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

Percentage Accurate: 96.9% → 96.9%

Time: 11.9s

Alternatives: 13

Speedup: 1.0×

• could not determine a ground truth

  1. x = 3.8477356556966834e+189
  2. y = -3.9681970140320344e+61
  3. z = -1.2952503877855142e+192
  4. t = -8.661483625417427e+275

Specification

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Initial Program: 96.9% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Alternative 1: 96.9% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 97.1%

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

3. Final simplification 97.1%

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

Alternative 2: 68.5% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := t \cdot \frac{x}{z - y}\\ \mathbf{if}\;y \leq -1.65 \cdot 10^{+148}:\\ \;\;\;\;t\\ \mathbf{elif}\;y \leq -1.8 \cdot 10^{+117}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y \leq -1.02 \cdot 10^{+86}:\\ \;\;\;\;t\\ \mathbf{elif}\;y \leq -2.1 \cdot 10^{-26}:\\ \;\;\;\;\left(x - y\right) \cdot \frac{t}{z}\\ \mathbf{elif}\;y \leq 6.8 \cdot 10^{+72}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;t\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (* t (/ x (- z y)))))
   (if (<= y -1.65e+148)
     t
     (if (<= y -1.8e+117)
       t_1
       (if (<= y -1.02e+86)
         t
         (if (<= y -2.1e-26)
           (* (- x y) (/ t z))
           (if (<= y 6.8e+72) t_1 t)))))))

C

double code(double x, double y, double z, double t) {
	double t_1 = t * (x / (z - y));
	double tmp;
	if (y <= -1.65e+148) {
		tmp = t;
	} else if (y <= -1.8e+117) {
		tmp = t_1;
	} else if (y <= -1.02e+86) {
		tmp = t;
	} else if (y <= -2.1e-26) {
		tmp = (x - y) * (t / z);
	} else if (y <= 6.8e+72) {
		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 / (z - y))
    if (y <= (-1.65d+148)) then
        tmp = t
    else if (y <= (-1.8d+117)) then
        tmp = t_1
    else if (y <= (-1.02d+86)) then
        tmp = t
    else if (y <= (-2.1d-26)) then
        tmp = (x - y) * (t / z)
    else if (y <= 6.8d+72) 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 / (z - y));
	double tmp;
	if (y <= -1.65e+148) {
		tmp = t;
	} else if (y <= -1.8e+117) {
		tmp = t_1;
	} else if (y <= -1.02e+86) {
		tmp = t;
	} else if (y <= -2.1e-26) {
		tmp = (x - y) * (t / z);
	} else if (y <= 6.8e+72) {
		tmp = t_1;
	} else {
		tmp = t;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = t * (x / (z - y))
	tmp = 0
	if y <= -1.65e+148:
		tmp = t
	elif y <= -1.8e+117:
		tmp = t_1
	elif y <= -1.02e+86:
		tmp = t
	elif y <= -2.1e-26:
		tmp = (x - y) * (t / z)
	elif y <= 6.8e+72:
		tmp = t_1
	else:
		tmp = t
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(t * Float64(x / Float64(z - y)))
	tmp = 0.0
	if (y <= -1.65e+148)
		tmp = t;
	elseif (y <= -1.8e+117)
		tmp = t_1;
	elseif (y <= -1.02e+86)
		tmp = t;
	elseif (y <= -2.1e-26)
		tmp = Float64(Float64(x - y) * Float64(t / z));
	elseif (y <= 6.8e+72)
		tmp = t_1;
	else
		tmp = t;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = t * (x / (z - y));
	tmp = 0.0;
	if (y <= -1.65e+148)
		tmp = t;
	elseif (y <= -1.8e+117)
		tmp = t_1;
	elseif (y <= -1.02e+86)
		tmp = t;
	elseif (y <= -2.1e-26)
		tmp = (x - y) * (t / z);
	elseif (y <= 6.8e+72)
		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 / N[(z - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -1.65e+148], t, If[LessEqual[y, -1.8e+117], t$95$1, If[LessEqual[y, -1.02e+86], t, If[LessEqual[y, -2.1e-26], N[(N[(x - y), $MachinePrecision] * N[(t / z), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 6.8e+72], t$95$1, t]]]]]]

Derivation

1. Split input into 3 regimes

2. if y < -1.65000000000000005e148 or -1.80000000000000006e117 < y < -1.01999999999999996e86 or 6.7999999999999997e72 < y

   1. Initial program 100.0%

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

      1. associate-*l/ 61.1%

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

      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 80.6%

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

   if -1.65000000000000005e148 < y < -1.80000000000000006e117 or -2.10000000000000008e-26 < y < 6.7999999999999997e72

