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

Percentage Accurate: 97.1% → 97.1%

Time: 8.9s

Alternatives: 14

Speedup: 1.0×

Specification

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Initial Program: 97.1% 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

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 98.0%

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

   1. *-commutative 98.0%

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

   2. associate-*r/ 84.4%

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

   3. associate-/l* 98.1%

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

   4. sub-neg 98.1%

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

   5. +-commutative 98.1%

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

   6. neg-sub0 98.1%

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

   7. associate-+l- 98.1%

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

   8. sub0-neg 98.1%

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

   9. neg-mul-1 98.1%

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

   10. associate-/r* 98.1%

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

3. Simplified 98.1%

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

4. Final simplification 98.1%

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

Alternative 2: 60.9% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -1.3 \cdot 10^{+39}:\\ \;\;\;\;t\\ \mathbf{elif}\;y \leq 8.5 \cdot 10^{-14}:\\ \;\;\;\;\frac{t}{\frac{z}{x}}\\ \mathbf{elif}\;y \leq 5.5 \cdot 10^{+44}:\\ \;\;\;\;\frac{t}{z} \cdot \left(-y\right)\\ \mathbf{elif}\;y \leq 6.4 \cdot 10^{+81}:\\ \;\;\;\;t\\ \mathbf{elif}\;y \leq 5.5 \cdot 10^{+91}:\\ \;\;\;\;\frac{x}{y} \cdot \left(-t\right)\\ \mathbf{else}:\\ \;\;\;\;t\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= y -1.3e+39)
   t
   (if (<= y 8.5e-14)
     (/ t (/ z x))
     (if (<= y 5.5e+44)
       (* (/ t z) (- y))
       (if (<= y 6.4e+81) t (if (<= y 5.5e+91) (* (/ x y) (- t)) t))))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (y <= -1.3e+39) {
		tmp = t;
	} else if (y <= 8.5e-14) {
		tmp = t / (z / x);
	} else if (y <= 5.5e+44) {
		tmp = (t / z) * -y;
	} else if (y <= 6.4e+81) {
		tmp = t;
	} else if (y <= 5.5e+91) {
		tmp = (x / y) * -t;
	} 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 <= (-1.3d+39)) then
        tmp = t
    else if (y <= 8.5d-14) then
        tmp = t / (z / x)
    else if (y <= 5.5d+44) then
        tmp = (t / z) * -y
    else if (y <= 6.4d+81) then
        tmp = t
    else if (y <= 5.5d+91) then
        tmp = (x / y) * -t
    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 <= -1.3e+39) {
		tmp = t;
	} else if (y <= 8.5e-14) {
		tmp = t / (z / x);
	} else if (y <= 5.5e+44) {
		tmp = (t / z) * -y;
	} else if (y <= 6.4e+81) {
		tmp = t;
	} else if (y <= 5.5e+91) {
		tmp = (x / y) * -t;
	} else {
		tmp = t;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if y <= -1.3e+39:
		tmp = t
	elif y <= 8.5e-14:
		tmp = t / (z / x)
	elif y <= 5.5e+44:
		tmp = (t / z) * -y
	elif y <= 6.4e+81:
		tmp = t
	elif y <= 5.5e+91:
		tmp = (x / y) * -t
	else:
		tmp = t
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (y <= -1.3e+39)
		tmp = t;
	elseif (y <= 8.5e-14)
		tmp = Float64(t / Float64(z / x));
	elseif (y <= 5.5e+44)
		tmp = Float64(Float64(t / z) * Float64(-y));
	elseif (y <= 6.4e+81)
		tmp = t;
	elseif (y <= 5.5e+91)
		tmp = Float64(Float64(x / y) * Float64(-t));
	else
		tmp = t;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (y <= -1.3e+39)
		tmp = t;
	elseif (y <= 8.5e-14)
		tmp = t / (z / x);
	elseif (y <= 5.5e+44)
		tmp = (t / z) * -y;
	elseif (y <= 6.4e+81)
		tmp = t;
	elseif (y <= 5.5e+91)
		tmp = (x / y) * -t;
	else
		tmp = t;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[y, -1.3e+39], t, If[LessEqual[y, 8.5e-14], N[(t / N[(z / x), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 5.5e+44], N[(N[(t / z), $MachinePrecision] * (-y)), $MachinePrecision], If[LessEqual[y, 6.4e+81], t, If[LessEqual[y, 5.5e+91], N[(N[(x / y), $MachinePrecision] * (-t)), $MachinePrecision], t]]]]]

Derivation

1. Split input into 4 regimes

2. if y < -1.3e39 or 5.5000000000000001e44 < y < 6.4e81 or 5.4999999999999998e91 < y

