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

Percentage Accurate: 96.8% → 96.8%

Time: 11.8s

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: 96.8% 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: 96.8% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 96.1%

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

   1. associate-*l/ 83.3%

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

   2. associate-/l* 86.3%

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

3. Simplified 86.3%

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

   1. associate-*r/ 83.3%

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

   2. associate-*l/ 96.1%

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

   3. *-commutative 96.1%

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

   4. clear-num 96.1%

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

   5. un-div-inv 96.2%

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

6. Applied egg-rr 96.2%

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

7. Final simplification 96.2%

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

Alternative 2: 71.6% accurate, 0.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{t \cdot y}{y - z}\\ \mathbf{if}\;y \leq -3.8 \cdot 10^{+172}:\\ \;\;\;\;t\\ \mathbf{elif}\;y \leq -1.6 \cdot 10^{+39}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y \leq -2.15 \cdot 10^{-169}:\\ \;\;\;\;\frac{t \cdot x}{z - y}\\ \mathbf{elif}\;y \leq 4.8 \cdot 10^{-72}:\\ \;\;\;\;\frac{t \cdot \left(x - y\right)}{z}\\ \mathbf{elif}\;y \leq 3 \cdot 10^{+25}:\\ \;\;\;\;t \cdot \frac{x}{z - y}\\ \mathbf{elif}\;y \leq 10^{+154}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;t\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (/ (* t y) (- y z))))
   (if (<= y -3.8e+172)
     t
     (if (<= y -1.6e+39)
       t_1
       (if (<= y -2.15e-169)
         (/ (* t x) (- z y))
         (if (<= y 4.8e-72)
           (/ (* t (- x y)) z)
           (if (<= y 3e+25) (* t (/ x (- z y))) (if (<= y 1e+154) t_1 t))))))))

C

double code(double x, double y, double z, double t) {
	double t_1 = (t * y) / (y - z);
	double tmp;
	if (y <= -3.8e+172) {
		tmp = t;
	} else if (y <= -1.6e+39) {
		tmp = t_1;
	} else if (y <= -2.15e-169) {
		tmp = (t * x) / (z - y);
	} else if (y <= 4.8e-72) {
		tmp = (t * (x - y)) / z;
	} else if (y <= 3e+25) {
		tmp = t * (x / (z - y));
	} else if (y <= 1e+154) {
		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 * y) / (y - z)
    if (y <= (-3.8d+172)) then
        tmp = t
    else if (y <= (-1.6d+39)) then
        tmp = t_1
    else if (y <= (-2.15d-169)) then
        tmp = (t * x) / (z - y)
    else if (y <= 4.8d-72) then
        tmp = (t * (x - y)) / z
    else if (y <= 3d+25) then
        tmp = t * (x / (z - y))
    else if (y <= 1d+154) 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 * y) / (y - z);
	double tmp;
	if (y <= -3.8e+172) {
		tmp = t;
	} else if (y <= -1.6e+39) {
		tmp = t_1;
	} else if (y <= -2.15e-169) {
		tmp = (t * x) / (z - y);
	} else if (y <= 4.8e-72) {
		tmp = (t * (x - y)) / z;
	} else if (y <= 3e+25) {
		tmp = t * (x / (z - y));
	} else if (y <= 1e+154) {
		tmp = t_1;
	} else {
		tmp = t;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = (t * y) / (y - z)
	tmp = 0
	if y <= -3.8e+172:
		tmp = t
	elif y <= -1.6e+39:
		tmp = t_1
	elif y <= -2.15e-169:
		tmp = (t * x) / (z - y)
	elif y <= 4.8e-72:
		tmp = (t * (x - y)) / z
	elif y <= 3e+25:
		tmp = t * (x / (z - y))
	elif y <= 1e+154:
		tmp = t_1
	else:
		tmp = t
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(Float64(t * y) / Float64(y - z))
	tmp = 0.0
	if (y <= -3.8e+172)
		tmp = t;
	elseif (y <= -1.6e+39)
		tmp = t_1;
	elseif (y <= -2.15e-169)
		tmp = Float64(Float64(t * x) / Float64(z - y));
	elseif (y <= 4.8e-72)
		tmp = Float64(Float64(t * Float64(x - y)) / z);
	elseif (y <= 3e+25)
		tmp = Float64(t * Float64(x / Float64(z - y)));
	elseif (y <= 1e+154)
		tmp = t_1;
	else
		tmp = t;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = (t * y) / (y - z);
	tmp = 0.0;
	if (y <= -3.8e+172)
		tmp = t;
	elseif (y <= -1.6e+39)
		tmp = t_1;
	elseif (y <= -2.15e-169)
		tmp = (t * x) / (z - y);
	elseif (y <= 4.8e-72)
		tmp = (t * (x - y)) / z;
	elseif (y <= 3e+25)
		tmp = t * (x / (z - y));
	elseif (y <= 1e+154)
		tmp = t_1;
	else
		tmp = t;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(N[(t * y), $MachinePrecision] / N[(y - z), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -3.8e+172], t, If[LessEqual[y, -1.6e+39], t$95$1, If[LessEqual[y, -2.15e-169], N[(N[(t * x), $MachinePrecision] / N[(z - y), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 4.8e-72], N[(N[(t * N[(x - y), $MachinePrecision]), $MachinePrecision] / z), $MachinePrecision], If[LessEqual[y, 3e+25], N[(t * N[(x / N[(z - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 1e+154], t$95$1, t]]]]]]]

Derivation

1. Split input into 5 regimes

2. if y < -3.7999999999999997e172 or 1.00000000000000004e154 < y

   1. Initial program 99.9%

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

      1. associate-*l/ 58.9%

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

      2. associate-/l* 73.8%

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

   3. Simplified 73.8%

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

   5. Taylor expanded in y around inf 89.2%

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

   if -3.7999999999999997e172 < y < -1.59999999999999996e39 or 3.00000000000000006e25 < y < 1.00000000000000004e154

