

      1. *-commutative 99.7%

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

      2. associate-*r/ 96.2%

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

      3. associate-/l* 99.8%

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

      4. sub-neg 99.8%

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

      5. +-commutative 99.8%

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

      6. neg-sub0 99.8%

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

      7. associate-+l- 99.8%

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

      8. sub0-neg 99.8%

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

      9. neg-mul-1 99.8%

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

      10. associate-/r* 99.8%

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

   3. Simplified 99.8%

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

   4. Taylor expanded in x around 0 47.8%

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

      1. div-sub 47.8%

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

      2. *-inverses 47.8%

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

   6. Simplified 47.8%

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

   7. Taylor expanded in z around inf 39.3%

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

      1. mul-1-neg 39.3%

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

      2. associate-/l* 42.6%

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

      3. associate-/r/ 39.3%

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

   9. Simplified 39.3%

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

   if -2.7500000000000001e-67 < y < 4.79999999999999962e28

   1. Initial program 91.6%

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

      1. *-commutative 91.6%

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

      2. associate-*r/ 90.3%

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

      3. associate-/l* 92.5%

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

      4. sub-neg 92.5%

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

      5. +-commutative 92.5%

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

      6. neg-sub0 92.5%

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

      7. associate-+l- 92.5%

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

      8. sub0-neg 92.5%

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

      9. neg-mul-1 92.5%

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

      10. associate-/r* 92.5%

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

   3. Simplified 92.5%

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

   4. Taylor expanded in y around 0 69.0%

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

4. Final simplification 67.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -2 \cdot 10^{+94}:\\ \;\;\;\;t\\ \mathbf{elif}\;y \leq -5.4 \cdot 10^{+48}:\\ \;\;\;\;t \cdot \frac{x}{z}\\ \mathbf{elif}\;y \leq -2.75 \cdot 10^{-67}:\\ \;\;\;\;t \cdot \frac{-y}{z}\\ \mathbf{elif}\;y \leq 4.8 \cdot 10^{+28}:\\ \;\;\;\;\frac{t}{\frac{z}{x}}\\ \mathbf{else}:\\ \;\;\;\;t\\ \end{array} \]

Alternative 11: 60.1% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -4.7 \cdot 10^{+94}:\\ \;\;\;\;t\\ \mathbf{elif}\;y \leq -4.2 \cdot 10^{+46}:\\ \;\;\;\;t \cdot \frac{x}{z}\\ \mathbf{elif}\;y \leq -3.4 \cdot 10^{-68}:\\ \;\;\;\;\frac{-y}{\frac{z}{t}}\\ \mathbf{elif}\;y \leq 6 \cdot 10^{+30}:\\ \;\;\;\;\frac{t}{\frac{z}{x}}\\ \mathbf{else}:\\ \;\;\;\;t\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= y -4.7e+94)
   t
   (if (<= y -4.2e+46)
     (* t (/ x z))
     (if (<= y -3.4e-68)
       (/ (- y) (/ z t))
       (if (<= y 6e+30) (/ t (/ z x)) t)))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (y <= -4.7e+94) {
		tmp = t;
	} else if (y <= -4.2e+46) {
		tmp = t * (x / z);
	} else if (y <= -3.4e-68) {
		tmp = -y / (z / t);
	} else if (y <= 6e+30) {
		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 <= (-4.7d+94)) then
        tmp = t
    else if (y <= (-4.2d+46)) then
        tmp = t * (x / z)
    else if (y <= (-3.4d-68)) then
        tmp = -y / (z / t)
    else if (y <= 6d+30) 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 <= -4.7e+94) {
		tmp = t;
	} else if (y <= -4.2e+46) {
		tmp = t * (x / z);
	} else if (y <= -3.4e-68) {
		tmp = -y / (z / t);
	} else if (y <= 6e+30) {
		tmp = t / (z / x);
	} else {
		tmp = t;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if y <= -4.7e+94:
		tmp = t
	elif y <= -4.2e+46:
		tmp = t * (x / z)
	elif y <= -3.4e-68:
		tmp = -y / (z / t)
	elif y <= 6e+30:
		tmp = t / (z / x)
	else:
		tmp = t
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (y <= -4.7e+94)
		tmp = t;
	elseif (y <= -4.2e+46)
		tmp = Float64(t * Float64(x / z));
	elseif (y <= -3.4e-68)
		tmp = Float64(Float64(-y) / Float64(z / t));
	elseif (y <= 6e+30)
		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 <= -4.7e+94)
		tmp = t;
	elseif (y <= -4.2e+46)
		tmp = t * (x / z);
	elseif (y <= -3.4e-68)
		tmp = -y / (z / t);
	elseif (y <= 6e+30)
		tmp = t / (z / x);
	else
		tmp = t;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[y, -4.7e+94], t, If[LessEqual[y, -4.2e+46], N[(t * N[(x / z), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, -3.4e-68], N[((-y) / N[(z / t), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 6e+30], N[(t / N[(z / x), $MachinePrecision]), $MachinePrecision], t]]]]