   1. Initial program 99.9%

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

   2. Taylor expanded in y around inf 64.7%

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

   if -1.3e39 < y < 8.50000000000000038e-14

   1. Initial program 96.4%

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

   2. Taylor expanded in y around 0 63.3%

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

      1. associate-/l* 64.9%

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

   4. Simplified 64.9%

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

   if 8.50000000000000038e-14 < y < 5.5000000000000001e44

   1. Initial program 99.3%

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

      1. *-commutative 99.3%

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

      2. associate-*r/ 99.5%

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

      3. associate-/l* 99.5%

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

      4. sub-neg 99.5%

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

      5. +-commutative 99.5%

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

      6. neg-sub0 99.5%

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

      7. associate-+l- 99.5%

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

      8. sub0-neg 99.5%

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

      9. neg-mul-1 99.5%

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

      10. associate-/r* 99.5%

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

   3. Simplified 99.5%

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

   4. Taylor expanded in x around 0 54.8%

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

      1. associate-/r/ 54.7%

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

   6. Applied egg-rr 54.7%

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

   7. Taylor expanded in y around 0 51.6%

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

      1. associate-*r/ 51.6%

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

      2. neg-mul-1 51.6%

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

   9. Simplified 51.6%

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

   if 6.4e81 < y < 5.4999999999999998e91

   1. Initial program 100.0%

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

   2. Taylor expanded in x around inf 99.2%

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

      1. associate-/l* 99.2%

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

   4. Simplified 99.2%

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

   5. Taylor expanded in z around 0 99.2%

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

      1. mul-1-neg 99.2%

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

      2. associate-*r/ 100.0%

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

      3. distribute-rgt-neg-in 100.0%

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

   7. Simplified 100.0%

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

4. Final simplification 64.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.3 \cdot 10^{+39}:\\ \;\;\;\;t\\ \mathbf{elif}\;y \leq 8.5 \cdot 10^{-14}:\\ \;\;\;\;\frac{t}{\frac{z}{x}}\\ \mathbf{elif}\;y \leq 5.5 \cdot 10^{+44}:\\ \;\;\;\;\frac{t}{z} \cdot \left(-y\right)\\ \mathbf{elif}\;y \leq 6.4 \cdot 10^{+81}:\\ \;\;\;\;t\\ \mathbf{elif}\;y \leq 5.5 \cdot 10^{+91}:\\ \;\;\;\;\frac{x}{y} \cdot \left(-t\right)\\ \mathbf{else}:\\ \;\;\;\;t\\ \end{array} \]

Alternative 3: 60.9% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -6.8 \cdot 10^{+38}:\\ \;\;\;\;t\\ \mathbf{elif}\;y \leq 7.8 \cdot 10^{-11}:\\ \;\;\;\;\frac{t}{\frac{z}{x}}\\ \mathbf{elif}\;y \leq 1.55 \cdot 10^{+45}:\\ \;\;\;\;t \cdot \frac{-y}{z}\\ \mathbf{elif}\;y \leq 5.2 \cdot 10^{+81}:\\ \;\;\;\;t\\ \mathbf{elif}\;y \leq 5.5 \cdot 10^{+91}:\\ \;\;\;\;\frac{x}{y} \cdot \left(-t\right)\\ \mathbf{else}:\\ \;\;\;\;t\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= y -6.8e+38)
   t
   (if (<= y 7.8e-11)
     (/ t (/ z x))
     (if (<= y 1.55e+45)
       (* t (/ (- y) z))
       (if (<= y 5.2e+81) t (if (<= y 5.5e+91) (* (/ x y) (- t)) t))))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (y <= -6.8e+38) {
		tmp = t;
	} else if (y <= 7.8e-11) {
		tmp = t / (z / x);
	} else if (y <= 1.55e+45) {
		tmp = t * (-y / z);
	} else if (y <= 5.2e+81) {
		tmp = t;
	} else if (y <= 5.5e+91) {
		tmp = (x / y) * -t;
	} 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 <= (-6.8d+38)) then
        tmp = t
    else if (y <= 7.8d-11) then
        tmp = t / (z / x)
    else if (y <= 1.55d+45) then
        tmp = t * (-y / z)
    else if (y <= 5.2d+81) then
        tmp = t
    else if (y <= 5.5d+91) then
        tmp = (x / y) * -t
    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 <= -6.8e+38) {
		tmp = t;
	} else if (y <= 7.8e-11) {
		tmp = t / (z / x);
	} else if (y <= 1.55e+45) {
		tmp = t * (-y / z);
	} else if (y <= 5.2e+81) {
		tmp = t;
	} else if (y <= 5.5e+91) {
		tmp = (x / y) * -t;
	} else {
		tmp = t;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if y <= -6.8e+38:
		tmp = t
	elif y <= 7.8e-11:
		tmp = t / (z / x)
	elif y <= 1.55e+45:
		tmp = t * (-y / z)
	elif y <= 5.2e+81:
		tmp = t
	elif y <= 5.5e+91:
		tmp = (x / y) * -t
	else:
		tmp = t
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (y <= -6.8e+38)
		tmp = t;
	elseif (y <= 7.8e-11)
		tmp = Float64(t / Float64(z / x));
	elseif (y <= 1.55e+45)
		tmp = Float64(t * Float64(Float64(-y) / z));
	elseif (y <= 5.2e+81)
		tmp = t;
	elseif (y <= 5.5e+91)
		tmp = Float64(Float64(x / y) * Float64(-t));
	else
		tmp = t;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (y <= -6.8e+38)
		tmp = t;
	elseif (y <= 7.8e-11)
		tmp = t / (z / x);
	elseif (y <= 1.55e+45)
		tmp = t * (-y / z);
	elseif (y <= 5.2e+81)
		tmp = t;
	elseif (y <= 5.5e+91)
		tmp = (x / y) * -t;
	else
		tmp = t;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[y, -6.8e+38], t, If[LessEqual[y, 7.8e-11], N[(t / N[(z / x), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 1.55e+45], N[(t * N[((-y) / z), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 5.2e+81], t, If[LessEqual[y, 5.5e+91], N[(N[(x / y), $MachinePrecision] * (-t)), $MachinePrecision], t]]]]]

