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

Percentage Accurate: 97.1% → 97.1%

Time: 10.0s

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: 97.1% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Alternative 1: 97.1% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 96.9%

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

   1. associate-*l/ 84.7%

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

   2. associate-/l* 85.9%

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

3. Simplified 85.9%

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

   1. associate-*r/ 84.7%

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

   2. associate-*l/ 96.9%

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

   3. *-commutative 96.9%

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

   4. clear-num 96.8%

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

   5. un-div-inv 97.1%

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

6. Applied egg-rr 97.1%

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

7. Final simplification 97.1%

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

Alternative 2: 59.8% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := t \cdot \frac{x}{-y}\\ \mathbf{if}\;y \leq -7.2 \cdot 10^{+96}:\\ \;\;\;\;t\\ \mathbf{elif}\;y \leq -1.02 \cdot 10^{-81}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y \leq 7.5 \cdot 10^{-7}:\\ \;\;\;\;\frac{x}{\frac{z}{t}}\\ \mathbf{elif}\;y \leq 3.1 \cdot 10^{+71}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;t\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (* t (/ x (- y)))))
   (if (<= y -7.2e+96)
     t
     (if (<= y -1.02e-81)
       t_1
       (if (<= y 7.5e-7) (/ x (/ z t)) (if (<= y 3.1e+71) t_1 t))))))

C

double code(double x, double y, double z, double t) {
	double t_1 = t * (x / -y);
	double tmp;
	if (y <= -7.2e+96) {
		tmp = t;
	} else if (y <= -1.02e-81) {
		tmp = t_1;
	} else if (y <= 7.5e-7) {
		tmp = x / (z / t);
	} else if (y <= 3.1e+71) {
		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)
    if (y <= (-7.2d+96)) then
        tmp = t
    else if (y <= (-1.02d-81)) then
        tmp = t_1
    else if (y <= 7.5d-7) then
        tmp = x / (z / t)
    else if (y <= 3.1d+71) 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);
	double tmp;
	if (y <= -7.2e+96) {
		tmp = t;
	} else if (y <= -1.02e-81) {
		tmp = t_1;
	} else if (y <= 7.5e-7) {
		tmp = x / (z / t);
	} else if (y <= 3.1e+71) {
		tmp = t_1;
	} else {
		tmp = t;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = t * (x / -y)
	tmp = 0
	if y <= -7.2e+96:
		tmp = t
	elif y <= -1.02e-81:
		tmp = t_1
	elif y <= 7.5e-7:
		tmp = x / (z / t)
	elif y <= 3.1e+71:
		tmp = t_1
	else:
		tmp = t
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(t * Float64(x / Float64(-y)))
	tmp = 0.0
	if (y <= -7.2e+96)
		tmp = t;
	elseif (y <= -1.02e-81)
		tmp = t_1;
	elseif (y <= 7.5e-7)
		tmp = Float64(x / Float64(z / t));
	elseif (y <= 3.1e+71)
		tmp = t_1;
	else
		tmp = t;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = t * (x / -y);
	tmp = 0.0;
	if (y <= -7.2e+96)
		tmp = t;
	elseif (y <= -1.02e-81)
		tmp = t_1;
	elseif (y <= 7.5e-7)
		tmp = x / (z / t);
	elseif (y <= 3.1e+71)
		tmp = t_1;
	else
		tmp = t;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(t * N[(x / (-y)), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -7.2e+96], t, If[LessEqual[y, -1.02e-81], t$95$1, If[LessEqual[y, 7.5e-7], N[(x / N[(z / t), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 3.1e+71], t$95$1, t]]]]]

Derivation

1. Split input into 3 regimes

2. if y < -7.20000000000000026e96 or 3.10000000000000018e71 < y

   1. Initial program 99.9%

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

      1. associate-*l/ 74.8%

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

      2. associate-/l* 65.2%

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

   3. Simplified 65.2%

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

   5. Taylor expanded in y around inf 68.1%

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

   if -7.20000000000000026e96 < y < -1.01999999999999998e-81 or 7.5000000000000002e-7 < y < 3.10000000000000018e71

   1. Initial program 97.8%

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

      1. associate-*l/ 91.1%

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

      2. associate-/l* 95.8%

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

   3. Simplified 95.8%

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

   5. Taylor expanded in z around 0 57.1%

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

      1. associate-*r/ 57.1%

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

      2. neg-mul-1 57.1%

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

   7. Simplified 57.1%

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

   8. Taylor expanded in x around inf 47.0%

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

      1. mul-1-neg 47.0%

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

      2. associate-/l* 50.3%

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

      3. distribute-rgt-neg-in 50.3%

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

      4. distribute-frac-neg 50.3%

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

   10. Simplified 50.3%

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

   if -1.01999999999999998e-81 < y < 7.5000000000000002e-7

   1. Initial program 94.4%

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

      1. associate-*l/ 88.7%

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

      2. associate-/l* 95.9%

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

   3. Simplified 95.9%

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

   5. Taylor expanded in y around 0 69.2%

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

      1. frac-2neg 69.2%

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

      2. neg-sub0 69.2%

         \[\leadsto \frac{\color{blue}{0 - t \cdot x}}{-z} \]

      3. div-sub 69.2%

         \[\leadsto \color{blue}{\frac{0}{-z} - \frac{t \cdot x}{-z}} \]

      4. add-sqr-sqrt 39.5%

         \[\leadsto \frac{0}{-z} - \frac{\color{blue}{\sqrt{t \cdot x} \cdot \sqrt{t \cdot x}}}{-z} \]

      5. sqrt-unprod 32.0%

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

      6. sqr-neg 32.0%

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

      7. sqrt-unprod 12.4%

         \[\leadsto \frac{0}{-z} - \frac{\color{blue}{\sqrt{-t \cdot x} \cdot \sqrt{-t \cdot x}}}{-z} \]

      8. add-sqr-sqrt 16.5%

         \[\leadsto \frac{0}{-z} - \frac{\color{blue}{-t \cdot x}}{-z} \]

      9. frac-2neg 16.5%

         \[\leadsto \frac{0}{-z} - \color{blue}{\frac{t \cdot x}{z}} \]

      10. *-commutative 16.5%

          \[\leadsto \frac{0}{-z} - \frac{\color{blue}{x \cdot t}}{z} \]

      11. associate-/l* 16.5%

          \[\leadsto \frac{0}{-z} - \color{blue}{x \cdot \frac{t}{z}} \]

   7. Applied egg-rr 16.5%

      \[\leadsto \color{blue}{\frac{0}{-z} - x \cdot \frac{t}{z}} \]
   8. Step-by-step derivation

      1. div0 16.5%

         \[\leadsto \color{blue}{0} - x \cdot \frac{t}{z} \]