   1. Initial program 95.1%

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

   3. Taylor expanded in x around inf 76.0%

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

   if -1.01999999999999996e86 < y < -2.10000000000000008e-26

   1. Initial program 98.2%

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

      1. associate-*l/ 82.2%

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

      2. associate-/l* 88.4%

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

   3. Simplified 88.4%

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

   5. Taylor expanded in z around inf 52.8%

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

4. Final simplification 76.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.65 \cdot 10^{+148}:\\ \;\;\;\;t\\ \mathbf{elif}\;y \leq -1.8 \cdot 10^{+117}:\\ \;\;\;\;t \cdot \frac{x}{z - y}\\ \mathbf{elif}\;y \leq -1.02 \cdot 10^{+86}:\\ \;\;\;\;t\\ \mathbf{elif}\;y \leq -2.1 \cdot 10^{-26}:\\ \;\;\;\;\left(x - y\right) \cdot \frac{t}{z}\\ \mathbf{elif}\;y \leq 6.8 \cdot 10^{+72}:\\ \;\;\;\;t \cdot \frac{x}{z - y}\\ \mathbf{else}:\\ \;\;\;\;t\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 73.1% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -1.9 \cdot 10^{+117}:\\ \;\;\;\;t - t \cdot \frac{x}{y}\\ \mathbf{elif}\;y \leq -3.05 \cdot 10^{-30}:\\ \;\;\;\;\frac{y \cdot t}{y - z}\\ \mathbf{elif}\;y \leq -4.8 \cdot 10^{-149}:\\ \;\;\;\;\frac{x \cdot t}{z - y}\\ \mathbf{elif}\;y \leq 1.05 \cdot 10^{-88}:\\ \;\;\;\;\left(x - y\right) \cdot \frac{t}{z}\\ \mathbf{elif}\;y \leq 3.3 \cdot 10^{-48}:\\ \;\;\;\;t \cdot \frac{x}{z - y}\\ \mathbf{else}:\\ \;\;\;\;t - \frac{t}{\frac{y}{x}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= y -1.9e+117)
   (- t (* t (/ x y)))
   (if (<= y -3.05e-30)
     (/ (* y t) (- y z))
     (if (<= y -4.8e-149)
       (/ (* x t) (- z y))
       (if (<= y 1.05e-88)
         (* (- x y) (/ t z))
         (if (<= y 3.3e-48) (* t (/ x (- z y))) (- t (/ t (/ y x)))))))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (y <= -1.9e+117) {
		tmp = t - (t * (x / y));
	} else if (y <= -3.05e-30) {
		tmp = (y * t) / (y - z);
	} else if (y <= -4.8e-149) {
		tmp = (x * t) / (z - y);
	} else if (y <= 1.05e-88) {
		tmp = (x - y) * (t / z);
	} else if (y <= 3.3e-48) {
		tmp = t * (x / (z - y));
	} else {
		tmp = t - (t / (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 <= (-1.9d+117)) then
        tmp = t - (t * (x / y))
    else if (y <= (-3.05d-30)) then
        tmp = (y * t) / (y - z)
    else if (y <= (-4.8d-149)) then
        tmp = (x * t) / (z - y)
    else if (y <= 1.05d-88) then
        tmp = (x - y) * (t / z)
    else if (y <= 3.3d-48) then
        tmp = t * (x / (z - y))
    else
        tmp = t - (t / (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 <= -1.9e+117) {
		tmp = t - (t * (x / y));
	} else if (y <= -3.05e-30) {
		tmp = (y * t) / (y - z);
	} else if (y <= -4.8e-149) {
		tmp = (x * t) / (z - y);
	} else if (y <= 1.05e-88) {
		tmp = (x - y) * (t / z);
	} else if (y <= 3.3e-48) {
		tmp = t * (x / (z - y));
	} else {
		tmp = t - (t / (y / x));
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if y <= -1.9e+117:
		tmp = t - (t * (x / y))
	elif y <= -3.05e-30:
		tmp = (y * t) / (y - z)
	elif y <= -4.8e-149:
		tmp = (x * t) / (z - y)
	elif y <= 1.05e-88:
		tmp = (x - y) * (t / z)
	elif y <= 3.3e-48:
		tmp = t * (x / (z - y))
	else:
		tmp = t - (t / (y / x))
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (y <= -1.9e+117)
		tmp = Float64(t - Float64(t * Float64(x / y)));
	elseif (y <= -3.05e-30)
		tmp = Float64(Float64(y * t) / Float64(y - z));
	elseif (y <= -4.8e-149)
		tmp = Float64(Float64(x * t) / Float64(z - y));
	elseif (y <= 1.05e-88)
		tmp = Float64(Float64(x - y) * Float64(t / z));
	elseif (y <= 3.3e-48)
		tmp = Float64(t * Float64(x / Float64(z - y)));
	else
		tmp = Float64(t - Float64(t / Float64(y / x)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (y <= -1.9e+117)
		tmp = t - (t * (x / y));
	elseif (y <= -3.05e-30)
		tmp = (y * t) / (y - z);
	elseif (y <= -4.8e-149)
		tmp = (x * t) / (z - y);
	elseif (y <= 1.05e-88)
		tmp = (x - y) * (t / z);
	elseif (y <= 3.3e-48)
		tmp = t * (x / (z - y));
	else
		tmp = t - (t / (y / x));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[y, -1.9e+117], N[(t - N[(t * N[(x / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, -3.05e-30], N[(N[(y * t), $MachinePrecision] / N[(y - z), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, -4.8e-149], N[(N[(x * t), $MachinePrecision] / N[(z - y), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 1.05e-88], N[(N[(x - y), $MachinePrecision] * N[(t / z), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 3.3e-48], N[(t * N[(x / N[(z - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(t - N[(t / N[(y / x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]

Derivation

1. Split input into 6 regimes

2. if y < -1.9000000000000001e117

   1. Initial program 100.0%

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

   3. Taylor expanded in z around 0 82.4%

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

      1. associate-*r/ 82.4%

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

      2. neg-mul-1 82.4%

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

   5. Simplified 82.4%

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

   6. Taylor expanded in x around 0 68.0%

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

      1. mul-1-neg 68.0%

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

      2. unsub-neg 68.0%

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

      3. associate-/l* 82.4%

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

   8. Simplified 82.4%

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

   if -1.9000000000000001e117 < y < -3.0499999999999999e-30

   1. Initial program 98.9%

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

      1. associate-*l/ 85.4%

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

      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 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 -3.0499999999999999e-30 < y < -4.8000000000000002e-149

   1. Initial program 96.3%

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

      1. associate-*l/ 95.3%

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

      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 x around inf 83.5%

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

   if -4.8000000000000002e-149 < y < 1.05e-88

   1. Initial program 92.2%

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

      1. associate-*l/ 90.1%

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

      2. associate-/l* 94.4%

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

   3. Simplified 94.4%

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

   5. Taylor expanded in z around inf 88.0%

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

   if 1.05e-88 < y < 3.3e-48

   1. Initial program 100.0%

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

   3. Taylor expanded in x around inf 100.0%

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

   if 3.3e-48 < y

   1. Initial program 99.7%

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

   3. Taylor expanded in z around 0 78.4%

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

      1. associate-*r/ 78.4%

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

      2. neg-mul-1 78.4%

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

   5. Simplified 78.4%

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

   6. Taylor expanded in x around 0 75.2%

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

      1. mul-1-neg 75.2%

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

      2. unsub-neg 75.2%

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

      3. associate-/l* 78.4%

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

   8. Simplified 78.4%

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

      1. clear-num 78.4%

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

      2. un-div-inv 78.4%

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

   10. Applied egg-rr 78.4%

       \[\leadsto t - \color{blue}{\frac{t}{\frac{y}{x}}} \]
3. Recombined 6 regimes into one program.