Derivation

1. Split input into 4 regimes

2. if y < -6.79999999999999992e38 or 1.54999999999999994e45 < y < 5.19999999999999984e81 or 5.4999999999999998e91 < y

   1. Initial program 99.9%

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

   2. Taylor expanded in y around inf 64.7%

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

   if -6.79999999999999992e38 < y < 7.80000000000000021e-11

   1. Initial program 96.4%

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

   2. Taylor expanded in y around 0 63.3%

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

      1. associate-/l* 64.9%

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

   4. Simplified 64.9%

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

   if 7.80000000000000021e-11 < y < 1.54999999999999994e45

   1. Initial program 99.3%

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

   2. Taylor expanded in z around inf 57.1%

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

   3. Taylor expanded in x around 0 51.9%

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

      1. neg-mul-1 51.9%

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

      2. distribute-neg-frac 51.9%

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

   5. Simplified 51.9%

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

   if 5.19999999999999984e81 < y < 5.4999999999999998e91

   1. Initial program 100.0%

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

   2. Taylor expanded in x around inf 99.2%

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

      1. associate-/l* 99.2%

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

   4. Simplified 99.2%

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

   5. Taylor expanded in z around 0 99.2%

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

      1. mul-1-neg 99.2%

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

      2. associate-*r/ 100.0%

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

      3. distribute-rgt-neg-in 100.0%

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

   7. Simplified 100.0%

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

4. Final simplification 64.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -6.8 \cdot 10^{+38}:\\ \;\;\;\;t\\ \mathbf{elif}\;y \leq 7.8 \cdot 10^{-11}:\\ \;\;\;\;\frac{t}{\frac{z}{x}}\\ \mathbf{elif}\;y \leq 1.55 \cdot 10^{+45}:\\ \;\;\;\;t \cdot \frac{-y}{z}\\ \mathbf{elif}\;y \leq 5.2 \cdot 10^{+81}:\\ \;\;\;\;t\\ \mathbf{elif}\;y \leq 5.5 \cdot 10^{+91}:\\ \;\;\;\;\frac{x}{y} \cdot \left(-t\right)\\ \mathbf{else}:\\ \;\;\;\;t\\ \end{array} \]

Alternative 4: 65.8% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := y \cdot \frac{t}{y - z}\\ \mathbf{if}\;y \leq -1.12 \cdot 10^{+201}:\\ \;\;\;\;t\\ \mathbf{elif}\;y \leq -4.4 \cdot 10^{-31}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq 3.5 \cdot 10^{-28}:\\ \;\;\;\;\frac{t}{\frac{z}{x}}\\ \mathbf{elif}\;y \leq 7.8 \cdot 10^{+178}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (* y (/ t (- y z)))))
   (if (<= y -1.12e+201)
     t
     (if (<= y -4.4e-31)
       t_1
       (if (<= y 3.5e-28) (/ t (/ z x)) (if (<= y 7.8e+178) t_1 t))))))