Derivation

1. Split input into 4 regimes

2. if y < -4.70000000000000017e94 or 5.99999999999999956e30 < y

   1. Initial program 99.9%

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

   2. Taylor expanded in y around inf 72.1%

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

   if -4.70000000000000017e94 < y < -4.2e46

   1. Initial program 99.8%

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

   2. Taylor expanded in y around 0 67.2%

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

   if -4.2e46 < y < -3.40000000000000018e-68

   1. Initial program 99.7%

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

      1. *-commutative 99.7%

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

      2. associate-*r/ 96.2%

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

      3. associate-/l* 99.8%

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

      4. sub-neg 99.8%

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

      5. +-commutative 99.8%

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

      6. neg-sub0 99.8%

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

      7. associate-+l- 99.8%

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

      8. sub0-neg 99.8%

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

      9. neg-mul-1 99.8%

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

      10. associate-/r* 99.8%

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

   3. Simplified 99.8%

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

   4. Taylor expanded in x around 0 47.8%

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

      1. div-sub 47.8%

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

      2. *-inverses 47.8%

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

   6. Simplified 47.8%

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

   7. Taylor expanded in z around inf 39.3%

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

      1. mul-1-neg 39.3%

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

      2. associate-/l* 42.6%

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

   9. Simplified 42.6%

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

   if -3.40000000000000018e-68 < y < 5.99999999999999956e30

   1. Initial program 91.6%

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

      1. *-commutative 91.6%

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

      2. associate-*r/ 90.3%

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

      3. associate-/l* 92.5%

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

      4. sub-neg 92.5%

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

      5. +-commutative 92.5%

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

      6. neg-sub0 92.5%

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

      7. associate-+l- 92.5%

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

      8. sub0-neg 92.5%

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

      9. neg-mul-1 92.5%

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

      10. associate-/r* 92.5%

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

   3. Simplified 92.5%

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

   4. Taylor expanded in y around 0 69.0%

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

4. Final simplification 67.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -4.7 \cdot 10^{+94}:\\ \;\;\;\;t\\ \mathbf{elif}\;y \leq -4.2 \cdot 10^{+46}:\\ \;\;\;\;t \cdot \frac{x}{z}\\ \mathbf{elif}\;y \leq -3.4 \cdot 10^{-68}:\\ \;\;\;\;\frac{-y}{\frac{z}{t}}\\ \mathbf{elif}\;y \leq 6 \cdot 10^{+30}:\\ \;\;\;\;\frac{t}{\frac{z}{x}}\\ \mathbf{else}:\\ \;\;\;\;t\\ \end{array} \]

Alternative 12: 71.6% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -8 \cdot 10^{+103}:\\ \;\;\;\;\frac{t \cdot x}{z - y}\\ \mathbf{elif}\;x \leq 2.6 \cdot 10^{+52}:\\ \;\;\;\;\frac{t}{1 - \frac{z}{y}}\\ \mathbf{else}:\\ \;\;\;\;\frac{-x}{\frac{y - z}{t}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= x -8e+103)
   (/ (* t x) (- z y))
   (if (<= x 2.6e+52) (/ t (- 1.0 (/ z y))) (/ (- x) (/ (- y z) t)))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (x <= -8e+103) {
		tmp = (t * x) / (z - y);
	} else if (x <= 2.6e+52) {
		tmp = t / (1.0 - (z / y));
	} else {
		tmp = -x / ((y - z) / 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 (x <= (-8d+103)) then
        tmp = (t * x) / (z - y)
    else if (x <= 2.6d+52) then
        tmp = t / (1.0d0 - (z / y))
    else
        tmp = -x / ((y - z) / t)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if (x <= -8e+103) {
		tmp = (t * x) / (z - y);
	} else if (x <= 2.6e+52) {
		tmp = t / (1.0 - (z / y));
	} else {
		tmp = -x / ((y - z) / t);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if x <= -8e+103:
		tmp = (t * x) / (z - y)
	elif x <= 2.6e+52:
		tmp = t / (1.0 - (z / y))
	else:
		tmp = -x / ((y - z) / t)
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (x <= -8e+103)
		tmp = Float64(Float64(t * x) / Float64(z - y));
	elseif (x <= 2.6e+52)
		tmp = Float64(t / Float64(1.0 - Float64(z / y)));
	else
		tmp = Float64(Float64(-x) / Float64(Float64(y - z) / t));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (x <= -8e+103)
		tmp = (t * x) / (z - y);
	elseif (x <= 2.6e+52)
		tmp = t / (1.0 - (z / y));
	else
		tmp = -x / ((y - z) / t);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[x, -8e+103], N[(N[(t * x), $MachinePrecision] / N[(z - y), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 2.6e+52], N[(t / N[(1.0 - N[(z / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[((-x) / N[(N[(y - z), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if x < -8e103