4. Final simplification 82.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.9 \cdot 10^{+117}:\\ \;\;\;\;t - t \cdot \frac{x}{y}\\ \mathbf{elif}\;y \leq -3.05 \cdot 10^{-30}:\\ \;\;\;\;\frac{y \cdot t}{y - z}\\ \mathbf{elif}\;y \leq -4.8 \cdot 10^{-149}:\\ \;\;\;\;\frac{x \cdot t}{z - y}\\ \mathbf{elif}\;y \leq 1.05 \cdot 10^{-88}:\\ \;\;\;\;\left(x - y\right) \cdot \frac{t}{z}\\ \mathbf{elif}\;y \leq 3.3 \cdot 10^{-48}:\\ \;\;\;\;t \cdot \frac{x}{z - y}\\ \mathbf{else}:\\ \;\;\;\;t - \frac{t}{\frac{y}{x}}\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 74.3% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := t - t \cdot \frac{x}{y}\\ \mathbf{if}\;y \leq -1.85 \cdot 10^{+83}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y \leq -5.4 \cdot 10^{+65}:\\ \;\;\;\;t \cdot \frac{x - y}{z}\\ \mathbf{elif}\;y \leq -5.5 \cdot 10^{-30} \lor \neg \left(y \leq 3.3 \cdot 10^{-48}\right):\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;t \cdot \frac{x}{z - y}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (- t (* t (/ x y)))))
   (if (<= y -1.85e+83)
     t_1
     (if (<= y -5.4e+65)
       (* t (/ (- x y) z))
       (if (or (<= y -5.5e-30) (not (<= y 3.3e-48)))
         t_1
         (* t (/ x (- z y))))))))

C

double code(double x, double y, double z, double t) {
	double t_1 = t - (t * (x / y));
	double tmp;
	if (y <= -1.85e+83) {
		tmp = t_1;
	} else if (y <= -5.4e+65) {
		tmp = t * ((x - y) / z);
	} else if ((y <= -5.5e-30) || !(y <= 3.3e-48)) {
		tmp = t_1;
	} 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) :: t_1
    real(8) :: tmp
    t_1 = t - (t * (x / y))
    if (y <= (-1.85d+83)) then
        tmp = t_1
    else if (y <= (-5.4d+65)) then
        tmp = t * ((x - y) / z)
    else if ((y <= (-5.5d-30)) .or. (.not. (y <= 3.3d-48))) then
        tmp = t_1
    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 t_1 = t - (t * (x / y));
	double tmp;
	if (y <= -1.85e+83) {
		tmp = t_1;
	} else if (y <= -5.4e+65) {
		tmp = t * ((x - y) / z);
	} else if ((y <= -5.5e-30) || !(y <= 3.3e-48)) {
		tmp = t_1;
	} else {
		tmp = t * (x / (z - y));
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = t - (t * (x / y))
	tmp = 0
	if y <= -1.85e+83:
		tmp = t_1
	elif y <= -5.4e+65:
		tmp = t * ((x - y) / z)
	elif (y <= -5.5e-30) or not (y <= 3.3e-48):
		tmp = t_1
	else:
		tmp = t * (x / (z - y))
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(t - Float64(t * Float64(x / y)))
	tmp = 0.0
	if (y <= -1.85e+83)
		tmp = t_1;
	elseif (y <= -5.4e+65)
		tmp = Float64(t * Float64(Float64(x - y) / z));
	elseif ((y <= -5.5e-30) || !(y <= 3.3e-48))
		tmp = t_1;
	else
		tmp = Float64(t * Float64(x / Float64(z - y)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = t - (t * (x / y));
	tmp = 0.0;
	if (y <= -1.85e+83)
		tmp = t_1;
	elseif (y <= -5.4e+65)
		tmp = t * ((x - y) / z);
	elseif ((y <= -5.5e-30) || ~((y <= 3.3e-48)))
		tmp = t_1;
	else
		tmp = t * (x / (z - y));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(t - N[(t * N[(x / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -1.85e+83], t$95$1, If[LessEqual[y, -5.4e+65], N[(t * N[(N[(x - y), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision], If[Or[LessEqual[y, -5.5e-30], N[Not[LessEqual[y, 3.3e-48]], $MachinePrecision]], t$95$1, N[(t * N[(x / N[(z - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]

Derivation

1. Split input into 3 regimes

2. if y < -1.8500000000000001e83 or -5.40000000000000038e65 < y < -5.49999999999999976e-30 or 3.3e-48 < y