      2. neg-sub0 16.5%

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

      3. distribute-rgt-neg-in 16.5%

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

   9. Simplified 16.5%

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

       1. add-sqr-sqrt 12.5%

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

       2. sqrt-unprod 34.7%

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

       3. sqr-neg 34.7%

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

       4. sqrt-unprod 35.6%

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

       5. add-sqr-sqrt 76.3%

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

       6. clear-num 76.2%

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

       7. un-div-inv 76.9%

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

   11. Applied egg-rr 76.9%

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

4. Final simplification 68.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -7.2 \cdot 10^{+96}:\\ \;\;\;\;t\\ \mathbf{elif}\;y \leq -1.02 \cdot 10^{-81}:\\ \;\;\;\;t \cdot \frac{x}{-y}\\ \mathbf{elif}\;y \leq 7.5 \cdot 10^{-7}:\\ \;\;\;\;\frac{x}{\frac{z}{t}}\\ \mathbf{elif}\;y \leq 3.1 \cdot 10^{+71}:\\ \;\;\;\;t \cdot \frac{x}{-y}\\ \mathbf{else}:\\ \;\;\;\;t\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 59.9% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -4.2 \cdot 10^{+97}:\\ \;\;\;\;t\\ \mathbf{elif}\;y \leq -6.3 \cdot 10^{-84}:\\ \;\;\;\;\frac{t}{\frac{y}{-x}}\\ \mathbf{elif}\;y \leq 450:\\ \;\;\;\;\frac{x}{\frac{z}{t}}\\ \mathbf{elif}\;y \leq 3 \cdot 10^{+71}:\\ \;\;\;\;t \cdot \frac{x}{-y}\\ \mathbf{else}:\\ \;\;\;\;t\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= y -4.2e+97)
   t
   (if (<= y -6.3e-84)
     (/ t (/ y (- x)))
     (if (<= y 450.0) (/ x (/ z t)) (if (<= y 3e+71) (* t (/ x (- y))) t)))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (y <= -4.2e+97) {
		tmp = t;
	} else if (y <= -6.3e-84) {
		tmp = t / (y / -x);
	} else if (y <= 450.0) {
		tmp = x / (z / t);
	} else if (y <= 3e+71) {
		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 <= (-4.2d+97)) then
        tmp = t
    else if (y <= (-6.3d-84)) then
        tmp = t / (y / -x)
    else if (y <= 450.0d0) then
        tmp = x / (z / t)
    else if (y <= 3d+71) 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 <= -4.2e+97) {
		tmp = t;
	} else if (y <= -6.3e-84) {
		tmp = t / (y / -x);
	} else if (y <= 450.0) {
		tmp = x / (z / t);
	} else if (y <= 3e+71) {
		tmp = t * (x / -y);
	} else {
		tmp = t;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if y <= -4.2e+97:
		tmp = t
	elif y <= -6.3e-84:
		tmp = t / (y / -x)
	elif y <= 450.0:
		tmp = x / (z / t)
	elif y <= 3e+71:
		tmp = t * (x / -y)
	else:
		tmp = t
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (y <= -4.2e+97)
		tmp = t;
	elseif (y <= -6.3e-84)
		tmp = Float64(t / Float64(y / Float64(-x)));
	elseif (y <= 450.0)
		tmp = Float64(x / Float64(z / t));
	elseif (y <= 3e+71)
		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 <= -4.2e+97)
		tmp = t;
	elseif (y <= -6.3e-84)
		tmp = t / (y / -x);
	elseif (y <= 450.0)
		tmp = x / (z / t);
	elseif (y <= 3e+71)
		tmp = t * (x / -y);
	else
		tmp = t;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[y, -4.2e+97], t, If[LessEqual[y, -6.3e-84], N[(t / N[(y / (-x)), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 450.0], N[(x / N[(z / t), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 3e+71], N[(t * N[(x / (-y)), $MachinePrecision]), $MachinePrecision], t]]]]

Derivation

1. Split input into 4 regimes

2. if y < -4.20000000000000023e97 or 3.00000000000000013e71 < y

   1. Initial program 99.9%

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

      1. associate-*l/ 74.8%

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

      2. associate-/l* 65.2%

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

   3. Simplified 65.2%

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

   5. Taylor expanded in y around inf 68.1%

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

   if -4.20000000000000023e97 < y < -6.3000000000000004e-84

   1. Initial program 96.7%

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

      1. associate-*l/ 96.6%

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

      2. associate-/l* 96.7%

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

   3. Simplified 96.7%

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

      1. associate-*r/ 96.6%

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

      2. associate-*l/ 96.7%

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

      3. *-commutative 96.7%

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

      4. clear-num 96.6%

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

      5. un-div-inv 96.8%

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

   6. Applied egg-rr 96.8%

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

   7. Taylor expanded in x around inf 61.5%

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

   8. Taylor expanded in z around 0 49.6%

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

      1. neg-mul-1 49.6%

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

      2. distribute-neg-frac 49.6%

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

   10. Simplified 49.6%

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

   if -6.3000000000000004e-84 < y < 450

   1. Initial program 94.4%

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

      1. associate-*l/ 88.7%

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

      2. associate-/l* 95.9%

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

   3. Simplified 95.9%

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

   5. Taylor expanded in y around 0 69.2%

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

      1. frac-2neg 69.2%

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

      2. neg-sub0 69.2%

         \[\leadsto \frac{\color{blue}{0 - t \cdot x}}{-z} \]

      3. div-sub 69.2%

         \[\leadsto \color{blue}{\frac{0}{-z} - \frac{t \cdot x}{-z}} \]

      4. add-sqr-sqrt 39.5%

         \[\leadsto \frac{0}{-z} - \frac{\color{blue}{\sqrt{t \cdot x} \cdot \sqrt{t \cdot x}}}{-z} \]

      5. sqrt-unprod 32.0%

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

      6. sqr-neg 32.0%

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

      7. sqrt-unprod 12.4%

         \[\leadsto \frac{0}{-z} - \frac{\color{blue}{\sqrt{-t \cdot x} \cdot \sqrt{-t \cdot x}}}{-z} \]

      8. add-sqr-sqrt 16.5%

         \[\leadsto \frac{0}{-z} - \frac{\color{blue}{-t \cdot x}}{-z} \]

      9. frac-2neg 16.5%

         \[\leadsto \frac{0}{-z} - \color{blue}{\frac{t \cdot x}{z}} \]

      10. *-commutative 16.5%

          \[\leadsto \frac{0}{-z} - \frac{\color{blue}{x \cdot t}}{z} \]

      11. associate-/l* 16.5%

          \[\leadsto \frac{0}{-z} - \color{blue}{x \cdot \frac{t}{z}} \]

   7. Applied egg-rr 16.5%

      \[\leadsto \color{blue}{\frac{0}{-z} - x \cdot \frac{t}{z}} \]
   8. Step-by-step derivation

      1. div0 16.5%

         \[\leadsto \color{blue}{0} - x \cdot \frac{t}{z} \]