   1. Initial program 99.7%

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

      1. associate-*l/ 83.0%

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

      2. associate-/l* 89.5%

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

   3. Simplified 89.5%

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

   5. Taylor expanded in x around 0 71.0%

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

      1. mul-1-neg 71.0%

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

   7. Simplified 71.0%

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

   if -1.59999999999999996e39 < y < -2.14999999999999992e-169

   1. Initial program 95.1%

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

      1. associate-*l/ 99.8%

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

      2. associate-/l* 90.5%

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

   3. Simplified 90.5%

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

   5. Taylor expanded in x around inf 71.5%

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

   if -2.14999999999999992e-169 < y < 4.8e-72

   1. Initial program 90.5%

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

      1. associate-*l/ 92.9%

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

      2. associate-/l* 88.7%

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

   3. Simplified 88.7%

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

   5. Taylor expanded in z around inf 82.7%

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

   if 4.8e-72 < y < 3.00000000000000006e25

   1. Initial program 99.7%

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

   3. Taylor expanded in x around inf 86.8%

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

4. Final simplification 80.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -3.8 \cdot 10^{+172}:\\ \;\;\;\;t\\ \mathbf{elif}\;y \leq -1.6 \cdot 10^{+39}:\\ \;\;\;\;\frac{t \cdot y}{y - z}\\ \mathbf{elif}\;y \leq -2.15 \cdot 10^{-169}:\\ \;\;\;\;\frac{t \cdot x}{z - y}\\ \mathbf{elif}\;y \leq 4.8 \cdot 10^{-72}:\\ \;\;\;\;\frac{t \cdot \left(x - y\right)}{z}\\ \mathbf{elif}\;y \leq 3 \cdot 10^{+25}:\\ \;\;\;\;t \cdot \frac{x}{z - y}\\ \mathbf{elif}\;y \leq 10^{+154}:\\ \;\;\;\;\frac{t \cdot y}{y - z}\\ \mathbf{else}:\\ \;\;\;\;t\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 71.2% accurate, 0.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := y \cdot \frac{t}{y - z}\\ \mathbf{if}\;y \leq -6.4 \cdot 10^{+183}:\\ \;\;\;\;t\\ \mathbf{elif}\;y \leq -1.04 \cdot 10^{+40}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y \leq -2.75 \cdot 10^{-170}:\\ \;\;\;\;\frac{t \cdot x}{z - y}\\ \mathbf{elif}\;y \leq 1.65 \cdot 10^{-72}:\\ \;\;\;\;\frac{t \cdot \left(x - y\right)}{z}\\ \mathbf{elif}\;y \leq 7.8 \cdot 10^{+31}:\\ \;\;\;\;t \cdot \frac{x}{z - y}\\ \mathbf{elif}\;y \leq 3.9 \cdot 10^{+174}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;t\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (* y (/ t (- y z)))))
   (if (<= y -6.4e+183)
     t
     (if (<= y -1.04e+40)
       t_1
       (if (<= y -2.75e-170)
         (/ (* t x) (- z y))
         (if (<= y 1.65e-72)
           (/ (* t (- x y)) z)
           (if (<= y 7.8e+31)
             (* t (/ x (- z y)))
             (if (<= y 3.9e+174) t_1 t))))))))

C

double code(double x, double y, double z, double t) {
	double t_1 = y * (t / (y - z));
	double tmp;
	if (y <= -6.4e+183) {
		tmp = t;
	} else if (y <= -1.04e+40) {
		tmp = t_1;
	} else if (y <= -2.75e-170) {
		tmp = (t * x) / (z - y);
	} else if (y <= 1.65e-72) {
		tmp = (t * (x - y)) / z;
	} else if (y <= 7.8e+31) {
		tmp = t * (x / (z - y));
	} else if (y <= 3.9e+174) {
		tmp = t_1;
	} else {
		tmp = t;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: t_1
    real(8) :: tmp
    t_1 = y * (t / (y - z))
    if (y <= (-6.4d+183)) then
        tmp = t
    else if (y <= (-1.04d+40)) then
        tmp = t_1
    else if (y <= (-2.75d-170)) then
        tmp = (t * x) / (z - y)
    else if (y <= 1.65d-72) then
        tmp = (t * (x - y)) / z
    else if (y <= 7.8d+31) then
        tmp = t * (x / (z - y))
    else if (y <= 3.9d+174) then
        tmp = t_1
    else
        tmp = t
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double t_1 = y * (t / (y - z));
	double tmp;
	if (y <= -6.4e+183) {
		tmp = t;
	} else if (y <= -1.04e+40) {
		tmp = t_1;
	} else if (y <= -2.75e-170) {
		tmp = (t * x) / (z - y);
	} else if (y <= 1.65e-72) {
		tmp = (t * (x - y)) / z;
	} else if (y <= 7.8e+31) {
		tmp = t * (x / (z - y));
	} else if (y <= 3.9e+174) {
		tmp = t_1;
	} else {
		tmp = t;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = y * (t / (y - z))
	tmp = 0
	if y <= -6.4e+183:
		tmp = t
	elif y <= -1.04e+40:
		tmp = t_1
	elif y <= -2.75e-170:
		tmp = (t * x) / (z - y)
	elif y <= 1.65e-72:
		tmp = (t * (x - y)) / z
	elif y <= 7.8e+31:
		tmp = t * (x / (z - y))
	elif y <= 3.9e+174:
		tmp = t_1
	else:
		tmp = t
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(y * Float64(t / Float64(y - z)))
	tmp = 0.0
	if (y <= -6.4e+183)
		tmp = t;
	elseif (y <= -1.04e+40)
		tmp = t_1;
	elseif (y <= -2.75e-170)
		tmp = Float64(Float64(t * x) / Float64(z - y));
	elseif (y <= 1.65e-72)
		tmp = Float64(Float64(t * Float64(x - y)) / z);
	elseif (y <= 7.8e+31)
		tmp = Float64(t * Float64(x / Float64(z - y)));
	elseif (y <= 3.9e+174)
		tmp = t_1;
	else
		tmp = t;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = y * (t / (y - z));
	tmp = 0.0;
	if (y <= -6.4e+183)
		tmp = t;
	elseif (y <= -1.04e+40)
		tmp = t_1;
	elseif (y <= -2.75e-170)
		tmp = (t * x) / (z - y);
	elseif (y <= 1.65e-72)
		tmp = (t * (x - y)) / z;
	elseif (y <= 7.8e+31)
		tmp = t * (x / (z - y));
	elseif (y <= 3.9e+174)
		tmp = t_1;
	else
		tmp = t;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(y * N[(t / N[(y - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -6.4e+183], t, If[LessEqual[y, -1.04e+40], t$95$1, If[LessEqual[y, -2.75e-170], N[(N[(t * x), $MachinePrecision] / N[(z - y), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 1.65e-72], N[(N[(t * N[(x - y), $MachinePrecision]), $MachinePrecision] / z), $MachinePrecision], If[LessEqual[y, 7.8e+31], N[(t * N[(x / N[(z - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 3.9e+174], t$95$1, t]]]]]]]

Derivation

1. Split input into 5 regimes

2. if y < -6.4000000000000004e183 or 3.89999999999999981e174 < y

   1. Initial program 99.9%

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

      1. associate-*l/ 61.5%

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

      2. associate-/l* 71.6%

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

   3. Simplified 71.6%

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

   5. Taylor expanded in y around inf 89.3%

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

   if -6.4000000000000004e183 < y < -1.04e40 or 7.79999999999999999e31 < y < 3.89999999999999981e174

   1. Initial program 99.8%

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

      1. associate-*l/ 77.7%

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

      2. associate-/l* 89.4%

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

   3. Simplified 89.4%

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

      1. associate-*r/ 77.7%

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

      2. associate-*l/ 99.8%

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

      3. *-commutative 99.8%

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

      4. clear-num 99.8%

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

      5. un-div-inv 100.0%

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

   6. Applied egg-rr 100.0%

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

   7. Taylor expanded in x around 0 67.2%

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

      1. associate-*r/ 67.2%

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

      2. neg-mul-1 67.2%

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

      3. distribute-rgt-neg-in 67.2%

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

      4. associate-*l/ 76.9%

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

   9. Simplified 76.9%

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

   if -1.04e40 < y < -2.75000000000000009e-170

   1. Initial program 95.1%

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

      1. associate-*l/ 99.8%

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

      2. associate-/l* 90.5%

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

   3. Simplified 90.5%

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

   5. Taylor expanded in x around inf 71.5%

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

   if -2.75000000000000009e-170 < y < 1.65e-72

   1. Initial program 90.5%

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

      1. associate-*l/ 92.9%

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

      2. associate-/l* 88.7%

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

   3. Simplified 88.7%

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

   5. Taylor expanded in z around inf 82.7%

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

   if 1.65e-72 < y < 7.79999999999999999e31

   1. Initial program 99.7%

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

   3. Taylor expanded in x around inf 86.8%

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

4. Final simplification 81.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -6.4 \cdot 10^{+183}:\\ \;\;\;\;t\\ \mathbf{elif}\;y \leq -1.04 \cdot 10^{+40}:\\ \;\;\;\;y \cdot \frac{t}{y - z}\\ \mathbf{elif}\;y \leq -2.75 \cdot 10^{-170}:\\ \;\;\;\;\frac{t \cdot x}{z - y}\\ \mathbf{elif}\;y \leq 1.65 \cdot 10^{-72}:\\ \;\;\;\;\frac{t \cdot \left(x - y\right)}{z}\\ \mathbf{elif}\;y \leq 7.8 \cdot 10^{+31}:\\ \;\;\;\;t \cdot \frac{x}{z - y}\\ \mathbf{elif}\;y \leq 3.9 \cdot 10^{+174}:\\ \;\;\;\;y \cdot \frac{t}{y - z}\\ \mathbf{else}:\\ \;\;\;\;t\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 88.5% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(x - y\right) \cdot \frac{t}{z - y}\\ \mathbf{if}\;y \leq -4.5 \cdot 10^{+190}:\\ \;\;\;\;\frac{t}{\frac{y}{y - x}}\\ \mathbf{elif}\;y \leq -7.5 \cdot 10^{-277}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y \leq 6.8 \cdot 10^{-140}:\\ \;\;\;\;\frac{t \cdot \left(x - y\right)}{z}\\ \mathbf{elif}\;y \leq 5.2 \cdot 10^{+82}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;t \cdot \frac{y}{y - z}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (* (- x y) (/ t (- z y)))))
   (if (<= y -4.5e+190)
     (/ t (/ y (- y x)))
     (if (<= y -7.5e-277)
       t_1
       (if (<= y 6.8e-140)
         (/ (* t (- x y)) z)
         (if (<= y 5.2e+82) t_1 (* t (/ y (- y z)))))))))