   1. Initial program 99.7%

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

   3. Taylor expanded in z around 0 76.9%

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

      1. associate-*r/ 76.9%

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

      2. neg-mul-1 76.9%

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

   5. Simplified 76.9%

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

   6. Taylor expanded in x around 0 69.8%

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

      1. mul-1-neg 69.8%

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

      2. unsub-neg 69.8%

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

      3. associate-/l* 76.9%

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

   8. Simplified 76.9%

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

   if -1.8500000000000001e83 < y < -5.40000000000000038e65

   1. Initial program 100.0%

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

   3. Taylor expanded in z around inf 99.0%

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

   if -5.49999999999999976e-30 < y < 3.3e-48

   1. Initial program 93.6%

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

   3. Taylor expanded in x around inf 83.8%

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

4. Final simplification 80.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.85 \cdot 10^{+83}:\\ \;\;\;\;t - t \cdot \frac{x}{y}\\ \mathbf{elif}\;y \leq -5.4 \cdot 10^{+65}:\\ \;\;\;\;t \cdot \frac{x - y}{z}\\ \mathbf{elif}\;y \leq -5.5 \cdot 10^{-30} \lor \neg \left(y \leq 3.3 \cdot 10^{-48}\right):\\ \;\;\;\;t - t \cdot \frac{x}{y}\\ \mathbf{else}:\\ \;\;\;\;t \cdot \frac{x}{z - y}\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 74.2% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := t - t \cdot \frac{x}{y}\\ \mathbf{if}\;y \leq -1.95 \cdot 10^{+85}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y \leq -9.2 \cdot 10^{+64}:\\ \;\;\;\;t \cdot \frac{x - y}{z}\\ \mathbf{elif}\;y \leq -7.5 \cdot 10^{-30}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y \leq 3.3 \cdot 10^{-48}:\\ \;\;\;\;t \cdot \frac{x}{z - y}\\ \mathbf{else}:\\ \;\;\;\;t - \frac{t}{\frac{y}{x}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (- t (* t (/ x y)))))
   (if (<= y -1.95e+85)
     t_1
     (if (<= y -9.2e+64)
       (* t (/ (- x y) z))
       (if (<= y -7.5e-30)
         t_1
         (if (<= y 3.3e-48) (* t (/ x (- z y))) (- t (/ t (/ y x)))))))))

C

double code(double x, double y, double z, double t) {
	double t_1 = t - (t * (x / y));
	double tmp;
	if (y <= -1.95e+85) {
		tmp = t_1;
	} else if (y <= -9.2e+64) {
		tmp = t * ((x - y) / z);
	} else if (y <= -7.5e-30) {
		tmp = t_1;
	} else if (y <= 3.3e-48) {
		tmp = t * (x / (z - y));
	} else {
		tmp = t - (t / (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) :: t_1
    real(8) :: tmp
    t_1 = t - (t * (x / y))
    if (y <= (-1.95d+85)) then
        tmp = t_1
    else if (y <= (-9.2d+64)) then
        tmp = t * ((x - y) / z)
    else if (y <= (-7.5d-30)) then
        tmp = t_1
    else if (y <= 3.3d-48) then
        tmp = t * (x / (z - y))
    else
        tmp = t - (t / (y / x))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double t_1 = t - (t * (x / y));
	double tmp;
	if (y <= -1.95e+85) {
		tmp = t_1;
	} else if (y <= -9.2e+64) {
		tmp = t * ((x - y) / z);
	} else if (y <= -7.5e-30) {
		tmp = t_1;
	} else if (y <= 3.3e-48) {
		tmp = t * (x / (z - y));
	} else {
		tmp = t - (t / (y / x));
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = t - (t * (x / y))
	tmp = 0
	if y <= -1.95e+85:
		tmp = t_1
	elif y <= -9.2e+64:
		tmp = t * ((x - y) / z)
	elif y <= -7.5e-30:
		tmp = t_1
	elif y <= 3.3e-48:
		tmp = t * (x / (z - y))
	else:
		tmp = t - (t / (y / x))
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(t - Float64(t * Float64(x / y)))
	tmp = 0.0
	if (y <= -1.95e+85)
		tmp = t_1;
	elseif (y <= -9.2e+64)
		tmp = Float64(t * Float64(Float64(x - y) / z));
	elseif (y <= -7.5e-30)
		tmp = t_1;
	elseif (y <= 3.3e-48)
		tmp = Float64(t * Float64(x / Float64(z - y)));
	else
		tmp = Float64(t - Float64(t / Float64(y / x)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = t - (t * (x / y));
	tmp = 0.0;
	if (y <= -1.95e+85)
		tmp = t_1;
	elseif (y <= -9.2e+64)
		tmp = t * ((x - y) / z);
	elseif (y <= -7.5e-30)
		tmp = t_1;
	elseif (y <= 3.3e-48)
		tmp = t * (x / (z - y));
	else
		tmp = t - (t / (y / x));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(t - N[(t * N[(x / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -1.95e+85], t$95$1, If[LessEqual[y, -9.2e+64], N[(t * N[(N[(x - y), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, -7.5e-30], t$95$1, If[LessEqual[y, 3.3e-48], N[(t * N[(x / N[(z - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(t - N[(t / N[(y / x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]