      2. neg-sub0 16.5%

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

      3. distribute-rgt-neg-in 16.5%

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

   9. Simplified 16.5%

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

       1. add-sqr-sqrt 12.5%

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

       2. sqrt-unprod 34.7%

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

       3. sqr-neg 34.7%

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

       4. sqrt-unprod 35.6%

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

       5. add-sqr-sqrt 76.3%

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

       6. clear-num 76.2%

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

       7. un-div-inv 76.9%

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

   11. Applied egg-rr 76.9%

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

   if 450 < y < 3.00000000000000013e71

   1. Initial program 99.4%

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

      1. associate-*l/ 83.2%

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

      2. associate-/l* 94.5%

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

   3. Simplified 94.5%

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

   5. Taylor expanded in z around 0 56.0%

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

      1. associate-*r/ 56.0%

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

      2. neg-mul-1 56.0%

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

   7. Simplified 56.0%

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

   8. Taylor expanded in x around inf 39.1%

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

      1. mul-1-neg 39.1%

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

      2. associate-/l* 51.4%

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

      3. distribute-rgt-neg-in 51.4%

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

      4. distribute-frac-neg 51.4%

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

   10. Simplified 51.4%

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

4. Final simplification 68.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -4.2 \cdot 10^{+97}:\\ \;\;\;\;t\\ \mathbf{elif}\;y \leq -6.3 \cdot 10^{-84}:\\ \;\;\;\;\frac{t}{\frac{y}{-x}}\\ \mathbf{elif}\;y \leq 450:\\ \;\;\;\;\frac{x}{\frac{z}{t}}\\ \mathbf{elif}\;y \leq 3 \cdot 10^{+71}:\\ \;\;\;\;t \cdot \frac{x}{-y}\\ \mathbf{else}:\\ \;\;\;\;t\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 59.8% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -2.1 \cdot 10^{+97}:\\ \;\;\;\;t\\ \mathbf{elif}\;y \leq -9.6 \cdot 10^{-82}:\\ \;\;\;\;\frac{x \cdot \left(-t\right)}{y}\\ \mathbf{elif}\;y \leq 0.0105:\\ \;\;\;\;\frac{x}{\frac{z}{t}}\\ \mathbf{elif}\;y \leq 3.1 \cdot 10^{+72}:\\ \;\;\;\;t \cdot \frac{x}{-y}\\ \mathbf{else}:\\ \;\;\;\;t\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= y -2.1e+97)
   t
   (if (<= y -9.6e-82)
     (/ (* x (- t)) y)
     (if (<= y 0.0105)
       (/ x (/ z t))
       (if (<= y 3.1e+72) (* t (/ x (- y))) t)))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (y <= -2.1e+97) {
		tmp = t;
	} else if (y <= -9.6e-82) {
		tmp = (x * -t) / y;
	} else if (y <= 0.0105) {
		tmp = x / (z / t);
	} else if (y <= 3.1e+72) {
		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 <= (-2.1d+97)) then
        tmp = t
    else if (y <= (-9.6d-82)) then
        tmp = (x * -t) / y
    else if (y <= 0.0105d0) then
        tmp = x / (z / t)
    else if (y <= 3.1d+72) 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 <= -2.1e+97) {
		tmp = t;
	} else if (y <= -9.6e-82) {
		tmp = (x * -t) / y;
	} else if (y <= 0.0105) {
		tmp = x / (z / t);
	} else if (y <= 3.1e+72) {
		tmp = t * (x / -y);
	} else {
		tmp = t;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if y <= -2.1e+97:
		tmp = t
	elif y <= -9.6e-82:
		tmp = (x * -t) / y
	elif y <= 0.0105:
		tmp = x / (z / t)
	elif y <= 3.1e+72:
		tmp = t * (x / -y)
	else:
		tmp = t
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (y <= -2.1e+97)
		tmp = t;
	elseif (y <= -9.6e-82)
		tmp = Float64(Float64(x * Float64(-t)) / y);
	elseif (y <= 0.0105)
		tmp = Float64(x / Float64(z / t));
	elseif (y <= 3.1e+72)
		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 <= -2.1e+97)
		tmp = t;
	elseif (y <= -9.6e-82)
		tmp = (x * -t) / y;
	elseif (y <= 0.0105)
		tmp = x / (z / t);
	elseif (y <= 3.1e+72)
		tmp = t * (x / -y);
	else
		tmp = t;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[y, -2.1e+97], t, If[LessEqual[y, -9.6e-82], N[(N[(x * (-t)), $MachinePrecision] / y), $MachinePrecision], If[LessEqual[y, 0.0105], N[(x / N[(z / t), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 3.1e+72], N[(t * N[(x / (-y)), $MachinePrecision]), $MachinePrecision], t]]]]

Derivation

1. Split input into 4 regimes

2. if y < -2.10000000000000012e97 or 3.09999999999999988e72 < y

   1. Initial program 99.9%

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

      1. associate-*l/ 74.8%

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

      2. associate-/l* 65.2%

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

   3. Simplified 65.2%

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

   5. Taylor expanded in y around inf 68.1%

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

   if -2.10000000000000012e97 < y < -9.60000000000000033e-82

   1. Initial program 96.7%

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

      1. associate-*l/ 96.6%

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

      2. associate-/l* 96.7%

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

   3. Simplified 96.7%

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

   5. Taylor expanded in z around 0 57.8%

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

      1. associate-*r/ 57.8%

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

      2. neg-mul-1 57.8%

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

   7. Simplified 57.8%

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

   8. Taylor expanded in x around inf 52.4%

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

      1. associate-*r/ 52.4%

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

      2. mul-1-neg 52.4%

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

   10. Simplified 52.4%

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

   if -9.60000000000000033e-82 < y < 0.0105000000000000007

   1. Initial program 94.4%

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

      1. associate-*l/ 88.7%

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

      2. associate-/l* 95.9%

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

   3. Simplified 95.9%

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

   5. Taylor expanded in y around 0 69.2%

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

      1. frac-2neg 69.2%

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

      2. neg-sub0 69.2%

         \[\leadsto \frac{\color{blue}{0 - t \cdot x}}{-z} \]

      3. div-sub 69.2%

         \[\leadsto \color{blue}{\frac{0}{-z} - \frac{t \cdot x}{-z}} \]

      4. add-sqr-sqrt 39.5%

         \[\leadsto \frac{0}{-z} - \frac{\color{blue}{\sqrt{t \cdot x} \cdot \sqrt{t \cdot x}}}{-z} \]

      5. sqrt-unprod 32.0%

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

      6. sqr-neg 32.0%

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

      7. sqrt-unprod 12.4%

         \[\leadsto \frac{0}{-z} - \frac{\color{blue}{\sqrt{-t \cdot x} \cdot \sqrt{-t \cdot x}}}{-z} \]

      8. add-sqr-sqrt 16.5%

         \[\leadsto \frac{0}{-z} - \frac{\color{blue}{-t \cdot x}}{-z} \]

      9. frac-2neg 16.5%

         \[\leadsto \frac{0}{-z} - \color{blue}{\frac{t \cdot x}{z}} \]

      10. *-commutative 16.5%

          \[\leadsto \frac{0}{-z} - \frac{\color{blue}{x \cdot t}}{z} \]

      11. associate-/l* 16.5%

          \[\leadsto \frac{0}{-z} - \color{blue}{x \cdot \frac{t}{z}} \]

   7. Applied egg-rr 16.5%

      \[\leadsto \color{blue}{\frac{0}{-z} - x \cdot \frac{t}{z}} \]
   8. Step-by-step derivation

      1. div0 16.5%

         \[\leadsto \color{blue}{0} - x \cdot \frac{t}{z} \]