C

double code(double x, double y, double z, double t) {
	double t_1 = (x - y) * (t / (z - y));
	double tmp;
	if (y <= -4.5e+190) {
		tmp = t / (y / (y - x));
	} else if (y <= -7.5e-277) {
		tmp = t_1;
	} else if (y <= 6.8e-140) {
		tmp = (t * (x - y)) / z;
	} else if (y <= 5.2e+82) {
		tmp = t_1;
	} else {
		tmp = t * (y / (y - z));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: t_1
    real(8) :: tmp
    t_1 = (x - y) * (t / (z - y))
    if (y <= (-4.5d+190)) then
        tmp = t / (y / (y - x))
    else if (y <= (-7.5d-277)) then
        tmp = t_1
    else if (y <= 6.8d-140) then
        tmp = (t * (x - y)) / z
    else if (y <= 5.2d+82) then
        tmp = t_1
    else
        tmp = t * (y / (y - z))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double t_1 = (x - y) * (t / (z - y));
	double tmp;
	if (y <= -4.5e+190) {
		tmp = t / (y / (y - x));
	} else if (y <= -7.5e-277) {
		tmp = t_1;
	} else if (y <= 6.8e-140) {
		tmp = (t * (x - y)) / z;
	} else if (y <= 5.2e+82) {
		tmp = t_1;
	} else {
		tmp = t * (y / (y - z));
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = (x - y) * (t / (z - y))
	tmp = 0
	if y <= -4.5e+190:
		tmp = t / (y / (y - x))
	elif y <= -7.5e-277:
		tmp = t_1
	elif y <= 6.8e-140:
		tmp = (t * (x - y)) / z
	elif y <= 5.2e+82:
		tmp = t_1
	else:
		tmp = t * (y / (y - z))
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(Float64(x - y) * Float64(t / Float64(z - y)))
	tmp = 0.0
	if (y <= -4.5e+190)
		tmp = Float64(t / Float64(y / Float64(y - x)));
	elseif (y <= -7.5e-277)
		tmp = t_1;
	elseif (y <= 6.8e-140)
		tmp = Float64(Float64(t * Float64(x - y)) / z);
	elseif (y <= 5.2e+82)
		tmp = t_1;
	else
		tmp = Float64(t * Float64(y / Float64(y - z)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = (x - y) * (t / (z - y));
	tmp = 0.0;
	if (y <= -4.5e+190)
		tmp = t / (y / (y - x));
	elseif (y <= -7.5e-277)
		tmp = t_1;
	elseif (y <= 6.8e-140)
		tmp = (t * (x - y)) / z;
	elseif (y <= 5.2e+82)
		tmp = t_1;
	else
		tmp = t * (y / (y - z));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(N[(x - y), $MachinePrecision] * N[(t / N[(z - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -4.5e+190], N[(t / N[(y / N[(y - x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, -7.5e-277], t$95$1, If[LessEqual[y, 6.8e-140], N[(N[(t * N[(x - y), $MachinePrecision]), $MachinePrecision] / z), $MachinePrecision], If[LessEqual[y, 5.2e+82], t$95$1, N[(t * N[(y / N[(y - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]

Derivation

1. Split input into 4 regimes

2. if y < -4.4999999999999999e190

   1. Initial program 99.9%

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

      1. associate-*l/ 66.6%

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

      2. associate-/l* 68.3%

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

   3. Simplified 68.3%

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

      1. associate-*r/ 66.6%

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

      2. associate-*l/ 99.9%

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

      3. *-commutative 99.9%

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

      4. clear-num 99.9%

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

      5. un-div-inv 100.0%

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

   6. Applied egg-rr 100.0%

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

   7. Taylor expanded in z around 0 95.3%

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

      1. neg-mul-1 95.3%

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

      2. distribute-neg-frac2 95.3%

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

      3. neg-sub0 95.3%

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

      4. associate--r- 95.3%

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

      5. neg-sub0 95.3%

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

   9. Simplified 95.3%

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

   if -4.4999999999999999e190 < y < -7.49999999999999971e-277 or 6.80000000000000017e-140 < y < 5.1999999999999997e82

   1. Initial program 96.3%

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

      1. associate-*l/ 86.9%

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

      2. associate-/l* 93.6%

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

   3. Simplified 93.6%

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

   if -7.49999999999999971e-277 < y < 6.80000000000000017e-140

   1. Initial program 89.5%

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

      1. associate-*l/ 97.8%

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

      2. associate-/l* 82.4%

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

   3. Simplified 82.4%

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

   5. Taylor expanded in z around inf 91.6%

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

   if 5.1999999999999997e82 < y

   1. Initial program 99.9%

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

   3. Taylor expanded in x around 0 93.2%

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

      1. neg-mul-1 93.2%

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

      2. distribute-neg-frac 93.2%

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

   5. Simplified 93.2%

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

4. Final simplification 93.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -4.5 \cdot 10^{+190}:\\ \;\;\;\;\frac{t}{\frac{y}{y - x}}\\ \mathbf{elif}\;y \leq -7.5 \cdot 10^{-277}:\\ \;\;\;\;\left(x - y\right) \cdot \frac{t}{z - y}\\ \mathbf{elif}\;y \leq 6.8 \cdot 10^{-140}:\\ \;\;\;\;\frac{t \cdot \left(x - y\right)}{z}\\ \mathbf{elif}\;y \leq 5.2 \cdot 10^{+82}:\\ \;\;\;\;\left(x - y\right) \cdot \frac{t}{z - y}\\ \mathbf{else}:\\ \;\;\;\;t \cdot \frac{y}{y - z}\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 69.1% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -2.55 \cdot 10^{+39}:\\ \;\;\;\;t\\ \mathbf{elif}\;y \leq 2.1 \cdot 10^{-97}:\\ \;\;\;\;\frac{t \cdot x}{z - y}\\ \mathbf{elif}\;y \leq 2.2 \cdot 10^{-69}:\\ \;\;\;\;\left(x - y\right) \cdot \frac{t}{z}\\ \mathbf{elif}\;y \leq 2.75 \cdot 10^{+48}:\\ \;\;\;\;t \cdot \frac{x}{z - y}\\ \mathbf{else}:\\ \;\;\;\;t\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= y -2.55e+39)
   t
   (if (<= y 2.1e-97)
     (/ (* t x) (- z y))
     (if (<= y 2.2e-69)
       (* (- x y) (/ t z))
       (if (<= y 2.75e+48) (* t (/ x (- z y))) t)))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (y <= -2.55e+39) {
		tmp = t;
	} else if (y <= 2.1e-97) {
		tmp = (t * x) / (z - y);
	} else if (y <= 2.2e-69) {
		tmp = (x - y) * (t / z);
	} else if (y <= 2.75e+48) {
		tmp = t * (x / (z - y));
	} else {
		tmp = t;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if (y <= (-2.55d+39)) then
        tmp = t
    else if (y <= 2.1d-97) then
        tmp = (t * x) / (z - y)
    else if (y <= 2.2d-69) then
        tmp = (x - y) * (t / z)
    else if (y <= 2.75d+48) then
        tmp = t * (x / (z - y))
    else
        tmp = t
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if (y <= -2.55e+39) {
		tmp = t;
	} else if (y <= 2.1e-97) {
		tmp = (t * x) / (z - y);
	} else if (y <= 2.2e-69) {
		tmp = (x - y) * (t / z);
	} else if (y <= 2.75e+48) {
		tmp = t * (x / (z - y));
	} else {
		tmp = t;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if y <= -2.55e+39:
		tmp = t
	elif y <= 2.1e-97:
		tmp = (t * x) / (z - y)
	elif y <= 2.2e-69:
		tmp = (x - y) * (t / z)
	elif y <= 2.75e+48:
		tmp = t * (x / (z - y))
	else:
		tmp = t
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (y <= -2.55e+39)
		tmp = t;
	elseif (y <= 2.1e-97)
		tmp = Float64(Float64(t * x) / Float64(z - y));
	elseif (y <= 2.2e-69)
		tmp = Float64(Float64(x - y) * Float64(t / z));
	elseif (y <= 2.75e+48)
		tmp = Float64(t * Float64(x / Float64(z - y)));
	else
		tmp = t;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (y <= -2.55e+39)
		tmp = t;
	elseif (y <= 2.1e-97)
		tmp = (t * x) / (z - y);
	elseif (y <= 2.2e-69)
		tmp = (x - y) * (t / z);
	elseif (y <= 2.75e+48)
		tmp = t * (x / (z - y));
	else
		tmp = t;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[y, -2.55e+39], t, If[LessEqual[y, 2.1e-97], N[(N[(t * x), $MachinePrecision] / N[(z - y), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 2.2e-69], N[(N[(x - y), $MachinePrecision] * N[(t / z), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 2.75e+48], N[(t * N[(x / N[(z - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t]]]]