C

double code(double x, double y, double z, double t) {
	double t_1 = y * (t / (y - z));
	double tmp;
	if (y <= -1.12e+201) {
		tmp = t;
	} else if (y <= -4.4e-31) {
		tmp = t_1;
	} else if (y <= 3.5e-28) {
		tmp = t / (z / x);
	} else if (y <= 7.8e+178) {
		tmp = t_1;
	} else {
		tmp = t;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: t_1
    real(8) :: tmp
    t_1 = y * (t / (y - z))
    if (y <= (-1.12d+201)) then
        tmp = t
    else if (y <= (-4.4d-31)) then
        tmp = t_1
    else if (y <= 3.5d-28) then
        tmp = t / (z / x)
    else if (y <= 7.8d+178) then
        tmp = t_1
    else
        tmp = t
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double t_1 = y * (t / (y - z));
	double tmp;
	if (y <= -1.12e+201) {
		tmp = t;
	} else if (y <= -4.4e-31) {
		tmp = t_1;
	} else if (y <= 3.5e-28) {
		tmp = t / (z / x);
	} else if (y <= 7.8e+178) {
		tmp = t_1;
	} else {
		tmp = t;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = y * (t / (y - z))
	tmp = 0
	if y <= -1.12e+201:
		tmp = t
	elif y <= -4.4e-31:
		tmp = t_1
	elif y <= 3.5e-28:
		tmp = t / (z / x)
	elif y <= 7.8e+178:
		tmp = t_1
	else:
		tmp = t
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(y * Float64(t / Float64(y - z)))
	tmp = 0.0
	if (y <= -1.12e+201)
		tmp = t;
	elseif (y <= -4.4e-31)
		tmp = t_1;
	elseif (y <= 3.5e-28)
		tmp = Float64(t / Float64(z / x));
	elseif (y <= 7.8e+178)
		tmp = t_1;
	else
		tmp = t;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = y * (t / (y - z));
	tmp = 0.0;
	if (y <= -1.12e+201)
		tmp = t;
	elseif (y <= -4.4e-31)
		tmp = t_1;
	elseif (y <= 3.5e-28)
		tmp = t / (z / x);
	elseif (y <= 7.8e+178)
		tmp = t_1;
	else
		tmp = t;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(y * N[(t / N[(y - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -1.12e+201], t, If[LessEqual[y, -4.4e-31], t$95$1, If[LessEqual[y, 3.5e-28], N[(t / N[(z / x), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 7.8e+178], t$95$1, t]]]]]

Derivation

1. Split input into 3 regimes

2. if y < -1.11999999999999994e201 or 7.7999999999999995e178 < y

   1. Initial program 99.9%

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

   2. Taylor expanded in y around inf 84.4%

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

   if -1.11999999999999994e201 < y < -4.40000000000000019e-31 or 3.5e-28 < y < 7.7999999999999995e178

   1. Initial program 99.8%

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

      1. *-commutative 99.8%

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

      2. associate-*r/ 79.1%

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

      3. associate-/l* 99.8%

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

      4. sub-neg 99.8%

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

      5. +-commutative 99.8%

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

      6. neg-sub0 99.8%

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

      7. associate-+l- 99.8%

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

      8. sub0-neg 99.8%

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

      9. neg-mul-1 99.8%

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

      10. associate-/r* 99.8%

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

   3. Simplified 99.8%

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

   4. Taylor expanded in x around 0 53.9%

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

      1. associate-*l/ 63.3%

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

      2. *-commutative 63.3%

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

   6. Simplified 63.3%

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

   if -4.40000000000000019e-31 < y < 3.5e-28

   1. Initial program 95.9%

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

   2. Taylor expanded in y around 0 68.1%

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

      1. associate-/l* 69.9%

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

   4. Simplified 69.9%

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

4. Final simplification 70.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.12 \cdot 10^{+201}:\\ \;\;\;\;t\\ \mathbf{elif}\;y \leq -4.4 \cdot 10^{-31}:\\ \;\;\;\;y \cdot \frac{t}{y - z}\\ \mathbf{elif}\;y \leq 3.5 \cdot 10^{-28}:\\ \;\;\;\;\frac{t}{\frac{z}{x}}\\ \mathbf{elif}\;y \leq 7.8 \cdot 10^{+178}:\\ \;\;\;\;y \cdot \frac{t}{y - z}\\ \mathbf{else}:\\ \;\;\;\;t\\ \end{array} \]

Alternative 5: 69.2% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := y \cdot \frac{t}{y - z}\\ \mathbf{if}\;y \leq -1.12 \cdot 10^{+201}:\\ \;\;\;\;t\\ \mathbf{elif}\;y \leq -2.1 \cdot 10^{-28}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq 1.05 \cdot 10^{-27}:\\ \;\;\;\;\left(x - y\right) \cdot \frac{t}{z}\\ \mathbf{elif}\;y \leq 7.8 \cdot 10^{+178}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (* y (/ t (- y z)))))
   (if (<= y -1.12e+201)
     t
     (if (<= y -2.1e-28)
       t_1
       (if (<= y 1.05e-27) (* (- x y) (/ t z)) (if (<= y 7.8e+178) t_1 t))))))