      2. neg-sub0 16.5%

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

      3. distribute-rgt-neg-in 16.5%

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

   9. Simplified 16.5%

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

       1. add-sqr-sqrt 12.5%

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

       2. sqrt-unprod 34.7%

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

       3. sqr-neg 34.7%

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

       4. sqrt-unprod 35.6%

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

       5. add-sqr-sqrt 76.3%

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

       6. clear-num 76.2%

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

       7. un-div-inv 76.9%

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

   11. Applied egg-rr 76.9%

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

   if 0.0105000000000000007 < y < 3.09999999999999988e72

   1. Initial program 99.4%

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

      1. associate-*l/ 83.2%

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

      2. associate-/l* 94.5%

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

   3. Simplified 94.5%

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

   5. Taylor expanded in z around 0 56.0%

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

      1. associate-*r/ 56.0%

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

      2. neg-mul-1 56.0%

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

   7. Simplified 56.0%

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

   8. Taylor expanded in x around inf 39.1%

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

      1. mul-1-neg 39.1%

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

      2. associate-/l* 51.4%

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

      3. distribute-rgt-neg-in 51.4%

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

      4. distribute-frac-neg 51.4%

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

   10. Simplified 51.4%

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

4. Final simplification 68.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -2.1 \cdot 10^{+97}:\\ \;\;\;\;t\\ \mathbf{elif}\;y \leq -9.6 \cdot 10^{-82}:\\ \;\;\;\;\frac{x \cdot \left(-t\right)}{y}\\ \mathbf{elif}\;y \leq 0.0105:\\ \;\;\;\;\frac{x}{\frac{z}{t}}\\ \mathbf{elif}\;y \leq 3.1 \cdot 10^{+72}:\\ \;\;\;\;t \cdot \frac{x}{-y}\\ \mathbf{else}:\\ \;\;\;\;t\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 61.1% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -6.5 \cdot 10^{+96}:\\ \;\;\;\;t\\ \mathbf{elif}\;y \leq -0.0037:\\ \;\;\;\;\frac{y}{z} \cdot \left(-t\right)\\ \mathbf{elif}\;y \leq -1.95 \cdot 10^{-10}:\\ \;\;\;\;t\\ \mathbf{elif}\;y \leq 8.6 \cdot 10^{+68}:\\ \;\;\;\;t \cdot \frac{x}{z}\\ \mathbf{else}:\\ \;\;\;\;t\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= y -6.5e+96)
   t
   (if (<= y -0.0037)
     (* (/ y z) (- t))
     (if (<= y -1.95e-10) t (if (<= y 8.6e+68) (* t (/ x z)) t)))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (y <= -6.5e+96) {
		tmp = t;
	} else if (y <= -0.0037) {
		tmp = (y / z) * -t;
	} else if (y <= -1.95e-10) {
		tmp = t;
	} else if (y <= 8.6e+68) {
		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 <= (-6.5d+96)) then
        tmp = t
    else if (y <= (-0.0037d0)) then
        tmp = (y / z) * -t
    else if (y <= (-1.95d-10)) then
        tmp = t
    else if (y <= 8.6d+68) 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 <= -6.5e+96) {
		tmp = t;
	} else if (y <= -0.0037) {
		tmp = (y / z) * -t;
	} else if (y <= -1.95e-10) {
		tmp = t;
	} else if (y <= 8.6e+68) {
		tmp = t * (x / z);
	} else {
		tmp = t;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if y <= -6.5e+96:
		tmp = t
	elif y <= -0.0037:
		tmp = (y / z) * -t
	elif y <= -1.95e-10:
		tmp = t
	elif y <= 8.6e+68:
		tmp = t * (x / z)
	else:
		tmp = t
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (y <= -6.5e+96)
		tmp = t;
	elseif (y <= -0.0037)
		tmp = Float64(Float64(y / z) * Float64(-t));
	elseif (y <= -1.95e-10)
		tmp = t;
	elseif (y <= 8.6e+68)
		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 <= -6.5e+96)
		tmp = t;
	elseif (y <= -0.0037)
		tmp = (y / z) * -t;
	elseif (y <= -1.95e-10)
		tmp = t;
	elseif (y <= 8.6e+68)
		tmp = t * (x / z);
	else
		tmp = t;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[y, -6.5e+96], t, If[LessEqual[y, -0.0037], N[(N[(y / z), $MachinePrecision] * (-t)), $MachinePrecision], If[LessEqual[y, -1.95e-10], t, If[LessEqual[y, 8.6e+68], N[(t * N[(x / z), $MachinePrecision]), $MachinePrecision], t]]]]

Derivation

1. Split input into 3 regimes

2. if y < -6.5e96 or -0.0037000000000000002 < y < -1.95e-10 or 8.6000000000000002e68 < y

   1. Initial program 99.9%

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

      1. associate-*l/ 74.6%

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

      2. associate-/l* 66.4%

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

   3. Simplified 66.4%

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

   5. Taylor expanded in y around inf 68.1%

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

   if -6.5e96 < y < -0.0037000000000000002

   1. Initial program 99.7%

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

      1. associate-*l/ 99.7%

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

      2. associate-/l* 94.6%

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

   3. Simplified 94.6%

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

   5. Taylor expanded in z around inf 48.2%

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

      1. *-commutative 48.2%

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

      2. associate-/l* 48.2%

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

   7. Simplified 48.2%

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

   8. Taylor expanded in x around 0 44.1%

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

      1. mul-1-neg 44.1%

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

      2. associate-/l* 39.3%

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

      3. distribute-rgt-neg-in 39.3%

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

   10. Simplified 39.3%

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

   if -1.95e-10 < y < 8.6000000000000002e68

   1. Initial program 94.9%

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

   3. Taylor expanded in y around 0 67.9%

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

4. Final simplification 66.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -6.5 \cdot 10^{+96}:\\ \;\;\;\;t\\ \mathbf{elif}\;y \leq -0.0037:\\ \;\;\;\;\frac{y}{z} \cdot \left(-t\right)\\ \mathbf{elif}\;y \leq -1.95 \cdot 10^{-10}:\\ \;\;\;\;t\\ \mathbf{elif}\;y \leq 8.6 \cdot 10^{+68}:\\ \;\;\;\;t \cdot \frac{x}{z}\\ \mathbf{else}:\\ \;\;\;\;t\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 74.5% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := t \cdot \frac{y}{y - z}\\ \mathbf{if}\;y \leq -2 \cdot 10^{+191}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y \leq -2.3 \cdot 10^{-10}:\\ \;\;\;\;t - \frac{t \cdot x}{y}\\ \mathbf{elif}\;y \leq 1.1 \cdot 10^{+115}:\\ \;\;\;\;\frac{t}{\frac{z - y}{x}}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (* t (/ y (- y z)))))
   (if (<= y -2e+191)
     t_1
     (if (<= y -2.3e-10)
       (- t (/ (* t x) y))
       (if (<= y 1.1e+115) (/ t (/ (- z y) x)) t_1)))))

C

double code(double x, double y, double z, double t) {
	double t_1 = t * (y / (y - z));
	double tmp;
	if (y <= -2e+191) {
		tmp = t_1;
	} else if (y <= -2.3e-10) {
		tmp = t - ((t * x) / y);
	} else if (y <= 1.1e+115) {
		tmp = t / ((z - y) / x);
	} 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 <= (-2d+191)) then
        tmp = t_1
    else if (y <= (-2.3d-10)) then
        tmp = t - ((t * x) / y)
    else if (y <= 1.1d+115) then
        tmp = t / ((z - y) / x)
    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 <= -2e+191) {
		tmp = t_1;
	} else if (y <= -2.3e-10) {
		tmp = t - ((t * x) / y);
	} else if (y <= 1.1e+115) {
		tmp = t / ((z - y) / x);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = t * (y / (y - z))
	tmp = 0
	if y <= -2e+191:
		tmp = t_1
	elif y <= -2.3e-10:
		tmp = t - ((t * x) / y)
	elif y <= 1.1e+115:
		tmp = t / ((z - y) / x)
	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 <= -2e+191)
		tmp = t_1;
	elseif (y <= -2.3e-10)
		tmp = Float64(t - Float64(Float64(t * x) / y));
	elseif (y <= 1.1e+115)
		tmp = Float64(t / Float64(Float64(z - y) / x));
	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 <= -2e+191)
		tmp = t_1;
	elseif (y <= -2.3e-10)
		tmp = t - ((t * x) / y);
	elseif (y <= 1.1e+115)
		tmp = t / ((z - y) / x);
	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, -2e+191], t$95$1, If[LessEqual[y, -2.3e-10], N[(t - N[(N[(t * x), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 1.1e+115], N[(t / N[(N[(z - y), $MachinePrecision] / x), $MachinePrecision]), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if y < -2.00000000000000015e191 or 1.1e115 < y