Derivation

1. Split input into 4 regimes

2. if y < -2.5499999999999999e39 or 2.7500000000000001e48 < y

   1. Initial program 99.8%

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

      1. associate-*l/ 69.8%

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

      2. associate-/l* 81.0%

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

   3. Simplified 81.0%

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

   5. Taylor expanded in y around inf 72.1%

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

   if -2.5499999999999999e39 < y < 2.1000000000000001e-97

   1. Initial program 91.4%

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

      1. associate-*l/ 94.8%

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

      2. associate-/l* 88.5%

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

   3. Simplified 88.5%

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

   5. Taylor expanded in x around inf 77.9%

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

   if 2.1000000000000001e-97 < y < 2.2e-69

   1. Initial program 99.7%

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

      1. associate-*l/ 90.2%

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

      2. associate-/l* 99.8%

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

   3. Simplified 99.8%

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

   5. Taylor expanded in z around inf 83.1%

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

   if 2.2e-69 < y < 2.7500000000000001e48

   1. Initial program 99.7%

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

   3. Taylor expanded in x around inf 81.8%

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

4. Final simplification 75.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -2.55 \cdot 10^{+39}:\\ \;\;\;\;t\\ \mathbf{elif}\;y \leq 2.1 \cdot 10^{-97}:\\ \;\;\;\;\frac{t \cdot x}{z - y}\\ \mathbf{elif}\;y \leq 2.2 \cdot 10^{-69}:\\ \;\;\;\;\left(x - y\right) \cdot \frac{t}{z}\\ \mathbf{elif}\;y \leq 2.75 \cdot 10^{+48}:\\ \;\;\;\;t \cdot \frac{x}{z - y}\\ \mathbf{else}:\\ \;\;\;\;t\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 68.5% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -1.25 \cdot 10^{+44}:\\ \;\;\;\;t\\ \mathbf{elif}\;y \leq -4.3 \cdot 10^{-170}:\\ \;\;\;\;\frac{t \cdot x}{z - y}\\ \mathbf{elif}\;y \leq 8 \cdot 10^{-72}:\\ \;\;\;\;\frac{t \cdot \left(x - y\right)}{z}\\ \mathbf{elif}\;y \leq 6.6 \cdot 10^{+44}:\\ \;\;\;\;t \cdot \frac{x}{z - y}\\ \mathbf{else}:\\ \;\;\;\;t\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= y -1.25e+44)
   t
   (if (<= y -4.3e-170)
     (/ (* t x) (- z y))
     (if (<= y 8e-72)
       (/ (* t (- x y)) z)
       (if (<= y 6.6e+44) (* t (/ x (- z y))) t)))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (y <= -1.25e+44) {
		tmp = t;
	} else if (y <= -4.3e-170) {
		tmp = (t * x) / (z - y);
	} else if (y <= 8e-72) {
		tmp = (t * (x - y)) / z;
	} else if (y <= 6.6e+44) {
		tmp = t * (x / (z - y));
	} else {
		tmp = t;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if (y <= (-1.25d+44)) then
        tmp = t
    else if (y <= (-4.3d-170)) then
        tmp = (t * x) / (z - y)
    else if (y <= 8d-72) then
        tmp = (t * (x - y)) / z
    else if (y <= 6.6d+44) then
        tmp = t * (x / (z - y))
    else
        tmp = t
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if (y <= -1.25e+44) {
		tmp = t;
	} else if (y <= -4.3e-170) {
		tmp = (t * x) / (z - y);
	} else if (y <= 8e-72) {
		tmp = (t * (x - y)) / z;
	} else if (y <= 6.6e+44) {
		tmp = t * (x / (z - y));
	} else {
		tmp = t;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if y <= -1.25e+44:
		tmp = t
	elif y <= -4.3e-170:
		tmp = (t * x) / (z - y)
	elif y <= 8e-72:
		tmp = (t * (x - y)) / z
	elif y <= 6.6e+44:
		tmp = t * (x / (z - y))
	else:
		tmp = t
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (y <= -1.25e+44)
		tmp = t;
	elseif (y <= -4.3e-170)
		tmp = Float64(Float64(t * x) / Float64(z - y));
	elseif (y <= 8e-72)
		tmp = Float64(Float64(t * Float64(x - y)) / z);
	elseif (y <= 6.6e+44)
		tmp = Float64(t * Float64(x / Float64(z - y)));
	else
		tmp = t;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (y <= -1.25e+44)
		tmp = t;
	elseif (y <= -4.3e-170)
		tmp = (t * x) / (z - y);
	elseif (y <= 8e-72)
		tmp = (t * (x - y)) / z;
	elseif (y <= 6.6e+44)
		tmp = t * (x / (z - y));
	else
		tmp = t;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[y, -1.25e+44], t, If[LessEqual[y, -4.3e-170], N[(N[(t * x), $MachinePrecision] / N[(z - y), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 8e-72], N[(N[(t * N[(x - y), $MachinePrecision]), $MachinePrecision] / z), $MachinePrecision], If[LessEqual[y, 6.6e+44], N[(t * N[(x / N[(z - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t]]]]