C

double code(double x, double y, double z, double t) {
	double t_1 = y * (t / (y - z));
	double tmp;
	if (y <= -1.12e+201) {
		tmp = t;
	} else if (y <= -2.1e-28) {
		tmp = t_1;
	} else if (y <= 1.05e-27) {
		tmp = (x - y) * (t / z);
	} else if (y <= 7.8e+178) {
		tmp = t_1;
	} else {
		tmp = t;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: t_1
    real(8) :: tmp
    t_1 = y * (t / (y - z))
    if (y <= (-1.12d+201)) then
        tmp = t
    else if (y <= (-2.1d-28)) then
        tmp = t_1
    else if (y <= 1.05d-27) then
        tmp = (x - y) * (t / z)
    else if (y <= 7.8d+178) then
        tmp = t_1
    else
        tmp = t
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double t_1 = y * (t / (y - z));
	double tmp;
	if (y <= -1.12e+201) {
		tmp = t;
	} else if (y <= -2.1e-28) {
		tmp = t_1;
	} else if (y <= 1.05e-27) {
		tmp = (x - y) * (t / z);
	} else if (y <= 7.8e+178) {
		tmp = t_1;
	} else {
		tmp = t;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = y * (t / (y - z))
	tmp = 0
	if y <= -1.12e+201:
		tmp = t
	elif y <= -2.1e-28:
		tmp = t_1
	elif y <= 1.05e-27:
		tmp = (x - y) * (t / z)
	elif y <= 7.8e+178:
		tmp = t_1
	else:
		tmp = t
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(y * Float64(t / Float64(y - z)))
	tmp = 0.0
	if (y <= -1.12e+201)
		tmp = t;
	elseif (y <= -2.1e-28)
		tmp = t_1;
	elseif (y <= 1.05e-27)
		tmp = Float64(Float64(x - y) * Float64(t / z));
	elseif (y <= 7.8e+178)
		tmp = t_1;
	else
		tmp = t;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = y * (t / (y - z));
	tmp = 0.0;
	if (y <= -1.12e+201)
		tmp = t;
	elseif (y <= -2.1e-28)
		tmp = t_1;
	elseif (y <= 1.05e-27)
		tmp = (x - y) * (t / z);
	elseif (y <= 7.8e+178)
		tmp = t_1;
	else
		tmp = t;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(y * N[(t / N[(y - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -1.12e+201], t, If[LessEqual[y, -2.1e-28], t$95$1, If[LessEqual[y, 1.05e-27], N[(N[(x - y), $MachinePrecision] * N[(t / z), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 7.8e+178], t$95$1, t]]]]]

Derivation

1. Split input into 3 regimes

2. if y < -1.11999999999999994e201 or 7.7999999999999995e178 < y

   1. Initial program 99.9%

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

   2. Taylor expanded in y around inf 84.4%

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

   if -1.11999999999999994e201 < y < -2.10000000000000006e-28 or 1.05000000000000008e-27 < y < 7.7999999999999995e178

   1. Initial program 99.8%

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

      1. *-commutative 99.8%

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

      2. associate-*r/ 79.1%

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

      3. associate-/l* 99.8%

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

      4. sub-neg 99.8%

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

      5. +-commutative 99.8%

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

      6. neg-sub0 99.8%

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

      7. associate-+l- 99.8%

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

      8. sub0-neg 99.8%

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

      9. neg-mul-1 99.8%

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

      10. associate-/r* 99.8%

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

   3. Simplified 99.8%

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

   4. Taylor expanded in x around 0 53.9%

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

      1. associate-*l/ 63.3%

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

      2. *-commutative 63.3%

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

   6. Simplified 63.3%

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

   if -2.10000000000000006e-28 < y < 1.05000000000000008e-27

   1. Initial program 95.9%

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

   2. Taylor expanded in z around inf 75.3%

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

      1. associate-/l* 76.7%

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

   4. Simplified 76.7%

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

   5. Taylor expanded in t around 0 75.3%

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

      1. associate-/l* 76.7%

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

      2. associate-/r/ 75.2%

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

   7. Simplified 75.2%

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

4. Final simplification 72.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.12 \cdot 10^{+201}:\\ \;\;\;\;t\\ \mathbf{elif}\;y \leq -2.1 \cdot 10^{-28}:\\ \;\;\;\;y \cdot \frac{t}{y - z}\\ \mathbf{elif}\;y \leq 1.05 \cdot 10^{-27}:\\ \;\;\;\;\left(x - y\right) \cdot \frac{t}{z}\\ \mathbf{elif}\;y \leq 7.8 \cdot 10^{+178}:\\ \;\;\;\;y \cdot \frac{t}{y - z}\\ \mathbf{else}:\\ \;\;\;\;t\\ \end{array} \]