   1. Initial program 99.9%

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

   3. Taylor expanded in x around 0 92.7%

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

      1. neg-mul-1 92.7%

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

      2. distribute-neg-frac2 92.7%

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

   5. Simplified 92.7%

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

   if -2.00000000000000015e191 < y < -2.30000000000000007e-10

   1. Initial program 99.7%

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

      1. associate-*l/ 96.9%

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

      2. associate-/l* 83.7%

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

   3. Simplified 83.7%

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

   5. Taylor expanded in z around 0 64.6%

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

      1. associate-*r/ 64.6%

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

      2. neg-mul-1 64.6%

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

   7. Simplified 64.6%

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

   8. Taylor expanded in x around 0 72.8%

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

      1. mul-1-neg 72.8%

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

      2. sub-neg 72.8%

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

   10. Simplified 72.8%

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

   if -2.30000000000000007e-10 < y < 1.1e115

   1. Initial program 95.1%

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

      1. associate-*l/ 88.7%

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

      2. associate-/l* 95.5%

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

   3. Simplified 95.5%

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

      1. associate-*r/ 88.7%

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

      2. associate-*l/ 95.1%

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

      3. *-commutative 95.1%

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

      4. clear-num 95.0%

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

      5. un-div-inv 95.4%

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

   6. Applied egg-rr 95.4%

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

   7. Taylor expanded in x around inf 83.9%

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

4. Final simplification 84.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -2 \cdot 10^{+191}:\\ \;\;\;\;t \cdot \frac{y}{y - z}\\ \mathbf{elif}\;y \leq -2.3 \cdot 10^{-10}:\\ \;\;\;\;t - \frac{t \cdot x}{y}\\ \mathbf{elif}\;y \leq 1.1 \cdot 10^{+115}:\\ \;\;\;\;\frac{t}{\frac{z - y}{x}}\\ \mathbf{else}:\\ \;\;\;\;t \cdot \frac{y}{y - z}\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 74.4% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -9.6 \cdot 10^{+193}:\\ \;\;\;\;\frac{t}{\frac{-z}{y} - -1}\\ \mathbf{elif}\;y \leq -1.45 \cdot 10^{-10}:\\ \;\;\;\;t - \frac{t \cdot x}{y}\\ \mathbf{elif}\;y \leq 2 \cdot 10^{+115}:\\ \;\;\;\;\frac{t}{\frac{z - y}{x}}\\ \mathbf{else}:\\ \;\;\;\;t \cdot \frac{y}{y - z}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= y -9.6e+193)
   (/ t (- (/ (- z) y) -1.0))
   (if (<= y -1.45e-10)
     (- t (/ (* t x) y))
     (if (<= y 2e+115) (/ t (/ (- z y) x)) (* t (/ y (- y z)))))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (y <= -9.6e+193) {
		tmp = t / ((-z / y) - -1.0);
	} else if (y <= -1.45e-10) {
		tmp = t - ((t * x) / y);
	} else if (y <= 2e+115) {
		tmp = t / ((z - y) / x);
	} else {
		tmp = t * (y / (y - z));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if (y <= (-9.6d+193)) then
        tmp = t / ((-z / y) - (-1.0d0))
    else if (y <= (-1.45d-10)) then
        tmp = t - ((t * x) / y)
    else if (y <= 2d+115) then
        tmp = t / ((z - y) / x)
    else
        tmp = t * (y / (y - z))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if (y <= -9.6e+193) {
		tmp = t / ((-z / y) - -1.0);
	} else if (y <= -1.45e-10) {
		tmp = t - ((t * x) / y);
	} else if (y <= 2e+115) {
		tmp = t / ((z - y) / x);
	} else {
		tmp = t * (y / (y - z));
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if y <= -9.6e+193:
		tmp = t / ((-z / y) - -1.0)
	elif y <= -1.45e-10:
		tmp = t - ((t * x) / y)
	elif y <= 2e+115:
		tmp = t / ((z - y) / x)
	else:
		tmp = t * (y / (y - z))
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (y <= -9.6e+193)
		tmp = Float64(t / Float64(Float64(Float64(-z) / y) - -1.0));
	elseif (y <= -1.45e-10)
		tmp = Float64(t - Float64(Float64(t * x) / y));
	elseif (y <= 2e+115)
		tmp = Float64(t / Float64(Float64(z - y) / x));
	else
		tmp = Float64(t * Float64(y / Float64(y - z)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (y <= -9.6e+193)
		tmp = t / ((-z / y) - -1.0);
	elseif (y <= -1.45e-10)
		tmp = t - ((t * x) / y);
	elseif (y <= 2e+115)
		tmp = t / ((z - y) / x);
	else
		tmp = t * (y / (y - z));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[y, -9.6e+193], N[(t / N[(N[((-z) / y), $MachinePrecision] - -1.0), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, -1.45e-10], N[(t - N[(N[(t * x), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 2e+115], N[(t / N[(N[(z - y), $MachinePrecision] / x), $MachinePrecision]), $MachinePrecision], N[(t * N[(y / N[(y - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 4 regimes