   1. Initial program 93.6%

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

   2. Taylor expanded in x around inf 76.6%

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

   if -8e103 < x < 2.6e52

   1. Initial program 96.9%

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

      1. *-commutative 96.9%

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

      2. associate-*r/ 81.9%

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

      3. associate-/l* 96.9%

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

      4. sub-neg 96.9%

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

      5. +-commutative 96.9%

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

      6. neg-sub0 96.9%

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

      7. associate-+l- 96.9%

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

      8. sub0-neg 96.9%

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

      9. neg-mul-1 96.9%

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

      10. associate-/r* 96.9%

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

   3. Simplified 96.9%

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

   4. Taylor expanded in x around 0 77.6%

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

      1. div-sub 77.6%

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

      2. *-inverses 77.6%

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

   6. Simplified 77.6%

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

   if 2.6e52 < x

   1. Initial program 96.5%

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

      1. *-commutative 96.5%

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

      2. associate-*r/ 80.1%

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

      3. associate-/l* 98.0%

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

      4. sub-neg 98.0%

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

      5. +-commutative 98.0%

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

      6. neg-sub0 98.0%

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

      7. associate-+l- 98.0%

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

      8. sub0-neg 98.0%

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

      9. neg-mul-1 98.0%

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

      10. associate-/r* 98.0%

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

   3. Simplified 98.0%

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

   4. Taylor expanded in x around inf 69.9%

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

      1. associate-*r/ 69.9%

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

      2. mul-1-neg 69.9%

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

      3. *-commutative 69.9%

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

      4. distribute-lft-neg-in 69.9%

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

      5. associate-/l* 76.3%

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

   6. Simplified 76.3%

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

4. Final simplification 77.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -8 \cdot 10^{+103}:\\ \;\;\;\;\frac{t \cdot x}{z - y}\\ \mathbf{elif}\;x \leq 2.6 \cdot 10^{+52}:\\ \;\;\;\;\frac{t}{1 - \frac{z}{y}}\\ \mathbf{else}:\\ \;\;\;\;\frac{-x}{\frac{y - z}{t}}\\ \end{array} \]

Alternative 13: 59.7% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -2.2 \cdot 10^{+94}:\\ \;\;\;\;t\\ \mathbf{elif}\;y \leq 1.5 \cdot 10^{+30}:\\ \;\;\;\;x \cdot \frac{t}{z}\\ \mathbf{else}:\\ \;\;\;\;t\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= y -2.2e+94) t (if (<= y 1.5e+30) (* x (/ t z)) t)))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (y <= -2.2e+94) {
		tmp = t;
	} else if (y <= 1.5e+30) {
		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 <= (-2.2d+94)) then
        tmp = t
    else if (y <= 1.5d+30) 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 <= -2.2e+94) {
		tmp = t;
	} else if (y <= 1.5e+30) {
		tmp = x * (t / z);
	} else {
		tmp = t;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if y <= -2.2e+94:
		tmp = t
	elif y <= 1.5e+30:
		tmp = x * (t / z)
	else:
		tmp = t
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (y <= -2.2e+94)
		tmp = t;
	elseif (y <= 1.5e+30)
		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 <= -2.2e+94)
		tmp = t;
	elseif (y <= 1.5e+30)
		tmp = x * (t / z);
	else
		tmp = t;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[y, -2.2e+94], t, If[LessEqual[y, 1.5e+30], N[(x * N[(t / z), $MachinePrecision]), $MachinePrecision], t]]

Derivation

1. Split input into 2 regimes

2. if y < -2.20000000000000012e94 or 1.49999999999999989e30 < y

   1. Initial program 99.9%

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

   2. Taylor expanded in y around inf 72.1%

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

   if -2.20000000000000012e94 < y < 1.49999999999999989e30

   1. Initial program 93.6%

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

   2. Taylor expanded in y around 0 55.6%

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

      1. associate-/l* 59.1%

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

      2. associate-/r/ 55.5%

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

   4. Simplified 55.5%

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

4. Final simplification 62.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -2.2 \cdot 10^{+94}:\\ \;\;\;\;t\\ \mathbf{elif}\;y \leq 1.5 \cdot 10^{+30}:\\ \;\;\;\;x \cdot \frac{t}{z}\\ \mathbf{else}:\\ \;\;\;\;t\\ \end{array} \]