Derivation

1. Split input into 4 regimes

2. if y < -1.95000000000000017e85 or -9.2e64 < y < -7.5000000000000006e-30

   1. Initial program 99.6%

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

   3. Taylor expanded in z around 0 75.3%

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

      1. associate-*r/ 75.3%

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

      2. neg-mul-1 75.3%

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

   5. Simplified 75.3%

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

   6. Taylor expanded in x around 0 64.0%

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

      1. mul-1-neg 64.0%

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

      2. unsub-neg 64.0%

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

      3. associate-/l* 75.3%

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

   8. Simplified 75.3%

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

   if -1.95000000000000017e85 < y < -9.2e64

   1. Initial program 100.0%

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

   3. Taylor expanded in z around inf 99.0%

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

   if -7.5000000000000006e-30 < y < 3.3e-48

   1. Initial program 93.6%

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

   3. Taylor expanded in x around inf 83.8%

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

   if 3.3e-48 < y

   1. Initial program 99.7%

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

   3. Taylor expanded in z around 0 78.4%

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

      1. associate-*r/ 78.4%

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

      2. neg-mul-1 78.4%

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

   5. Simplified 78.4%

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

   6. Taylor expanded in x around 0 75.2%

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

      1. mul-1-neg 75.2%

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

      2. unsub-neg 75.2%

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

      3. associate-/l* 78.4%

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

   8. Simplified 78.4%

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

      1. clear-num 78.4%

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

      2. un-div-inv 78.4%

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

   10. Applied egg-rr 78.4%

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

4. Final simplification 80.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.95 \cdot 10^{+85}:\\ \;\;\;\;t - t \cdot \frac{x}{y}\\ \mathbf{elif}\;y \leq -9.2 \cdot 10^{+64}:\\ \;\;\;\;t \cdot \frac{x - y}{z}\\ \mathbf{elif}\;y \leq -7.5 \cdot 10^{-30}:\\ \;\;\;\;t - t \cdot \frac{x}{y}\\ \mathbf{elif}\;y \leq 3.3 \cdot 10^{-48}:\\ \;\;\;\;t \cdot \frac{x}{z - y}\\ \mathbf{else}:\\ \;\;\;\;t - \frac{t}{\frac{y}{x}}\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 74.3% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := t \cdot \frac{y}{y - z}\\ \mathbf{if}\;y \leq -2.8 \cdot 10^{-31}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y \leq -1 \cdot 10^{-149}:\\ \;\;\;\;\frac{x \cdot t}{z - y}\\ \mathbf{elif}\;y \leq 1.86 \cdot 10^{-88}:\\ \;\;\;\;\left(x - y\right) \cdot \frac{t}{z}\\ \mathbf{elif}\;y \leq 1.85 \cdot 10^{-48}:\\ \;\;\;\;t \cdot \frac{x}{z - y}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (* t (/ y (- y z)))))
   (if (<= y -2.8e-31)
     t_1
     (if (<= y -1e-149)
       (/ (* x t) (- z y))
       (if (<= y 1.86e-88)
         (* (- x y) (/ t z))
         (if (<= y 1.85e-48) (* 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 <= -2.8e-31) {
		tmp = t_1;
	} else if (y <= -1e-149) {
		tmp = (x * t) / (z - y);
	} else if (y <= 1.86e-88) {
		tmp = (x - y) * (t / z);
	} else if (y <= 1.85e-48) {
		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 <= (-2.8d-31)) then
        tmp = t_1
    else if (y <= (-1d-149)) then
        tmp = (x * t) / (z - y)
    else if (y <= 1.86d-88) then
        tmp = (x - y) * (t / z)
    else if (y <= 1.85d-48) 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 <= -2.8e-31) {
		tmp = t_1;
	} else if (y <= -1e-149) {
		tmp = (x * t) / (z - y);
	} else if (y <= 1.86e-88) {
		tmp = (x - y) * (t / z);
	} else if (y <= 1.85e-48) {
		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 <= -2.8e-31:
		tmp = t_1
	elif y <= -1e-149:
		tmp = (x * t) / (z - y)
	elif y <= 1.86e-88:
		tmp = (x - y) * (t / z)
	elif y <= 1.85e-48:
		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 <= -2.8e-31)
		tmp = t_1;
	elseif (y <= -1e-149)
		tmp = Float64(Float64(x * t) / Float64(z - y));
	elseif (y <= 1.86e-88)
		tmp = Float64(Float64(x - y) * Float64(t / z));
	elseif (y <= 1.85e-48)
		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 <= -2.8e-31)
		tmp = t_1;
	elseif (y <= -1e-149)
		tmp = (x * t) / (z - y);
	elseif (y <= 1.86e-88)
		tmp = (x - y) * (t / z);
	elseif (y <= 1.85e-48)
		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, -2.8e-31], t$95$1, If[LessEqual[y, -1e-149], N[(N[(x * t), $MachinePrecision] / N[(z - y), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 1.86e-88], N[(N[(x - y), $MachinePrecision] * N[(t / z), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 1.85e-48], N[(t * N[(x / N[(z - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]]]