2. if y < -9.6e193

   1. Initial program 99.9%

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

      1. associate-*l/ 65.8%

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

      2. associate-/l* 62.6%

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

   3. Simplified 62.6%

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

      1. associate-*r/ 65.8%

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

      2. associate-*l/ 99.9%

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

      3. *-commutative 99.9%

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

      4. clear-num 99.9%

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

      5. un-div-inv 99.9%

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

   6. Applied egg-rr 99.9%

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

   7. Taylor expanded in x around 0 95.4%

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

      1. mul-1-neg 95.4%

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

      2. div-sub 95.5%

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

      3. sub-neg 95.5%

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

      4. *-inverses 95.5%

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

      5. metadata-eval 95.5%

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

   9. Simplified 95.5%

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

   if -9.6e193 < y < -1.4499999999999999e-10

   1. Initial program 99.7%

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

      1. associate-*l/ 96.9%

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

      2. associate-/l* 83.7%

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

   3. Simplified 83.7%

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

   5. Taylor expanded in z around 0 64.6%

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

      1. associate-*r/ 64.6%

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

      2. neg-mul-1 64.6%

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

   7. Simplified 64.6%

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

   8. Taylor expanded in x around 0 72.8%

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

      1. mul-1-neg 72.8%

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

      2. sub-neg 72.8%

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

   10. Simplified 72.8%

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

   if -1.4499999999999999e-10 < y < 2e115

   1. Initial program 95.1%

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

      1. associate-*l/ 88.7%

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

      2. associate-/l* 95.5%

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

   3. Simplified 95.5%

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

      1. associate-*r/ 88.7%

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

      2. associate-*l/ 95.1%

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

      3. *-commutative 95.1%

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

      4. clear-num 95.0%

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

      5. un-div-inv 95.4%

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

   6. Applied egg-rr 95.4%

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

   7. Taylor expanded in x around inf 83.9%

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

   if 2e115 < y

   1. Initial program 99.9%

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

   3. Taylor expanded in x around 0 91.1%

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

      1. neg-mul-1 91.1%

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

      2. distribute-neg-frac2 91.1%

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

   5. Simplified 91.1%

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

4. Final simplification 84.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -9.6 \cdot 10^{+193}:\\ \;\;\;\;\frac{t}{\frac{-z}{y} - -1}\\ \mathbf{elif}\;y \leq -1.45 \cdot 10^{-10}:\\ \;\;\;\;t - \frac{t \cdot x}{y}\\ \mathbf{elif}\;y \leq 2 \cdot 10^{+115}:\\ \;\;\;\;\frac{t}{\frac{z - y}{x}}\\ \mathbf{else}:\\ \;\;\;\;t \cdot \frac{y}{y - z}\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 90.1% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -1.8 \cdot 10^{+204}:\\ \;\;\;\;\frac{t}{\frac{-z}{y} - -1}\\ \mathbf{elif}\;y \leq 1.35 \cdot 10^{+132}:\\ \;\;\;\;\left(x - y\right) \cdot \frac{t}{z - y}\\ \mathbf{else}:\\ \;\;\;\;t \cdot \frac{y}{y - z}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= y -1.8e+204)
   (/ t (- (/ (- z) y) -1.0))
   (if (<= y 1.35e+132) (* (- x y) (/ t (- z y))) (* t (/ y (- y z))))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (y <= -1.8e+204) {
		tmp = t / ((-z / y) - -1.0);
	} else if (y <= 1.35e+132) {
		tmp = (x - y) * (t / (z - y));
	} else {
		tmp = t * (y / (y - z));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if (y <= (-1.8d+204)) then
        tmp = t / ((-z / y) - (-1.0d0))
    else if (y <= 1.35d+132) then
        tmp = (x - y) * (t / (z - y))
    else
        tmp = t * (y / (y - z))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if (y <= -1.8e+204) {
		tmp = t / ((-z / y) - -1.0);
	} else if (y <= 1.35e+132) {
		tmp = (x - y) * (t / (z - y));
	} else {
		tmp = t * (y / (y - z));
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if y <= -1.8e+204:
		tmp = t / ((-z / y) - -1.0)
	elif y <= 1.35e+132:
		tmp = (x - y) * (t / (z - y))
	else:
		tmp = t * (y / (y - z))
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (y <= -1.8e+204)
		tmp = Float64(t / Float64(Float64(Float64(-z) / y) - -1.0));
	elseif (y <= 1.35e+132)
		tmp = Float64(Float64(x - y) * Float64(t / Float64(z - y)));
	else
		tmp = Float64(t * Float64(y / Float64(y - z)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (y <= -1.8e+204)
		tmp = t / ((-z / y) - -1.0);
	elseif (y <= 1.35e+132)
		tmp = (x - y) * (t / (z - y));
	else
		tmp = t * (y / (y - z));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[y, -1.8e+204], N[(t / N[(N[((-z) / y), $MachinePrecision] - -1.0), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 1.35e+132], N[(N[(x - y), $MachinePrecision] * N[(t / N[(z - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(t * N[(y / N[(y - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if y < -1.8000000000000001e204

   1. Initial program 99.9%

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

      1. associate-*l/ 64.3%

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

      2. associate-/l* 60.8%

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

   3. Simplified 60.8%

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

      1. associate-*r/ 64.3%

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

      2. associate-*l/ 99.9%

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

      3. *-commutative 99.9%

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

      4. clear-num 99.9%

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

      5. un-div-inv 99.9%

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

   6. Applied egg-rr 99.9%

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

   7. Taylor expanded in x around 0 95.2%

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

      1. mul-1-neg 95.2%

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

      2. div-sub 95.3%

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

      3. sub-neg 95.3%

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

      4. *-inverses 95.3%

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

      5. metadata-eval 95.3%

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

   9. Simplified 95.3%

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

   if -1.8000000000000001e204 < y < 1.35e132

   1. Initial program 96.0%

      \[\frac{x - y}{z - y} \cdot t \]
   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* 93.4%

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

   3. Simplified 93.4%

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

   if 1.35e132 < y

   1. Initial program 99.9%

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

   3. Taylor expanded in x around 0 91.1%

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

      1. neg-mul-1 91.1%

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

      2. distribute-neg-frac2 91.1%

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

   5. Simplified 91.1%

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

4. Final simplification 93.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.8 \cdot 10^{+204}:\\ \;\;\;\;\frac{t}{\frac{-z}{y} - -1}\\ \mathbf{elif}\;y \leq 1.35 \cdot 10^{+132}:\\ \;\;\;\;\left(x - y\right) \cdot \frac{t}{z - y}\\ \mathbf{else}:\\ \;\;\;\;t \cdot \frac{y}{y - z}\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 72.0% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -2.2 \cdot 10^{-10} \lor \neg \left(y \leq 1.1 \cdot 10^{+115}\right):\\ \;\;\;\;t - \frac{t \cdot x}{y}\\ \mathbf{else}:\\ \;\;\;\;t \cdot \frac{x}{z - y}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= y -2.2e-10) (not (<= y 1.1e+115)))
   (- t (/ (* t x) y))
   (* t (/ x (- z y)))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((y <= -2.2e-10) || !(y <= 1.1e+115)) {
		tmp = t - ((t * x) / y);
	} else {
		tmp = t * (x / (z - y));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if ((y <= (-2.2d-10)) .or. (.not. (y <= 1.1d+115))) then
        tmp = t - ((t * x) / y)
    else
        tmp = t * (x / (z - y))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if ((y <= -2.2e-10) || !(y <= 1.1e+115)) {
		tmp = t - ((t * x) / y);
	} else {
		tmp = t * (x / (z - y));
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (y <= -2.2e-10) or not (y <= 1.1e+115):
		tmp = t - ((t * x) / y)
	else:
		tmp = t * (x / (z - y))
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((y <= -2.2e-10) || !(y <= 1.1e+115))
		tmp = Float64(t - Float64(Float64(t * x) / y));
	else
		tmp = Float64(t * Float64(x / Float64(z - y)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((y <= -2.2e-10) || ~((y <= 1.1e+115)))
		tmp = t - ((t * x) / y);
	else
		tmp = t * (x / (z - y));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[y, -2.2e-10], N[Not[LessEqual[y, 1.1e+115]], $MachinePrecision]], N[(t - N[(N[(t * x), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision], N[(t * N[(x / N[(z - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -2.1999999999999999e-10 or 1.1e115 < y

   1. Initial program 99.9%

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

      1. associate-*l/ 78.2%

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

      2. associate-/l* 69.9%

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

   3. Simplified 69.9%

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

   5. Taylor expanded in z around 0 54.7%

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

      1. associate-*r/ 54.7%

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

      2. neg-mul-1 54.7%

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

   7. Simplified 54.7%

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

   8. Taylor expanded in x around 0 76.0%

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

      1. mul-1-neg 76.0%

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

      2. sub-neg 76.0%

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

   10. Simplified 76.0%

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

   if -2.1999999999999999e-10 < y < 1.1e115

   1. Initial program 95.1%

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

   3. Taylor expanded in x around inf 83.6%

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

4. Final simplification 80.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -2.2 \cdot 10^{-10} \lor \neg \left(y \leq 1.1 \cdot 10^{+115}\right):\\ \;\;\;\;t - \frac{t \cdot x}{y}\\ \mathbf{else}:\\ \;\;\;\;t \cdot \frac{x}{z - y}\\ \end{array} \]
5. Add Preprocessing

Alternative 10: 72.1% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -3.1 \cdot 10^{-10} \lor \neg \left(y \leq 1.1 \cdot 10^{+115}\right):\\ \;\;\;\;t - \frac{t \cdot x}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{t}{\frac{z - y}{x}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= y -3.1e-10) (not (<= y 1.1e+115)))
   (- t (/ (* t x) y))
   (/ t (/ (- z y) x))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((y <= -3.1e-10) || !(y <= 1.1e+115)) {
		tmp = t - ((t * x) / y);
	} else {
		tmp = t / ((z - y) / x);
	}
	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 <= (-3.1d-10)) .or. (.not. (y <= 1.1d+115))) then
        tmp = t - ((t * x) / y)
    else
        tmp = t / ((z - y) / x)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if ((y <= -3.1e-10) || !(y <= 1.1e+115)) {
		tmp = t - ((t * x) / y);
	} else {
		tmp = t / ((z - y) / x);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (y <= -3.1e-10) or not (y <= 1.1e+115):
		tmp = t - ((t * x) / y)
	else:
		tmp = t / ((z - y) / x)
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((y <= -3.1e-10) || !(y <= 1.1e+115))
		tmp = Float64(t - Float64(Float64(t * x) / y));
	else
		tmp = Float64(t / Float64(Float64(z - y) / x));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((y <= -3.1e-10) || ~((y <= 1.1e+115)))
		tmp = t - ((t * x) / y);
	else
		tmp = t / ((z - y) / x);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[y, -3.1e-10], N[Not[LessEqual[y, 1.1e+115]], $MachinePrecision]], N[(t - N[(N[(t * x), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision], N[(t / N[(N[(z - y), $MachinePrecision] / x), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -3.10000000000000015e-10 or 1.1e115 < y