Derivation

1. Split input into 4 regimes

2. if y < -1.2499999999999999e44 or 6.60000000000000027e44 < y

   1. Initial program 99.8%

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

      1. associate-*l/ 69.8%

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

      2. associate-/l* 81.0%

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

   3. Simplified 81.0%

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

   5. Taylor expanded in y around inf 72.1%

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

   if -1.2499999999999999e44 < y < -4.2999999999999998e-170

   1. Initial program 95.1%

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

      1. associate-*l/ 99.8%

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

      2. associate-/l* 90.5%

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

   3. Simplified 90.5%

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

   5. Taylor expanded in x around inf 71.5%

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

   if -4.2999999999999998e-170 < y < 7.9999999999999997e-72

   1. Initial program 90.5%

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

      1. associate-*l/ 92.9%

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

      2. associate-/l* 88.7%

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

   3. Simplified 88.7%

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

   5. Taylor expanded in z around inf 82.7%

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

   if 7.9999999999999997e-72 < y < 6.60000000000000027e44

   1. Initial program 99.7%

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

   3. Taylor expanded in x around inf 82.8%

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

4. Final simplification 76.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.25 \cdot 10^{+44}:\\ \;\;\;\;t\\ \mathbf{elif}\;y \leq -4.3 \cdot 10^{-170}:\\ \;\;\;\;\frac{t \cdot x}{z - y}\\ \mathbf{elif}\;y \leq 8 \cdot 10^{-72}:\\ \;\;\;\;\frac{t \cdot \left(x - y\right)}{z}\\ \mathbf{elif}\;y \leq 6.6 \cdot 10^{+44}:\\ \;\;\;\;t \cdot \frac{x}{z - y}\\ \mathbf{else}:\\ \;\;\;\;t\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 75.5% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := t \cdot \frac{y}{y - z}\\ \mathbf{if}\;y \leq -2.3 \cdot 10^{+39}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y \leq -1.8 \cdot 10^{-169}:\\ \;\;\;\;\frac{t \cdot x}{z - y}\\ \mathbf{elif}\;y \leq 2.15 \cdot 10^{-72}:\\ \;\;\;\;\frac{t \cdot \left(x - y\right)}{z}\\ \mathbf{elif}\;y \leq 2.3 \cdot 10^{+25}:\\ \;\;\;\;t \cdot \frac{x}{z - y}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (* t (/ y (- y z)))))
   (if (<= y -2.3e+39)
     t_1
     (if (<= y -1.8e-169)
       (/ (* t x) (- z y))
       (if (<= y 2.15e-72)
         (/ (* t (- x y)) z)
         (if (<= y 2.3e+25) (* t (/ x (- z y))) t_1))))))

C

double code(double x, double y, double z, double t) {
	double t_1 = t * (y / (y - z));
	double tmp;
	if (y <= -2.3e+39) {
		tmp = t_1;
	} else if (y <= -1.8e-169) {
		tmp = (t * x) / (z - y);
	} else if (y <= 2.15e-72) {
		tmp = (t * (x - y)) / z;
	} else if (y <= 2.3e+25) {
		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 * (y / (y - z))
    if (y <= (-2.3d+39)) then
        tmp = t_1
    else if (y <= (-1.8d-169)) then
        tmp = (t * x) / (z - y)
    else if (y <= 2.15d-72) then
        tmp = (t * (x - y)) / z
    else if (y <= 2.3d+25) 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 * (y / (y - z));
	double tmp;
	if (y <= -2.3e+39) {
		tmp = t_1;
	} else if (y <= -1.8e-169) {
		tmp = (t * x) / (z - y);
	} else if (y <= 2.15e-72) {
		tmp = (t * (x - y)) / z;
	} else if (y <= 2.3e+25) {
		tmp = t * (x / (z - y));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = t * (y / (y - z))
	tmp = 0
	if y <= -2.3e+39:
		tmp = t_1
	elif y <= -1.8e-169:
		tmp = (t * x) / (z - y)
	elif y <= 2.15e-72:
		tmp = (t * (x - y)) / z
	elif y <= 2.3e+25:
		tmp = t * (x / (z - y))
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(t * Float64(y / Float64(y - z)))
	tmp = 0.0
	if (y <= -2.3e+39)
		tmp = t_1;
	elseif (y <= -1.8e-169)
		tmp = Float64(Float64(t * x) / Float64(z - y));
	elseif (y <= 2.15e-72)
		tmp = Float64(Float64(t * Float64(x - y)) / z);
	elseif (y <= 2.3e+25)
		tmp = Float64(t * Float64(x / Float64(z - y)));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = t * (y / (y - z));
	tmp = 0.0;
	if (y <= -2.3e+39)
		tmp = t_1;
	elseif (y <= -1.8e-169)
		tmp = (t * x) / (z - y);
	elseif (y <= 2.15e-72)
		tmp = (t * (x - y)) / z;
	elseif (y <= 2.3e+25)
		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[(y / N[(y - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -2.3e+39], t$95$1, If[LessEqual[y, -1.8e-169], N[(N[(t * x), $MachinePrecision] / N[(z - y), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 2.15e-72], N[(N[(t * N[(x - y), $MachinePrecision]), $MachinePrecision] / z), $MachinePrecision], If[LessEqual[y, 2.3e+25], N[(t * N[(x / N[(z - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]]]

Derivation

1. Split input into 4 regimes

2. if y < -2.30000000000000012e39 or 2.2999999999999998e25 < y

   1. Initial program 99.8%

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

   3. Taylor expanded in x around 0 87.0%

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

      1. neg-mul-1 87.0%

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

      2. distribute-neg-frac 87.0%

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

   5. Simplified 87.0%

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

   if -2.30000000000000012e39 < y < -1.80000000000000001e-169

   1. Initial program 95.1%

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

      1. associate-*l/ 99.8%

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

      2. associate-/l* 90.5%

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

   3. Simplified 90.5%

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

   5. Taylor expanded in x around inf 71.5%

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

   if -1.80000000000000001e-169 < y < 2.1499999999999999e-72

   1. Initial program 90.5%

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

      1. associate-*l/ 92.9%

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

      2. associate-/l* 88.7%

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

   3. Simplified 88.7%

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

   5. Taylor expanded in z around inf 82.7%

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

   if 2.1499999999999999e-72 < y < 2.2999999999999998e25

   1. Initial program 99.7%

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

   3. Taylor expanded in x around inf 86.8%

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

4. Final simplification 83.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -2.3 \cdot 10^{+39}:\\ \;\;\;\;t \cdot \frac{y}{y - z}\\ \mathbf{elif}\;y \leq -1.8 \cdot 10^{-169}:\\ \;\;\;\;\frac{t \cdot x}{z - y}\\ \mathbf{elif}\;y \leq 2.15 \cdot 10^{-72}:\\ \;\;\;\;\frac{t \cdot \left(x - y\right)}{z}\\ \mathbf{elif}\;y \leq 2.3 \cdot 10^{+25}:\\ \;\;\;\;t \cdot \frac{x}{z - y}\\ \mathbf{else}:\\ \;\;\;\;t \cdot \frac{y}{y - z}\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 59.8% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -9.5 \cdot 10^{+34}:\\ \;\;\;\;t\\ \mathbf{elif}\;y \leq 3.4 \cdot 10^{-136}:\\ \;\;\;\;\frac{t \cdot x}{z}\\ \mathbf{elif}\;y \leq 2.15 \cdot 10^{+27}:\\ \;\;\;\;x \cdot \frac{t}{-y}\\ \mathbf{else}:\\ \;\;\;\;t\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= y -9.5e+34)
   t
   (if (<= y 3.4e-136)
     (/ (* t x) z)
     (if (<= y 2.15e+27) (* x (/ t (- y))) t))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (y <= -9.5e+34) {
		tmp = t;
	} else if (y <= 3.4e-136) {
		tmp = (t * x) / z;
	} else if (y <= 2.15e+27) {
		tmp = x * (t / -y);
	} else {
		tmp = t;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if (y <= (-9.5d+34)) then
        tmp = t
    else if (y <= 3.4d-136) then
        tmp = (t * x) / z
    else if (y <= 2.15d+27) then
        tmp = x * (t / -y)
    else
        tmp = t
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if (y <= -9.5e+34) {
		tmp = t;
	} else if (y <= 3.4e-136) {
		tmp = (t * x) / z;
	} else if (y <= 2.15e+27) {
		tmp = x * (t / -y);
	} else {
		tmp = t;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if y <= -9.5e+34:
		tmp = t
	elif y <= 3.4e-136:
		tmp = (t * x) / z
	elif y <= 2.15e+27:
		tmp = x * (t / -y)
	else:
		tmp = t
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (y <= -9.5e+34)
		tmp = t;
	elseif (y <= 3.4e-136)
		tmp = Float64(Float64(t * x) / z);
	elseif (y <= 2.15e+27)
		tmp = Float64(x * Float64(t / Float64(-y)));
	else
		tmp = t;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (y <= -9.5e+34)
		tmp = t;
	elseif (y <= 3.4e-136)
		tmp = (t * x) / z;
	elseif (y <= 2.15e+27)
		tmp = x * (t / -y);
	else
		tmp = t;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[y, -9.5e+34], t, If[LessEqual[y, 3.4e-136], N[(N[(t * x), $MachinePrecision] / z), $MachinePrecision], If[LessEqual[y, 2.15e+27], N[(x * N[(t / (-y)), $MachinePrecision]), $MachinePrecision], t]]]