Derivation

1. Split input into 4 regimes

2. if y < -2.7999999999999999e-31 or 1.8499999999999999e-48 < y

   1. Initial program 99.7%

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

   3. Taylor expanded in x around 0 80.2%

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

      1. neg-mul-1 80.2%

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

      2. distribute-neg-frac 80.2%

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

   5. Simplified 80.2%

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

   if -2.7999999999999999e-31 < y < -9.99999999999999979e-150

   1. Initial program 96.3%

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

      1. associate-*l/ 95.3%

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

      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 x around inf 83.5%

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

   if -9.99999999999999979e-150 < y < 1.85999999999999991e-88

   1. Initial program 92.2%

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

      1. associate-*l/ 90.1%

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

      2. associate-/l* 94.4%

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

   3. Simplified 94.4%

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

   5. Taylor expanded in z around inf 88.0%

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

   if 1.85999999999999991e-88 < y < 1.8499999999999999e-48

   1. Initial program 100.0%

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

   3. Taylor expanded in x around inf 100.0%

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

4. Final simplification 83.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -2.8 \cdot 10^{-31}:\\ \;\;\;\;t \cdot \frac{y}{y - z}\\ \mathbf{elif}\;y \leq -1 \cdot 10^{-149}:\\ \;\;\;\;\frac{x \cdot t}{z - y}\\ \mathbf{elif}\;y \leq 1.86 \cdot 10^{-88}:\\ \;\;\;\;\left(x - y\right) \cdot \frac{t}{z}\\ \mathbf{elif}\;y \leq 1.85 \cdot 10^{-48}:\\ \;\;\;\;t \cdot \frac{x}{z - y}\\ \mathbf{else}:\\ \;\;\;\;t \cdot \frac{y}{y - z}\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 59.0% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -9 \cdot 10^{+148}:\\ \;\;\;\;t\\ \mathbf{elif}\;y \leq -4.2 \cdot 10^{-15}:\\ \;\;\;\;\frac{y}{z} \cdot \left(-t\right)\\ \mathbf{elif}\;y \leq -7 \cdot 10^{-30}:\\ \;\;\;\;t\\ \mathbf{elif}\;y \leq 3.3 \cdot 10^{-48}:\\ \;\;\;\;t \cdot \frac{x}{z}\\ \mathbf{else}:\\ \;\;\;\;t\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= y -9e+148)
   t
   (if (<= y -4.2e-15)
     (* (/ y z) (- t))
     (if (<= y -7e-30) t (if (<= y 3.3e-48) (* t (/ x z)) t)))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (y <= -9e+148) {
		tmp = t;
	} else if (y <= -4.2e-15) {
		tmp = (y / z) * -t;
	} else if (y <= -7e-30) {
		tmp = t;
	} else if (y <= 3.3e-48) {
		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 <= (-9d+148)) then
        tmp = t
    else if (y <= (-4.2d-15)) then
        tmp = (y / z) * -t
    else if (y <= (-7d-30)) then
        tmp = t
    else if (y <= 3.3d-48) 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 <= -9e+148) {
		tmp = t;
	} else if (y <= -4.2e-15) {
		tmp = (y / z) * -t;
	} else if (y <= -7e-30) {
		tmp = t;
	} else if (y <= 3.3e-48) {
		tmp = t * (x / z);
	} else {
		tmp = t;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if y <= -9e+148:
		tmp = t
	elif y <= -4.2e-15:
		tmp = (y / z) * -t
	elif y <= -7e-30:
		tmp = t
	elif y <= 3.3e-48:
		tmp = t * (x / z)
	else:
		tmp = t
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (y <= -9e+148)
		tmp = t;
	elseif (y <= -4.2e-15)
		tmp = Float64(Float64(y / z) * Float64(-t));
	elseif (y <= -7e-30)
		tmp = t;
	elseif (y <= 3.3e-48)
		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 <= -9e+148)
		tmp = t;
	elseif (y <= -4.2e-15)
		tmp = (y / z) * -t;
	elseif (y <= -7e-30)
		tmp = t;
	elseif (y <= 3.3e-48)
		tmp = t * (x / z);
	else
		tmp = t;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[y, -9e+148], t, If[LessEqual[y, -4.2e-15], N[(N[(y / z), $MachinePrecision] * (-t)), $MachinePrecision], If[LessEqual[y, -7e-30], t, If[LessEqual[y, 3.3e-48], N[(t * N[(x / z), $MachinePrecision]), $MachinePrecision], t]]]]

Derivation

1. Split input into 3 regimes

2. if y < -8.99999999999999987e148 or -4.19999999999999962e-15 < y < -7.0000000000000006e-30 or 3.3e-48 < y

   1. Initial program 99.6%

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

      1. associate-*l/ 67.6%

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

      2. associate-/l* 84.4%

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

   3. Simplified 84.4%

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

   5. Taylor expanded in y around inf 72.0%

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

   if -8.99999999999999987e148 < y < -4.19999999999999962e-15

   1. Initial program 100.0%

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

      1. associate-*l/ 82.8%

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

      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 z around inf 50.7%

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

   6. Taylor expanded in x around 0 39.4%

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

      1. mul-1-neg 39.4%

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

      2. associate-/l* 42.2%

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

   8. Simplified 42.2%

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

   if -7.0000000000000006e-30 < y < 3.3e-48

   1. Initial program 93.6%

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

   3. Taylor expanded in y around 0 74.6%

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

4. Final simplification 69.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -9 \cdot 10^{+148}:\\ \;\;\;\;t\\ \mathbf{elif}\;y \leq -4.2 \cdot 10^{-15}:\\ \;\;\;\;\frac{y}{z} \cdot \left(-t\right)\\ \mathbf{elif}\;y \leq -7 \cdot 10^{-30}:\\ \;\;\;\;t\\ \mathbf{elif}\;y \leq 3.3 \cdot 10^{-48}:\\ \;\;\;\;t \cdot \frac{x}{z}\\ \mathbf{else}:\\ \;\;\;\;t\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 68.6% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -1.75 \cdot 10^{+148}:\\ \;\;\;\;t\\ \mathbf{elif}\;y \leq -3.8 \cdot 10^{-27}:\\ \;\;\;\;t \cdot \frac{x - y}{z}\\ \mathbf{elif}\;y \leq 7 \cdot 10^{+72}:\\ \;\;\;\;t \cdot \frac{x}{z - y}\\ \mathbf{else}:\\ \;\;\;\;t\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= y -1.75e+148)
   t
   (if (<= y -3.8e-27)
     (* t (/ (- x y) z))
     (if (<= y 7e+72) (* t (/ x (- z y))) t))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (y <= -1.75e+148) {
		tmp = t;
	} else if (y <= -3.8e-27) {
		tmp = t * ((x - y) / z);
	} else if (y <= 7e+72) {
		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 <= (-1.75d+148)) then
        tmp = t
    else if (y <= (-3.8d-27)) then
        tmp = t * ((x - y) / z)
    else if (y <= 7d+72) 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 <= -1.75e+148) {
		tmp = t;
	} else if (y <= -3.8e-27) {
		tmp = t * ((x - y) / z);
	} else if (y <= 7e+72) {
		tmp = t * (x / (z - y));
	} else {
		tmp = t;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if y <= -1.75e+148:
		tmp = t
	elif y <= -3.8e-27:
		tmp = t * ((x - y) / z)
	elif y <= 7e+72:
		tmp = t * (x / (z - y))
	else:
		tmp = t
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (y <= -1.75e+148)
		tmp = t;
	elseif (y <= -3.8e-27)
		tmp = Float64(t * Float64(Float64(x - y) / z));
	elseif (y <= 7e+72)
		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 <= -1.75e+148)
		tmp = t;
	elseif (y <= -3.8e-27)
		tmp = t * ((x - y) / z);
	elseif (y <= 7e+72)
		tmp = t * (x / (z - y));
	else
		tmp = t;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[y, -1.75e+148], t, If[LessEqual[y, -3.8e-27], N[(t * N[(N[(x - y), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 7e+72], N[(t * N[(x / N[(z - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t]]]