   1. Initial program 99.9%

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

      1. associate-*l/ 78.2%

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

      2. associate-/l* 69.9%

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

   3. Simplified 69.9%

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

   5. Taylor expanded in z around 0 54.7%

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

      1. associate-*r/ 54.7%

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

      2. neg-mul-1 54.7%

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

   7. Simplified 54.7%

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

   8. Taylor expanded in x around 0 76.0%

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

      1. mul-1-neg 76.0%

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

      2. sub-neg 76.0%

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

   10. Simplified 76.0%

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

   if -3.10000000000000015e-10 < y < 1.1e115

   1. Initial program 95.1%

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

      1. associate-*l/ 88.7%

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

      2. associate-/l* 95.5%

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

   3. Simplified 95.5%

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

      1. associate-*r/ 88.7%

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

      2. associate-*l/ 95.1%

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

      3. *-commutative 95.1%

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

      4. clear-num 95.0%

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

      5. un-div-inv 95.4%

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

   6. Applied egg-rr 95.4%

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

   7. Taylor expanded in x around inf 83.9%

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

4. Final simplification 81.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -3.1 \cdot 10^{-10} \lor \neg \left(y \leq 1.1 \cdot 10^{+115}\right):\\ \;\;\;\;t - \frac{t \cdot x}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{t}{\frac{z - y}{x}}\\ \end{array} \]
5. Add Preprocessing

Alternative 11: 66.5% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -2.1 \cdot 10^{+97}:\\ \;\;\;\;t\\ \mathbf{elif}\;y \leq 1.9 \cdot 10^{+69}:\\ \;\;\;\;\left(x - y\right) \cdot \frac{t}{z}\\ \mathbf{else}:\\ \;\;\;\;t\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= y -2.1e+97) t (if (<= y 1.9e+69) (* (- x y) (/ t z)) t)))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (y <= -2.1e+97) {
		tmp = t;
	} else if (y <= 1.9e+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 <= (-2.1d+97)) then
        tmp = t
    else if (y <= 1.9d+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 <= -2.1e+97) {
		tmp = t;
	} else if (y <= 1.9e+69) {
		tmp = (x - y) * (t / z);
	} else {
		tmp = t;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if y <= -2.1e+97:
		tmp = t
	elif y <= 1.9e+69:
		tmp = (x - y) * (t / z)
	else:
		tmp = t
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (y <= -2.1e+97)
		tmp = t;
	elseif (y <= 1.9e+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 <= -2.1e+97)
		tmp = t;
	elseif (y <= 1.9e+69)
		tmp = (x - y) * (t / z);
	else
		tmp = t;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[y, -2.1e+97], t, If[LessEqual[y, 1.9e+69], N[(N[(x - y), $MachinePrecision] * N[(t / z), $MachinePrecision]), $MachinePrecision], t]]

Derivation

1. Split input into 2 regimes

2. if y < -2.10000000000000012e97 or 1.90000000000000014e69 < y

   1. Initial program 99.9%

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

      1. associate-*l/ 74.1%

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

      2. associate-/l* 65.6%

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

   3. Simplified 65.6%

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

   5. Taylor expanded in y around inf 67.3%

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

   if -2.10000000000000012e97 < y < 1.90000000000000014e69

   1. Initial program 95.5%

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

      1. associate-*l/ 89.9%

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

      2. associate-/l* 95.8%

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

   3. Simplified 95.8%

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

   5. Taylor expanded in z around inf 66.8%

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

      1. *-commutative 66.8%

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

      2. associate-/l* 72.1%

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

   7. Simplified 72.1%

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

4. Final simplification 70.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -2.1 \cdot 10^{+97}:\\ \;\;\;\;t\\ \mathbf{elif}\;y \leq 1.9 \cdot 10^{+69}:\\ \;\;\;\;\left(x - y\right) \cdot \frac{t}{z}\\ \mathbf{else}:\\ \;\;\;\;t\\ \end{array} \]
5. Add Preprocessing

Alternative 12: 70.0% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -3.1 \cdot 10^{+97}:\\ \;\;\;\;t\\ \mathbf{elif}\;y \leq 2 \cdot 10^{+115}:\\ \;\;\;\;t \cdot \frac{x}{z - y}\\ \mathbf{else}:\\ \;\;\;\;t\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= y -3.1e+97) t (if (<= y 2e+115) (* t (/ x (- z y))) t)))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (y <= -3.1e+97) {
		tmp = t;
	} else if (y <= 2e+115) {
		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 <= (-3.1d+97)) then
        tmp = t
    else if (y <= 2d+115) 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 <= -3.1e+97) {
		tmp = t;
	} else if (y <= 2e+115) {
		tmp = t * (x / (z - y));
	} else {
		tmp = t;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if y <= -3.1e+97:
		tmp = t
	elif y <= 2e+115:
		tmp = t * (x / (z - y))
	else:
		tmp = t
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (y <= -3.1e+97)
		tmp = t;
	elseif (y <= 2e+115)
		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 <= -3.1e+97)
		tmp = t;
	elseif (y <= 2e+115)
		tmp = t * (x / (z - y));
	else
		tmp = t;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[y, -3.1e+97], t, If[LessEqual[y, 2e+115], N[(t * N[(x / N[(z - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t]]

Derivation

1. Split input into 2 regimes

2. if y < -3.09999999999999981e97 or 2e115 < y

   1. Initial program 99.9%

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

      1. associate-*l/ 72.6%

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

      2. associate-/l* 63.2%

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

   3. Simplified 63.2%

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

   5. Taylor expanded in y around inf 71.4%

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

   if -3.09999999999999981e97 < y < 2e115

   1. Initial program 95.6%

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

   3. Taylor expanded in x around inf 80.2%

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

4. Final simplification 77.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -3.1 \cdot 10^{+97}:\\ \;\;\;\;t\\ \mathbf{elif}\;y \leq 2 \cdot 10^{+115}:\\ \;\;\;\;t \cdot \frac{x}{z - y}\\ \mathbf{else}:\\ \;\;\;\;t\\ \end{array} \]
5. Add Preprocessing

Alternative 13: 35.7% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -1.18 \cdot 10^{-148}:\\ \;\;\;\;t\\ \mathbf{elif}\;y \leq 8.2 \cdot 10^{-173}:\\ \;\;\;\;t \cdot \frac{x}{y}\\ \mathbf{else}:\\ \;\;\;\;t\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= y -1.18e-148) t (if (<= y 8.2e-173) (* t (/ x y)) t)))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (y <= -1.18e-148) {
		tmp = t;
	} else if (y <= 8.2e-173) {
		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 <= (-1.18d-148)) then
        tmp = t
    else if (y <= 8.2d-173) 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 <= -1.18e-148) {
		tmp = t;
	} else if (y <= 8.2e-173) {
		tmp = t * (x / y);
	} else {
		tmp = t;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if y <= -1.18e-148:
		tmp = t
	elif y <= 8.2e-173:
		tmp = t * (x / y)
	else:
		tmp = t
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (y <= -1.18e-148)
		tmp = t;
	elseif (y <= 8.2e-173)
		tmp = Float64(t * Float64(x / y));
	else
		tmp = t;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (y <= -1.18e-148)
		tmp = t;
	elseif (y <= 8.2e-173)
		tmp = t * (x / y);
	else
		tmp = t;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[y, -1.18e-148], t, If[LessEqual[y, 8.2e-173], N[(t * N[(x / y), $MachinePrecision]), $MachinePrecision], t]]