Derivation

1. Split input into 3 regimes

2. if y < -9.4999999999999999e34 or 2.15000000000000004e27 < y

   1. Initial program 99.8%

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

      1. associate-*l/ 70.5%

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

      2. associate-/l* 81.4%

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

   3. Simplified 81.4%

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

   5. Taylor expanded in y around inf 71.2%

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

   if -9.4999999999999999e34 < y < 3.4e-136

   1. Initial program 90.9%

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

      1. associate-*l/ 95.5%

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

      2. associate-/l* 87.9%

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

   3. Simplified 87.9%

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

   5. Taylor expanded in y around 0 65.3%

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

   if 3.4e-136 < y < 2.15000000000000004e27

   1. Initial program 99.7%

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

   3. Taylor expanded in x around inf 76.9%

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

   4. Taylor expanded in z around 0 58.2%

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

      1. associate-*r/ 58.2%

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

      2. associate-*r* 58.2%

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

      3. neg-mul-1 58.2%

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

      4. *-commutative 58.2%

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

      5. associate-/l* 58.1%

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

   6. Simplified 58.1%

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

4. Final simplification 67.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -9.5 \cdot 10^{+34}:\\ \;\;\;\;t\\ \mathbf{elif}\;y \leq 3.4 \cdot 10^{-136}:\\ \;\;\;\;\frac{t \cdot x}{z}\\ \mathbf{elif}\;y \leq 2.15 \cdot 10^{+27}:\\ \;\;\;\;x \cdot \frac{t}{-y}\\ \mathbf{else}:\\ \;\;\;\;t\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 59.6% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -2.4 \cdot 10^{+36}:\\ \;\;\;\;t\\ \mathbf{elif}\;y \leq 1.4 \cdot 10^{-135}:\\ \;\;\;\;\frac{t \cdot x}{z}\\ \mathbf{elif}\;y \leq 1.3 \cdot 10^{+25}:\\ \;\;\;\;t \cdot \frac{x}{-y}\\ \mathbf{else}:\\ \;\;\;\;t\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= y -2.4e+36)
   t
   (if (<= y 1.4e-135) (/ (* t x) z) (if (<= y 1.3e+25) (* t (/ x (- y))) t))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (y <= -2.4e+36) {
		tmp = t;
	} else if (y <= 1.4e-135) {
		tmp = (t * x) / z;
	} else if (y <= 1.3e+25) {
		tmp = t * (x / -y);
	} else {
		tmp = t;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if (y <= (-2.4d+36)) then
        tmp = t
    else if (y <= 1.4d-135) then
        tmp = (t * x) / z
    else if (y <= 1.3d+25) then
        tmp = t * (x / -y)
    else
        tmp = t
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if (y <= -2.4e+36) {
		tmp = t;
	} else if (y <= 1.4e-135) {
		tmp = (t * x) / z;
	} else if (y <= 1.3e+25) {
		tmp = t * (x / -y);
	} else {
		tmp = t;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if y <= -2.4e+36:
		tmp = t
	elif y <= 1.4e-135:
		tmp = (t * x) / z
	elif y <= 1.3e+25:
		tmp = t * (x / -y)
	else:
		tmp = t
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (y <= -2.4e+36)
		tmp = t;
	elseif (y <= 1.4e-135)
		tmp = Float64(Float64(t * x) / z);
	elseif (y <= 1.3e+25)
		tmp = Float64(t * Float64(x / Float64(-y)));
	else
		tmp = t;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (y <= -2.4e+36)
		tmp = t;
	elseif (y <= 1.4e-135)
		tmp = (t * x) / z;
	elseif (y <= 1.3e+25)
		tmp = t * (x / -y);
	else
		tmp = t;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[y, -2.4e+36], t, If[LessEqual[y, 1.4e-135], N[(N[(t * x), $MachinePrecision] / z), $MachinePrecision], If[LessEqual[y, 1.3e+25], N[(t * N[(x / (-y)), $MachinePrecision]), $MachinePrecision], t]]]

Derivation

1. Split input into 3 regimes

2. if y < -2.39999999999999992e36 or 1.2999999999999999e25 < y

   1. Initial program 99.8%

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

      1. associate-*l/ 70.5%

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

      2. associate-/l* 81.4%

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

   3. Simplified 81.4%

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

   5. Taylor expanded in y around inf 71.2%

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

   if -2.39999999999999992e36 < y < 1.40000000000000012e-135

   1. Initial program 90.9%

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

      1. associate-*l/ 95.5%

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

      2. associate-/l* 87.9%

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

   3. Simplified 87.9%

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

   5. Taylor expanded in y around 0 65.3%

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

   if 1.40000000000000012e-135 < y < 1.2999999999999999e25

   1. Initial program 99.7%

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

   3. Taylor expanded in x around inf 76.9%

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

   4. Taylor expanded in z around 0 58.1%

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

      1. associate-*r/ 58.1%

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

      2. neg-mul-1 58.1%

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

   6. Simplified 58.1%

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

4. Final simplification 67.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -2.4 \cdot 10^{+36}:\\ \;\;\;\;t\\ \mathbf{elif}\;y \leq 1.4 \cdot 10^{-135}:\\ \;\;\;\;\frac{t \cdot x}{z}\\ \mathbf{elif}\;y \leq 1.3 \cdot 10^{+25}:\\ \;\;\;\;t \cdot \frac{x}{-y}\\ \mathbf{else}:\\ \;\;\;\;t\\ \end{array} \]
5. Add Preprocessing

Alternative 10: 60.1% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -2 \cdot 10^{+31}:\\ \;\;\;\;t\\ \mathbf{elif}\;y \leq 1.4 \cdot 10^{-135}:\\ \;\;\;\;\frac{t \cdot x}{z}\\ \mathbf{elif}\;y \leq 1.1 \cdot 10^{+35}:\\ \;\;\;\;\frac{x \cdot \left(-t\right)}{y}\\ \mathbf{else}:\\ \;\;\;\;t\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= y -2e+31)
   t
   (if (<= y 1.4e-135) (/ (* t x) z) (if (<= y 1.1e+35) (/ (* x (- t)) y) t))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (y <= -2e+31) {
		tmp = t;
	} else if (y <= 1.4e-135) {
		tmp = (t * x) / z;
	} else if (y <= 1.1e+35) {
		tmp = (x * -t) / y;
	} else {
		tmp = t;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if (y <= (-2d+31)) then
        tmp = t
    else if (y <= 1.4d-135) then
        tmp = (t * x) / z
    else if (y <= 1.1d+35) then
        tmp = (x * -t) / y
    else
        tmp = t
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if (y <= -2e+31) {
		tmp = t;
	} else if (y <= 1.4e-135) {
		tmp = (t * x) / z;
	} else if (y <= 1.1e+35) {
		tmp = (x * -t) / y;
	} else {
		tmp = t;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if y <= -2e+31:
		tmp = t
	elif y <= 1.4e-135:
		tmp = (t * x) / z
	elif y <= 1.1e+35:
		tmp = (x * -t) / y
	else:
		tmp = t
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (y <= -2e+31)
		tmp = t;
	elseif (y <= 1.4e-135)
		tmp = Float64(Float64(t * x) / z);
	elseif (y <= 1.1e+35)
		tmp = Float64(Float64(x * Float64(-t)) / y);
	else
		tmp = t;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (y <= -2e+31)
		tmp = t;
	elseif (y <= 1.4e-135)
		tmp = (t * x) / z;
	elseif (y <= 1.1e+35)
		tmp = (x * -t) / y;
	else
		tmp = t;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[y, -2e+31], t, If[LessEqual[y, 1.4e-135], N[(N[(t * x), $MachinePrecision] / z), $MachinePrecision], If[LessEqual[y, 1.1e+35], N[(N[(x * (-t)), $MachinePrecision] / y), $MachinePrecision], t]]]