Alternative 6: 69.4% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := y \cdot \frac{t}{y - z}\\ \mathbf{if}\;y \leq -1.12 \cdot 10^{+201}:\\ \;\;\;\;t\\ \mathbf{elif}\;y \leq -3.7 \cdot 10^{-26}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq 3.6 \cdot 10^{-28}:\\ \;\;\;\;t \cdot \frac{x - y}{z}\\ \mathbf{elif}\;y \leq 9.5 \cdot 10^{+178}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (* y (/ t (- y z)))))
   (if (<= y -1.12e+201)
     t
     (if (<= y -3.7e-26)
       t_1
       (if (<= y 3.6e-28) (* t (/ (- x y) z)) (if (<= y 9.5e+178) t_1 t))))))

C

double code(double x, double y, double z, double t) {
	double t_1 = y * (t / (y - z));
	double tmp;
	if (y <= -1.12e+201) {
		tmp = t;
	} else if (y <= -3.7e-26) {
		tmp = t_1;
	} else if (y <= 3.6e-28) {
		tmp = t * ((x - y) / z);
	} else if (y <= 9.5e+178) {
		tmp = t_1;
	} else {
		tmp = t;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: t_1
    real(8) :: tmp
    t_1 = y * (t / (y - z))
    if (y <= (-1.12d+201)) then
        tmp = t
    else if (y <= (-3.7d-26)) then
        tmp = t_1
    else if (y <= 3.6d-28) then
        tmp = t * ((x - y) / z)
    else if (y <= 9.5d+178) then
        tmp = t_1
    else
        tmp = t
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double t_1 = y * (t / (y - z));
	double tmp;
	if (y <= -1.12e+201) {
		tmp = t;
	} else if (y <= -3.7e-26) {
		tmp = t_1;
	} else if (y <= 3.6e-28) {
		tmp = t * ((x - y) / z);
	} else if (y <= 9.5e+178) {
		tmp = t_1;
	} else {
		tmp = t;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = y * (t / (y - z))
	tmp = 0
	if y <= -1.12e+201:
		tmp = t
	elif y <= -3.7e-26:
		tmp = t_1
	elif y <= 3.6e-28:
		tmp = t * ((x - y) / z)
	elif y <= 9.5e+178:
		tmp = t_1
	else:
		tmp = t
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(y * Float64(t / Float64(y - z)))
	tmp = 0.0
	if (y <= -1.12e+201)
		tmp = t;
	elseif (y <= -3.7e-26)
		tmp = t_1;
	elseif (y <= 3.6e-28)
		tmp = Float64(t * Float64(Float64(x - y) / z));
	elseif (y <= 9.5e+178)
		tmp = t_1;
	else
		tmp = t;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = y * (t / (y - z));
	tmp = 0.0;
	if (y <= -1.12e+201)
		tmp = t;
	elseif (y <= -3.7e-26)
		tmp = t_1;
	elseif (y <= 3.6e-28)
		tmp = t * ((x - y) / z);
	elseif (y <= 9.5e+178)
		tmp = t_1;
	else
		tmp = t;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(y * N[(t / N[(y - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -1.12e+201], t, If[LessEqual[y, -3.7e-26], t$95$1, If[LessEqual[y, 3.6e-28], N[(t * N[(N[(x - y), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 9.5e+178], t$95$1, t]]]]]

Derivation

1. Split input into 3 regimes

2. if y < -1.11999999999999994e201 or 9.5e178 < y

   1. Initial program 99.9%

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

   2. Taylor expanded in y around inf 84.4%

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

   if -1.11999999999999994e201 < y < -3.6999999999999999e-26 or 3.5999999999999999e-28 < y < 9.5e178