Derivation

1. Split input into 3 regimes

2. if y < -1.7499999999999999e148 or 7.0000000000000002e72 < y

   1. Initial program 99.9%

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

      1. associate-*l/ 58.6%

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

      2. associate-/l* 80.8%

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

   3. Simplified 80.8%

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

   5. Taylor expanded in y around inf 81.9%

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

   if -1.7499999999999999e148 < y < -3.8e-27

   1. Initial program 99.2%

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

   3. Taylor expanded in z around inf 55.1%

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

   if -3.8e-27 < y < 7.0000000000000002e72

   1. Initial program 94.7%

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

   3. Taylor expanded in x around inf 76.8%

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

4. Final simplification 75.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.75 \cdot 10^{+148}:\\ \;\;\;\;t\\ \mathbf{elif}\;y \leq -3.8 \cdot 10^{-27}:\\ \;\;\;\;t \cdot \frac{x - y}{z}\\ \mathbf{elif}\;y \leq 7 \cdot 10^{+72}:\\ \;\;\;\;t \cdot \frac{x}{z - y}\\ \mathbf{else}:\\ \;\;\;\;t\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 90.0% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -4.6 \cdot 10^{+149} \lor \neg \left(y \leq 6.4 \cdot 10^{+205}\right):\\ \;\;\;\;t \cdot \frac{y}{y - z}\\ \mathbf{else}:\\ \;\;\;\;\left(y - x\right) \cdot \frac{t}{y - z}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= y -4.6e+149) (not (<= y 6.4e+205)))
   (* t (/ y (- y z)))
   (* (- y x) (/ t (- y z)))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((y <= -4.6e+149) || !(y <= 6.4e+205)) {
		tmp = t * (y / (y - z));
	} else {
		tmp = (y - x) * (t / (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 <= (-4.6d+149)) .or. (.not. (y <= 6.4d+205))) then
        tmp = t * (y / (y - z))
    else
        tmp = (y - x) * (t / (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 <= -4.6e+149) || !(y <= 6.4e+205)) {
		tmp = t * (y / (y - z));
	} else {
		tmp = (y - x) * (t / (y - z));
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (y <= -4.6e+149) or not (y <= 6.4e+205):
		tmp = t * (y / (y - z))
	else:
		tmp = (y - x) * (t / (y - z))
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((y <= -4.6e+149) || !(y <= 6.4e+205))
		tmp = Float64(t * Float64(y / Float64(y - z)));
	else
		tmp = Float64(Float64(y - x) * Float64(t / Float64(y - z)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((y <= -4.6e+149) || ~((y <= 6.4e+205)))
		tmp = t * (y / (y - z));
	else
		tmp = (y - x) * (t / (y - z));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[y, -4.6e+149], N[Not[LessEqual[y, 6.4e+205]], $MachinePrecision]], N[(t * N[(y / N[(y - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(y - x), $MachinePrecision] * N[(t / N[(y - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -4.5999999999999997e149 or 6.39999999999999993e205 < y

   1. Initial program 100.0%

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

   3. Taylor expanded in x around 0 96.0%

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

      1. neg-mul-1 96.0%

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

      2. distribute-neg-frac 96.0%

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

   5. Simplified 96.0%

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

   if -4.5999999999999997e149 < y < 6.39999999999999993e205

   1. Initial program 96.3%

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

      1. associate-*l/ 86.8%

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

      2. associate-/l* 94.0%

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

   3. Simplified 94.0%

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

4. Final simplification 94.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -4.6 \cdot 10^{+149} \lor \neg \left(y \leq 6.4 \cdot 10^{+205}\right):\\ \;\;\;\;t \cdot \frac{y}{y - z}\\ \mathbf{else}:\\ \;\;\;\;\left(y - x\right) \cdot \frac{t}{y - z}\\ \end{array} \]
5. Add Preprocessing

Alternative 10: 66.0% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -1.65 \cdot 10^{+148}:\\ \;\;\;\;t\\ \mathbf{elif}\;y \leq 7.6 \cdot 10^{+72}:\\ \;\;\;\;\left(x - y\right) \cdot \frac{t}{z}\\ \mathbf{else}:\\ \;\;\;\;t\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= y -1.65e+148) t (if (<= y 7.6e+72) (* (- x y) (/ t z)) t)))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (y <= -1.65e+148) {
		tmp = t;
	} else if (y <= 7.6e+72) {
		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 <= (-1.65d+148)) then
        tmp = t
    else if (y <= 7.6d+72) 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 <= -1.65e+148) {
		tmp = t;
	} else if (y <= 7.6e+72) {
		tmp = (x - y) * (t / z);
	} else {
		tmp = t;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if y <= -1.65e+148:
		tmp = t
	elif y <= 7.6e+72:
		tmp = (x - y) * (t / z)
	else:
		tmp = t
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (y <= -1.65e+148)
		tmp = t;
	elseif (y <= 7.6e+72)
		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 <= -1.65e+148)
		tmp = t;
	elseif (y <= 7.6e+72)
		tmp = (x - y) * (t / z);
	else
		tmp = t;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[y, -1.65e+148], t, If[LessEqual[y, 7.6e+72], N[(N[(x - y), $MachinePrecision] * N[(t / z), $MachinePrecision]), $MachinePrecision], t]]