Derivation

1. Split input into 2 regimes

2. if y < -1.18e-148 or 8.1999999999999995e-173 < y

   1. Initial program 98.7%

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

      1. associate-*l/ 84.3%

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

      2. associate-/l* 81.8%

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

   3. Simplified 81.8%

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

   5. Taylor expanded in y around inf 37.5%

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

   if -1.18e-148 < y < 8.1999999999999995e-173

   1. Initial program 92.4%

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

      1. associate-*l/ 85.9%

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

      2. associate-/l* 96.0%

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

   3. Simplified 96.0%

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

   5. Taylor expanded in z around 0 13.8%

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

      1. associate-*r/ 13.8%

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

      2. neg-mul-1 13.8%

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

   7. Simplified 13.8%

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

   8. Taylor expanded in x around inf 24.7%

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

      1. associate-*r/ 24.7%

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

      2. mul-1-neg 24.7%

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

   10. Simplified 24.7%

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

       1. add-sqr-sqrt 17.6%

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

       2. sqrt-unprod 25.4%

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

       3. sqr-neg 25.4%

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

       4. sqrt-unprod 15.6%

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

       5. add-sqr-sqrt 28.8%

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

       6. *-commutative 28.8%

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

       7. associate-/l* 21.3%

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

   12. Applied egg-rr 21.3%

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

       1. associate-*r/ 28.8%

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

       2. *-commutative 28.8%

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

       3. associate-*r/ 21.4%

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

   14. Simplified 21.4%

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

4. Final simplification 32.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.18 \cdot 10^{-148}:\\ \;\;\;\;t\\ \mathbf{elif}\;y \leq 8.2 \cdot 10^{-173}:\\ \;\;\;\;t \cdot \frac{x}{y}\\ \mathbf{else}:\\ \;\;\;\;t\\ \end{array} \]
5. Add Preprocessing

Alternative 14: 60.5% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -1.75 \cdot 10^{-10}:\\ \;\;\;\;t\\ \mathbf{elif}\;y \leq 6 \cdot 10^{+68}:\\ \;\;\;\;x \cdot \frac{t}{z}\\ \mathbf{else}:\\ \;\;\;\;t\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= y -1.75e-10) t (if (<= y 6e+68) (* x (/ t z)) t)))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (y <= -1.75e-10) {
		tmp = t;
	} else if (y <= 6e+68) {
		tmp = x * (t / z);
	} else {
		tmp = t;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if (y <= (-1.75d-10)) then
        tmp = t
    else if (y <= 6d+68) then
        tmp = x * (t / z)
    else
        tmp = t
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if (y <= -1.75e-10) {
		tmp = t;
	} else if (y <= 6e+68) {
		tmp = x * (t / z);
	} else {
		tmp = t;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if y <= -1.75e-10:
		tmp = t
	elif y <= 6e+68:
		tmp = x * (t / z)
	else:
		tmp = t
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (y <= -1.75e-10)
		tmp = t;
	elseif (y <= 6e+68)
		tmp = Float64(x * Float64(t / z));
	else
		tmp = t;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (y <= -1.75e-10)
		tmp = t;
	elseif (y <= 6e+68)
		tmp = x * (t / z);
	else
		tmp = t;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[y, -1.75e-10], t, If[LessEqual[y, 6e+68], N[(x * N[(t / z), $MachinePrecision]), $MachinePrecision], t]]

Derivation

1. Split input into 2 regimes

2. if y < -1.7499999999999999e-10 or 6.0000000000000004e68 < y

   1. Initial program 99.8%

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

      1. associate-*l/ 79.0%

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

      2. associate-/l* 71.3%

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

   3. Simplified 71.3%

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

   5. Taylor expanded in y around inf 59.0%

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

   if -1.7499999999999999e-10 < y < 6.0000000000000004e68

   1. Initial program 94.9%

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

      1. associate-*l/ 88.7%

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

      2. associate-/l* 95.9%

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

   3. Simplified 95.9%

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

   5. Taylor expanded in y around 0 61.2%

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

      1. *-commutative 61.2%

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

      2. associate-/l* 67.2%

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

   7. Simplified 67.2%

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

4. Final simplification 63.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.75 \cdot 10^{-10}:\\ \;\;\;\;t\\ \mathbf{elif}\;y \leq 6 \cdot 10^{+68}:\\ \;\;\;\;x \cdot \frac{t}{z}\\ \mathbf{else}:\\ \;\;\;\;t\\ \end{array} \]
5. Add Preprocessing

Alternative 15: 61.7% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -1.95 \cdot 10^{-10}:\\ \;\;\;\;t\\ \mathbf{elif}\;y \leq 2.45 \cdot 10^{+70}:\\ \;\;\;\;t \cdot \frac{x}{z}\\ \mathbf{else}:\\ \;\;\;\;t\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= y -1.95e-10) t (if (<= y 2.45e+70) (* t (/ x z)) t)))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (y <= -1.95e-10) {
		tmp = t;
	} else if (y <= 2.45e+70) {
		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 <= (-1.95d-10)) then
        tmp = t
    else if (y <= 2.45d+70) 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 <= -1.95e-10) {
		tmp = t;
	} else if (y <= 2.45e+70) {
		tmp = t * (x / z);
	} else {
		tmp = t;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if y <= -1.95e-10:
		tmp = t
	elif y <= 2.45e+70:
		tmp = t * (x / z)
	else:
		tmp = t
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (y <= -1.95e-10)
		tmp = t;
	elseif (y <= 2.45e+70)
		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 <= -1.95e-10)
		tmp = t;
	elseif (y <= 2.45e+70)
		tmp = t * (x / z);
	else
		tmp = t;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[y, -1.95e-10], t, If[LessEqual[y, 2.45e+70], N[(t * N[(x / z), $MachinePrecision]), $MachinePrecision], t]]

Derivation

1. Split input into 2 regimes

2. if y < -1.95e-10 or 2.45000000000000014e70 < y

   1. Initial program 99.8%

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

      1. associate-*l/ 79.0%

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

      2. associate-/l* 71.3%

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

   3. Simplified 71.3%

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

   5. Taylor expanded in y around inf 59.0%

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

   if -1.95e-10 < y < 2.45000000000000014e70

   1. Initial program 94.9%

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

   3. Taylor expanded in y around 0 67.9%

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

4. Final simplification 64.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.95 \cdot 10^{-10}:\\ \;\;\;\;t\\ \mathbf{elif}\;y \leq 2.45 \cdot 10^{+70}:\\ \;\;\;\;t \cdot \frac{x}{z}\\ \mathbf{else}:\\ \;\;\;\;t\\ \end{array} \]
5. Add Preprocessing

Alternative 16: 97.1% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 96.9%

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

3. Final simplification 96.9%

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

Alternative 17: 34.7% accurate, 9.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 96.9%

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

   1. associate-*l/ 84.7%

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

   2. associate-/l* 85.9%

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

3. Simplified 85.9%

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

5. Taylor expanded in y around inf 27.7%

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

6. Final simplification 27.7%

   \[\leadsto t \]
7. Add Preprocessing

Developer target: 97.1% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Reproduce

herbie shell --seed 2024071 
(FPCore (x y z t)
  :name "Numeric.Signal.Multichannel:$cput from hsignal-0.2.7.1"
  :precision binary64

  :alt
  (/ t (/ (- z y) (- x y)))

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