   1. Initial program 99.8%

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

      1. *-commutative 99.8%

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

      2. associate-*r/ 79.1%

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

      3. associate-/l* 99.8%

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

      4. sub-neg 99.8%

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

      5. +-commutative 99.8%

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

      6. neg-sub0 99.8%

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

      7. associate-+l- 99.8%

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

      8. sub0-neg 99.8%

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

      9. neg-mul-1 99.8%

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

      10. associate-/r* 99.8%

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

   3. Simplified 99.8%

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

   4. Taylor expanded in x around 0 53.9%

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

      1. associate-*l/ 63.3%

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

      2. *-commutative 63.3%

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

   6. Simplified 63.3%

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

   if -3.6999999999999999e-26 < y < 3.5999999999999999e-28

   1. Initial program 95.9%

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

   2. Taylor expanded in z around inf 76.5%

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

4. Final simplification 73.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.12 \cdot 10^{+201}:\\ \;\;\;\;t\\ \mathbf{elif}\;y \leq -3.7 \cdot 10^{-26}:\\ \;\;\;\;y \cdot \frac{t}{y - z}\\ \mathbf{elif}\;y \leq 3.6 \cdot 10^{-28}:\\ \;\;\;\;t \cdot \frac{x - y}{z}\\ \mathbf{elif}\;y \leq 9.5 \cdot 10^{+178}:\\ \;\;\;\;y \cdot \frac{t}{y - z}\\ \mathbf{else}:\\ \;\;\;\;t\\ \end{array} \]

Alternative 7: 89.7% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -1.08 \cdot 10^{+191} \lor \neg \left(y \leq 2.3 \cdot 10^{+207}\right):\\ \;\;\;\;\frac{t}{\frac{y - z}{y}}\\ \mathbf{else}:\\ \;\;\;\;\left(y - x\right) \cdot \frac{t}{y - z}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= y -1.08e+191) (not (<= y 2.3e+207)))
   (/ t (/ (- y z) y))
   (* (- y x) (/ t (- y z)))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((y <= -1.08e+191) || !(y <= 2.3e+207)) {
		tmp = t / ((y - z) / y);
	} 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 <= (-1.08d+191)) .or. (.not. (y <= 2.3d+207))) then
        tmp = t / ((y - z) / y)
    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 <= -1.08e+191) || !(y <= 2.3e+207)) {
		tmp = t / ((y - z) / y);
	} else {
		tmp = (y - x) * (t / (y - z));
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (y <= -1.08e+191) or not (y <= 2.3e+207):
		tmp = t / ((y - z) / y)
	else:
		tmp = (y - x) * (t / (y - z))
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((y <= -1.08e+191) || !(y <= 2.3e+207))
		tmp = Float64(t / Float64(Float64(y - z) / y));
	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 <= -1.08e+191) || ~((y <= 2.3e+207)))
		tmp = t / ((y - z) / y);
	else
		tmp = (y - x) * (t / (y - z));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[y, -1.08e+191], N[Not[LessEqual[y, 2.3e+207]], $MachinePrecision]], N[(t / N[(N[(y - z), $MachinePrecision] / y), $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 < -1.08000000000000002e191 or 2.29999999999999995e207 < y

   1. Initial program 99.8%

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

      1. *-commutative 99.8%

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

      2. associate-*r/ 74.0%

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

      3. associate-/l* 99.8%

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

      4. sub-neg 99.8%

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

      5. +-commutative 99.8%

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

      6. neg-sub0 99.8%

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

      7. associate-+l- 99.8%

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

      8. sub0-neg 99.8%

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

      9. neg-mul-1 99.8%

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

      10. associate-/r* 99.8%

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

   3. Simplified 99.8%

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

   4. Taylor expanded in x around 0 97.8%

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

   if -1.08000000000000002e191 < y < 2.29999999999999995e207

   1. Initial program 97.6%

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

      1. *-commutative 97.6%

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

      2. associate-*r/ 86.3%

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

      3. associate-/l* 97.8%

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

      4. sub-neg 97.8%

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

      5. +-commutative 97.8%

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

      6. neg-sub0 97.8%

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

      7. associate-+l- 97.8%

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

      8. sub0-neg 97.8%

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

      9. neg-mul-1 97.8%

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

      10. associate-/r* 97.8%

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

   3. Simplified 97.8%

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

      1. associate-/r/ 92.4%

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

   5. Applied egg-rr 92.4%

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

4. Final simplification 93.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.08 \cdot 10^{+191} \lor \neg \left(y \leq 2.3 \cdot 10^{+207}\right):\\ \;\;\;\;\frac{t}{\frac{y - z}{y}}\\ \mathbf{else}:\\ \;\;\;\;\left(y - x\right) \cdot \frac{t}{y - z}\\ \end{array} \]