Derivation

1. Split input into 2 regimes

2. if y < -1.65000000000000005e148 or 7.60000000000000012e72 < y

   1. Initial program 99.9%

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

      1. associate-*l/ 58.6%

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

      2. associate-/l* 80.8%

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

   3. Simplified 80.8%

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

   5. Taylor expanded in y around inf 81.9%

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

   if -1.65000000000000005e148 < y < 7.60000000000000012e72

   1. Initial program 95.6%

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

      1. associate-*l/ 90.8%

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

      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 inf 68.4%

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

4. Final simplification 72.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.65 \cdot 10^{+148}:\\ \;\;\;\;t\\ \mathbf{elif}\;y \leq 7.6 \cdot 10^{+72}:\\ \;\;\;\;\left(x - y\right) \cdot \frac{t}{z}\\ \mathbf{else}:\\ \;\;\;\;t\\ \end{array} \]
5. Add Preprocessing

Alternative 11: 59.8% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -4.2 \cdot 10^{-30}:\\ \;\;\;\;t\\ \mathbf{elif}\;y \leq 2.65 \cdot 10^{-48}:\\ \;\;\;\;x \cdot \frac{t}{z}\\ \mathbf{else}:\\ \;\;\;\;t\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= y -4.2e-30) t (if (<= y 2.65e-48) (* x (/ t z)) t)))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (y <= -4.2e-30) {
		tmp = t;
	} else if (y <= 2.65e-48) {
		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 <= (-4.2d-30)) then
        tmp = t
    else if (y <= 2.65d-48) 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 <= -4.2e-30) {
		tmp = t;
	} else if (y <= 2.65e-48) {
		tmp = x * (t / z);
	} else {
		tmp = t;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if y <= -4.2e-30:
		tmp = t
	elif y <= 2.65e-48:
		tmp = x * (t / z)
	else:
		tmp = t
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (y <= -4.2e-30)
		tmp = t;
	elseif (y <= 2.65e-48)
		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 <= -4.2e-30)
		tmp = t;
	elseif (y <= 2.65e-48)
		tmp = x * (t / z);
	else
		tmp = t;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[y, -4.2e-30], t, If[LessEqual[y, 2.65e-48], N[(x * N[(t / z), $MachinePrecision]), $MachinePrecision], t]]

Derivation

1. Split input into 2 regimes

2. if y < -4.2000000000000004e-30 or 2.65e-48 < y

   1. Initial program 99.7%

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

      1. associate-*l/ 71.1%

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

      2. associate-/l* 85.6%

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

   3. Simplified 85.6%

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

   5. Taylor expanded in y around inf 61.0%

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

   if -4.2000000000000004e-30 < y < 2.65e-48

   1. Initial program 93.6%

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

      1. associate-*l/ 91.9%

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

      2. associate-/l* 95.7%

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

   3. Simplified 95.7%

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

   5. Taylor expanded in y around 0 72.3%

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

      1. *-commutative 72.3%

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

      2. associate-/l* 74.3%

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

   7. Simplified 74.3%

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

4. Final simplification 66.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -4.2 \cdot 10^{-30}:\\ \;\;\;\;t\\ \mathbf{elif}\;y \leq 2.65 \cdot 10^{-48}:\\ \;\;\;\;x \cdot \frac{t}{z}\\ \mathbf{else}:\\ \;\;\;\;t\\ \end{array} \]
5. Add Preprocessing

Alternative 12: 60.5% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -5.2 \cdot 10^{-30}:\\ \;\;\;\;t\\ \mathbf{elif}\;y \leq 3.3 \cdot 10^{-48}:\\ \;\;\;\;t \cdot \frac{x}{z}\\ \mathbf{else}:\\ \;\;\;\;t\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= y -5.2e-30) t (if (<= y 3.3e-48) (* t (/ x z)) t)))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (y <= -5.2e-30) {
		tmp = t;
	} else if (y <= 3.3e-48) {
		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 <= (-5.2d-30)) then
        tmp = t
    else if (y <= 3.3d-48) 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 <= -5.2e-30) {
		tmp = t;
	} else if (y <= 3.3e-48) {
		tmp = t * (x / z);
	} else {
		tmp = t;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if y <= -5.2e-30:
		tmp = t
	elif y <= 3.3e-48:
		tmp = t * (x / z)
	else:
		tmp = t
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (y <= -5.2e-30)
		tmp = t;
	elseif (y <= 3.3e-48)
		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 <= -5.2e-30)
		tmp = t;
	elseif (y <= 3.3e-48)
		tmp = t * (x / z);
	else
		tmp = t;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[y, -5.2e-30], t, If[LessEqual[y, 3.3e-48], N[(t * N[(x / z), $MachinePrecision]), $MachinePrecision], t]]

Derivation

1. Split input into 2 regimes

2. if y < -5.19999999999999973e-30 or 3.3e-48 < y

   1. Initial program 99.7%

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

      1. associate-*l/ 71.1%

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

      2. associate-/l* 85.6%

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

   3. Simplified 85.6%

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

   5. Taylor expanded in y around inf 61.0%

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

   if -5.19999999999999973e-30 < y < 3.3e-48

   1. Initial program 93.6%

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

   3. Taylor expanded in y around 0 74.6%

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

4. Final simplification 66.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -5.2 \cdot 10^{-30}:\\ \;\;\;\;t\\ \mathbf{elif}\;y \leq 3.3 \cdot 10^{-48}:\\ \;\;\;\;t \cdot \frac{x}{z}\\ \mathbf{else}:\\ \;\;\;\;t\\ \end{array} \]
5. Add Preprocessing

Alternative 13: 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 97.1%

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

   1. associate-*l/ 80.0%

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

   2. associate-/l* 89.9%

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

3. Simplified 89.9%

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

5. Taylor expanded in y around inf 38.2%

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

6. Final simplification 38.2%

   \[\leadsto t \]
7. Add Preprocessing

Developer target: 97.0% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Reproduce

herbie shell --seed 2024045 
(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))