Derivation

1. Split input into 3 regimes

2. if y < -1.9999999999999999e31 or 1.0999999999999999e35 < y

   1. Initial program 99.8%

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

      1. associate-*l/ 70.5%

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

      2. associate-/l* 81.4%

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

   3. Simplified 81.4%

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

   5. Taylor expanded in y around inf 71.2%

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

   if -1.9999999999999999e31 < y < 1.40000000000000012e-135

   1. Initial program 90.9%

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

      1. associate-*l/ 95.5%

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

      2. associate-/l* 87.9%

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

   3. Simplified 87.9%

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

   5. Taylor expanded in y around 0 65.3%

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

   if 1.40000000000000012e-135 < y < 1.0999999999999999e35

   1. Initial program 99.7%

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

   3. Taylor expanded in x around inf 76.9%

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

   4. Taylor expanded in z around 0 58.2%

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

      1. associate-*r/ 58.2%

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

      2. associate-*r* 58.2%

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

      3. neg-mul-1 58.2%

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

      4. *-commutative 58.2%

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

   6. Simplified 58.2%

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

4. Final simplification 67.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -2 \cdot 10^{+31}:\\ \;\;\;\;t\\ \mathbf{elif}\;y \leq 1.4 \cdot 10^{-135}:\\ \;\;\;\;\frac{t \cdot x}{z}\\ \mathbf{elif}\;y \leq 1.1 \cdot 10^{+35}:\\ \;\;\;\;\frac{x \cdot \left(-t\right)}{y}\\ \mathbf{else}:\\ \;\;\;\;t\\ \end{array} \]
5. Add Preprocessing

Alternative 11: 67.2% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -5.8 \cdot 10^{+71}:\\ \;\;\;\;t\\ \mathbf{elif}\;y \leq 6.4 \cdot 10^{+69}:\\ \;\;\;\;\left(x - y\right) \cdot \frac{t}{z}\\ \mathbf{else}:\\ \;\;\;\;t\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= y -5.8e+71) t (if (<= y 6.4e+69) (* (- x y) (/ t z)) t)))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (y <= -5.8e+71) {
		tmp = t;
	} else if (y <= 6.4e+69) {
		tmp = (x - y) * (t / z);
	} else {
		tmp = t;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if (y <= (-5.8d+71)) then
        tmp = t
    else if (y <= 6.4d+69) then
        tmp = (x - y) * (t / z)
    else
        tmp = t
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if (y <= -5.8e+71) {
		tmp = t;
	} else if (y <= 6.4e+69) {
		tmp = (x - y) * (t / z);
	} else {
		tmp = t;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if y <= -5.8e+71:
		tmp = t
	elif y <= 6.4e+69:
		tmp = (x - y) * (t / z)
	else:
		tmp = t
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (y <= -5.8e+71)
		tmp = t;
	elseif (y <= 6.4e+69)
		tmp = Float64(Float64(x - y) * Float64(t / z));
	else
		tmp = t;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (y <= -5.8e+71)
		tmp = t;
	elseif (y <= 6.4e+69)
		tmp = (x - y) * (t / z);
	else
		tmp = t;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[y, -5.8e+71], t, If[LessEqual[y, 6.4e+69], N[(N[(x - y), $MachinePrecision] * N[(t / z), $MachinePrecision]), $MachinePrecision], t]]

Derivation

1. Split input into 2 regimes

2. if y < -5.80000000000000014e71 or 6.3999999999999997e69 < y

   1. Initial program 99.8%

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

      1. associate-*l/ 66.7%

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

      2. associate-/l* 79.0%

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

   3. Simplified 79.0%

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

   5. Taylor expanded in y around inf 75.4%

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

   if -5.80000000000000014e71 < y < 6.3999999999999997e69

   1. Initial program 93.5%

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

      1. associate-*l/ 94.9%

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

      2. associate-/l* 91.4%

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

   3. Simplified 91.4%

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

   5. Taylor expanded in z around inf 63.9%

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

4. Final simplification 68.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -5.8 \cdot 10^{+71}:\\ \;\;\;\;t\\ \mathbf{elif}\;y \leq 6.4 \cdot 10^{+69}:\\ \;\;\;\;\left(x - y\right) \cdot \frac{t}{z}\\ \mathbf{else}:\\ \;\;\;\;t\\ \end{array} \]
5. Add Preprocessing

Alternative 12: 69.6% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -8.2 \cdot 10^{+43}:\\ \;\;\;\;t\\ \mathbf{elif}\;y \leq 1.15 \cdot 10^{+47}:\\ \;\;\;\;t \cdot \frac{x}{z - y}\\ \mathbf{else}:\\ \;\;\;\;t\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= y -8.2e+43) t (if (<= y 1.15e+47) (* t (/ x (- z y))) t)))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (y <= -8.2e+43) {
		tmp = t;
	} else if (y <= 1.15e+47) {
		tmp = t * (x / (z - y));
	} else {
		tmp = t;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if (y <= (-8.2d+43)) then
        tmp = t
    else if (y <= 1.15d+47) then
        tmp = t * (x / (z - y))
    else
        tmp = t
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if (y <= -8.2e+43) {
		tmp = t;
	} else if (y <= 1.15e+47) {
		tmp = t * (x / (z - y));
	} else {
		tmp = t;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if y <= -8.2e+43:
		tmp = t
	elif y <= 1.15e+47:
		tmp = t * (x / (z - y))
	else:
		tmp = t
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (y <= -8.2e+43)
		tmp = t;
	elseif (y <= 1.15e+47)
		tmp = Float64(t * Float64(x / Float64(z - y)));
	else
		tmp = t;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (y <= -8.2e+43)
		tmp = t;
	elseif (y <= 1.15e+47)
		tmp = t * (x / (z - y));
	else
		tmp = t;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[y, -8.2e+43], t, If[LessEqual[y, 1.15e+47], N[(t * N[(x / N[(z - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t]]

Derivation

1. Split input into 2 regimes

2. if y < -8.2000000000000001e43 or 1.1499999999999999e47 < y

   1. Initial program 99.8%

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

      1. associate-*l/ 69.8%

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

      2. associate-/l* 81.0%

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

   3. Simplified 81.0%

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

   5. Taylor expanded in y around inf 72.1%

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

   if -8.2000000000000001e43 < y < 1.1499999999999999e47

   1. Initial program 93.0%

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

   3. Taylor expanded in x around inf 75.0%

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

4. Final simplification 73.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -8.2 \cdot 10^{+43}:\\ \;\;\;\;t\\ \mathbf{elif}\;y \leq 1.15 \cdot 10^{+47}:\\ \;\;\;\;t \cdot \frac{x}{z - y}\\ \mathbf{else}:\\ \;\;\;\;t\\ \end{array} \]
5. Add Preprocessing