Alternative 14: 60.9% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -1.55 \cdot 10^{+100}:\\ \;\;\;\;t\\ \mathbf{elif}\;y \leq 2.7 \cdot 10^{+29}:\\ \;\;\;\;t \cdot \frac{x}{z}\\ \mathbf{else}:\\ \;\;\;\;t\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= y -1.55e+100) t (if (<= y 2.7e+29) (* t (/ x z)) t)))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (y <= -1.55e+100) {
		tmp = t;
	} else if (y <= 2.7e+29) {
		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 <= (-1.55d+100)) then
        tmp = t
    else if (y <= 2.7d+29) 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 <= -1.55e+100) {
		tmp = t;
	} else if (y <= 2.7e+29) {
		tmp = t * (x / z);
	} else {
		tmp = t;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if y <= -1.55e+100:
		tmp = t
	elif y <= 2.7e+29:
		tmp = t * (x / z)
	else:
		tmp = t
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (y <= -1.55e+100)
		tmp = t;
	elseif (y <= 2.7e+29)
		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 <= -1.55e+100)
		tmp = t;
	elseif (y <= 2.7e+29)
		tmp = t * (x / z);
	else
		tmp = t;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[y, -1.55e+100], t, If[LessEqual[y, 2.7e+29], N[(t * N[(x / z), $MachinePrecision]), $MachinePrecision], t]]

Derivation

1. Split input into 2 regimes

2. if y < -1.55000000000000003e100 or 2.7e29 < y

   1. Initial program 99.9%

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

   2. Taylor expanded in y around inf 72.1%

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

   if -1.55000000000000003e100 < y < 2.7e29

   1. Initial program 93.6%

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

   2. Taylor expanded in y around 0 58.4%

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

4. Final simplification 64.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.55 \cdot 10^{+100}:\\ \;\;\;\;t\\ \mathbf{elif}\;y \leq 2.7 \cdot 10^{+29}:\\ \;\;\;\;t \cdot \frac{x}{z}\\ \mathbf{else}:\\ \;\;\;\;t\\ \end{array} \]

Alternative 15: 61.0% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -2 \cdot 10^{+94}:\\ \;\;\;\;t\\ \mathbf{elif}\;y \leq 4.8 \cdot 10^{+29}:\\ \;\;\;\;\frac{t}{\frac{z}{x}}\\ \mathbf{else}:\\ \;\;\;\;t\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= y -2e+94) t (if (<= y 4.8e+29) (/ t (/ z x)) t)))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (y <= -2e+94) {
		tmp = t;
	} else if (y <= 4.8e+29) {
		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 <= (-2d+94)) then
        tmp = t
    else if (y <= 4.8d+29) 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 <= -2e+94) {
		tmp = t;
	} else if (y <= 4.8e+29) {
		tmp = t / (z / x);
	} else {
		tmp = t;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if y <= -2e+94:
		tmp = t
	elif y <= 4.8e+29:
		tmp = t / (z / x)
	else:
		tmp = t
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (y <= -2e+94)
		tmp = t;
	elseif (y <= 4.8e+29)
		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 <= -2e+94)
		tmp = t;
	elseif (y <= 4.8e+29)
		tmp = t / (z / x);
	else
		tmp = t;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[y, -2e+94], t, If[LessEqual[y, 4.8e+29], N[(t / N[(z / x), $MachinePrecision]), $MachinePrecision], t]]

Derivation

1. Split input into 2 regimes

2. if y < -2e94 or 4.8000000000000002e29 < y

   1. Initial program 99.9%

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

   2. Taylor expanded in y around inf 72.1%

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

   if -2e94 < y < 4.8000000000000002e29

   1. Initial program 93.6%

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

      1. *-commutative 93.6%

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

      2. associate-*r/ 90.7%

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

      3. associate-/l* 94.3%

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

      4. sub-neg 94.3%

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

      5. +-commutative 94.3%

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

      6. neg-sub0 94.3%

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

      7. associate-+l- 94.3%

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

      8. sub0-neg 94.3%

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

      9. neg-mul-1 94.3%

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

      10. associate-/r* 94.3%

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

   3. Simplified 94.3%

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

   4. Taylor expanded in y around 0 59.1%

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

4. Final simplification 64.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -2 \cdot 10^{+94}:\\ \;\;\;\;t\\ \mathbf{elif}\;y \leq 4.8 \cdot 10^{+29}:\\ \;\;\;\;\frac{t}{\frac{z}{x}}\\ \mathbf{else}:\\ \;\;\;\;t\\ \end{array} \]

Alternative 16: 96.9% 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 96.2%

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

2. Final simplification 96.2%

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

Alternative 17: 34.8% 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 96.2%

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

2. Taylor expanded in y around inf 36.3%

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

3. Final simplification 36.3%

   \[\leadsto t \]

Developer target: 96.9% 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 2023268 
(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))