Alternative 13: 39.1% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -1.4 \cdot 10^{-99}:\\ \;\;\;\;t\\ \mathbf{elif}\;y \leq 8.5 \cdot 10^{-10}:\\ \;\;\;\;t \cdot \frac{y}{z}\\ \mathbf{else}:\\ \;\;\;\;t\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= y -1.4e-99) t (if (<= y 8.5e-10) (* t (/ y z)) t)))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (y <= -1.4e-99) {
		tmp = t;
	} else if (y <= 8.5e-10) {
		tmp = t * (y / 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 <= (-1.4d-99)) then
        tmp = t
    else if (y <= 8.5d-10) then
        tmp = t * (y / 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 <= -1.4e-99) {
		tmp = t;
	} else if (y <= 8.5e-10) {
		tmp = t * (y / z);
	} else {
		tmp = t;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if y <= -1.4e-99:
		tmp = t
	elif y <= 8.5e-10:
		tmp = t * (y / z)
	else:
		tmp = t
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (y <= -1.4e-99)
		tmp = t;
	elseif (y <= 8.5e-10)
		tmp = Float64(t * Float64(y / z));
	else
		tmp = t;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (y <= -1.4e-99)
		tmp = t;
	elseif (y <= 8.5e-10)
		tmp = t * (y / z);
	else
		tmp = t;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[y, -1.4e-99], t, If[LessEqual[y, 8.5e-10], N[(t * N[(y / z), $MachinePrecision]), $MachinePrecision], t]]

Derivation

1. Split input into 2 regimes

2. if y < -1.4e-99 or 8.4999999999999996e-10 < y

   1. Initial program 99.8%

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

      1. associate-*l/ 75.8%

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

      2. associate-/l* 83.8%

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

   3. Simplified 83.8%

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

   5. Taylor expanded in y around inf 62.5%

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

   if -1.4e-99 < y < 8.4999999999999996e-10

   1. Initial program 90.9%

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

   3. Taylor expanded in z around inf 73.3%

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

   4. Taylor expanded in x around 0 26.6%

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

      1. neg-mul-1 26.6%

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

      2. distribute-neg-frac2 26.6%

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

   6. Simplified 26.6%

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

      1. *-commutative 26.6%

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

      2. clear-num 26.6%

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

      3. un-div-inv 26.6%

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

      4. add-sqr-sqrt 17.0%

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

      5. sqrt-unprod 26.0%

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

      6. sqr-neg 26.0%

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

      7. sqrt-unprod 6.9%

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

      8. add-sqr-sqrt 19.4%

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

   8. Applied egg-rr 19.4%

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

      1. associate-/r/ 21.9%

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

      2. associate-*l/ 19.4%

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

      3. associate-/l* 19.4%

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

   10. Simplified 19.4%

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

4. Final simplification 44.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.4 \cdot 10^{-99}:\\ \;\;\;\;t\\ \mathbf{elif}\;y \leq 8.5 \cdot 10^{-10}:\\ \;\;\;\;t \cdot \frac{y}{z}\\ \mathbf{else}:\\ \;\;\;\;t\\ \end{array} \]
5. Add Preprocessing

Alternative 14: 61.1% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -2.5:\\ \;\;\;\;t\\ \mathbf{elif}\;y \leq 3.2 \cdot 10^{+45}:\\ \;\;\;\;x \cdot \frac{t}{z}\\ \mathbf{else}:\\ \;\;\;\;t\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= y -2.5) t (if (<= y 3.2e+45) (* x (/ t z)) t)))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (y <= -2.5) {
		tmp = t;
	} else if (y <= 3.2e+45) {
		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 <= (-2.5d0)) then
        tmp = t
    else if (y <= 3.2d+45) 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 <= -2.5) {
		tmp = t;
	} else if (y <= 3.2e+45) {
		tmp = x * (t / z);
	} else {
		tmp = t;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if y <= -2.5:
		tmp = t
	elif y <= 3.2e+45:
		tmp = x * (t / z)
	else:
		tmp = t
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (y <= -2.5)
		tmp = t;
	elseif (y <= 3.2e+45)
		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 <= -2.5)
		tmp = t;
	elseif (y <= 3.2e+45)
		tmp = x * (t / z);
	else
		tmp = t;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[y, -2.5], t, If[LessEqual[y, 3.2e+45], N[(x * N[(t / z), $MachinePrecision]), $MachinePrecision], t]]

Derivation

1. Split input into 2 regimes

2. if y < -2.5 or 3.2000000000000003e45 < y

   1. Initial program 99.8%

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

      1. associate-*l/ 72.2%

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

      2. associate-/l* 81.7%

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

   3. Simplified 81.7%

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

   5. Taylor expanded in y around inf 69.0%

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

   if -2.5 < y < 3.2000000000000003e45

   1. Initial program 92.5%

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

      1. associate-*l/ 94.1%

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

      2. associate-/l* 90.8%

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

   3. Simplified 90.8%

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

   5. Taylor expanded in y around 0 59.1%

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

      1. *-commutative 59.1%

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

      2. associate-/l* 57.9%

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

   7. Simplified 57.9%

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

4. Final simplification 63.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -2.5:\\ \;\;\;\;t\\ \mathbf{elif}\;y \leq 3.2 \cdot 10^{+45}:\\ \;\;\;\;x \cdot \frac{t}{z}\\ \mathbf{else}:\\ \;\;\;\;t\\ \end{array} \]
5. Add Preprocessing

Alternative 15: 62.3% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -3.6 \cdot 10^{+32}:\\ \;\;\;\;t\\ \mathbf{elif}\;y \leq 5.4 \cdot 10^{+47}:\\ \;\;\;\;t \cdot \frac{x}{z}\\ \mathbf{else}:\\ \;\;\;\;t\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= y -3.6e+32) t (if (<= y 5.4e+47) (* t (/ x z)) t)))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (y <= -3.6e+32) {
		tmp = t;
	} else if (y <= 5.4e+47) {
		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 <= (-3.6d+32)) then
        tmp = t
    else if (y <= 5.4d+47) 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 <= -3.6e+32) {
		tmp = t;
	} else if (y <= 5.4e+47) {
		tmp = t * (x / z);
	} else {
		tmp = t;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if y <= -3.6e+32:
		tmp = t
	elif y <= 5.4e+47:
		tmp = t * (x / z)
	else:
		tmp = t
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (y <= -3.6e+32)
		tmp = t;
	elseif (y <= 5.4e+47)
		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 <= -3.6e+32)
		tmp = t;
	elseif (y <= 5.4e+47)
		tmp = t * (x / z);
	else
		tmp = t;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[y, -3.6e+32], t, If[LessEqual[y, 5.4e+47], N[(t * N[(x / z), $MachinePrecision]), $MachinePrecision], t]]

Derivation

1. Split input into 2 regimes

2. if y < -3.5999999999999997e32 or 5.39999999999999991e47 < y

   1. Initial program 99.8%

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

      1. associate-*l/ 70.0%

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

      2. associate-/l* 81.1%

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

   3. Simplified 81.1%

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

   5. Taylor expanded in y around inf 71.6%

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

   if -3.5999999999999997e32 < y < 5.39999999999999991e47

   1. Initial program 93.0%

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

   3. Taylor expanded in y around 0 58.7%

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

4. Final simplification 64.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -3.6 \cdot 10^{+32}:\\ \;\;\;\;t\\ \mathbf{elif}\;y \leq 5.4 \cdot 10^{+47}:\\ \;\;\;\;t \cdot \frac{x}{z}\\ \mathbf{else}:\\ \;\;\;\;t\\ \end{array} \]
5. Add Preprocessing

Alternative 16: 96.8% 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 96.1%

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

3. Final simplification 96.1%

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

Alternative 17: 35.4% accurate, 9.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 96.1%

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

   1. associate-*l/ 83.3%

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

   2. associate-/l* 86.3%

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

3. Simplified 86.3%

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

5. Taylor expanded in y around inf 39.2%

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

6. Final simplification 39.2%

   \[\leadsto t \]
7. Add Preprocessing

Developer target: 96.8% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Reproduce

herbie shell --seed 2024039 
(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))