Alternative 8: 74.8% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -6 \cdot 10^{-27} \lor \neg \left(z \leq 0.115\right):\\ \;\;\;\;t \cdot \frac{x - y}{z}\\ \mathbf{else}:\\ \;\;\;\;t \cdot \frac{y - x}{y}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= z -6e-27) (not (<= z 0.115)))
   (* t (/ (- x y) z))
   (* t (/ (- y x) y))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((z <= -6e-27) || !(z <= 0.115)) {
		tmp = t * ((x - y) / z);
	} else {
		tmp = t * ((y - x) / 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 ((z <= (-6d-27)) .or. (.not. (z <= 0.115d0))) then
        tmp = t * ((x - y) / z)
    else
        tmp = t * ((y - x) / y)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if ((z <= -6e-27) || !(z <= 0.115)) {
		tmp = t * ((x - y) / z);
	} else {
		tmp = t * ((y - x) / y);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (z <= -6e-27) or not (z <= 0.115):
		tmp = t * ((x - y) / z)
	else:
		tmp = t * ((y - x) / y)
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((z <= -6e-27) || !(z <= 0.115))
		tmp = Float64(t * Float64(Float64(x - y) / z));
	else
		tmp = Float64(t * Float64(Float64(y - x) / y));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((z <= -6e-27) || ~((z <= 0.115)))
		tmp = t * ((x - y) / z);
	else
		tmp = t * ((y - x) / y);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[z, -6e-27], N[Not[LessEqual[z, 0.115]], $MachinePrecision]], N[(t * N[(N[(x - y), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision], N[(t * N[(N[(y - x), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -6.0000000000000002e-27 or 0.115000000000000005 < z

   1. Initial program 97.6%

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

   2. Taylor expanded in z around inf 74.7%

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

   if -6.0000000000000002e-27 < z < 0.115000000000000005

   1. Initial program 98.4%

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

   2. Taylor expanded in z around 0 81.4%

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

      1. associate-*r/ 81.4%

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

      2. neg-mul-1 81.4%

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

      3. neg-sub0 81.4%

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

      4. associate--r- 81.4%

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

      5. neg-sub0 81.4%

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

      6. +-commutative 81.4%

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

      7. sub-neg 81.4%

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

   4. Simplified 81.4%

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

4. Final simplification 77.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -6 \cdot 10^{-27} \lor \neg \left(z \leq 0.115\right):\\ \;\;\;\;t \cdot \frac{x - y}{z}\\ \mathbf{else}:\\ \;\;\;\;t \cdot \frac{y - x}{y}\\ \end{array} \]

Alternative 9: 75.7% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -2.1 \cdot 10^{-9}:\\ \;\;\;\;\frac{t}{\frac{y - z}{y}}\\ \mathbf{elif}\;y \leq 9 \cdot 10^{-26}:\\ \;\;\;\;\frac{t}{\frac{z - y}{x}}\\ \mathbf{else}:\\ \;\;\;\;t - \frac{t}{\frac{y}{x}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= y -2.1e-9)
   (/ t (/ (- y z) y))
   (if (<= y 9e-26) (/ t (/ (- z y) x)) (- t (/ t (/ y x))))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (y <= -2.1e-9) {
		tmp = t / ((y - z) / y);
	} else if (y <= 9e-26) {
		tmp = t / ((z - y) / x);
	} 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 <= (-2.1d-9)) then
        tmp = t / ((y - z) / y)
    else if (y <= 9d-26) then
        tmp = t / ((z - y) / x)
    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 <= -2.1e-9) {
		tmp = t / ((y - z) / y);
	} else if (y <= 9e-26) {
		tmp = t / ((z - y) / x);
	} else {
		tmp = t - (t / (y / x));
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if y <= -2.1e-9:
		tmp = t / ((y - z) / y)
	elif y <= 9e-26:
		tmp = t / ((z - y) / x)
	else:
		tmp = t - (t / (y / x))
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (y <= -2.1e-9)
		tmp = Float64(t / Float64(Float64(y - z) / y));
	elseif (y <= 9e-26)
		tmp = Float64(t / Float64(Float64(z - y) / x));
	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 <= -2.1e-9)
		tmp = t / ((y - z) / y);
	elseif (y <= 9e-26)
		tmp = t / ((z - y) / x);
	else
		tmp = t - (t / (y / x));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[y, -2.1e-9], N[(t / N[(N[(y - z), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 9e-26], N[(t / N[(N[(z - y), $MachinePrecision] / x), $MachinePrecision]), $MachinePrecision], N[(t - N[(t / N[(y / x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if y < -2.10000000000000019e-9

   1. Initial program 99.9%

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

      1. *-commutative 99.9%

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

      2. associate-*r/ 73.4%

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

      3. associate-/l* 99.9%

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

      4. sub-neg 99.9%

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

      5. +-commutative 99.9%

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

      6. neg-sub0 99.9%

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

      7. associate-+l- 99.9%

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

      8. sub0-neg 99.9%

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

      9. neg-mul-1 99.9%

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

      10. associate-/r* 99.9%

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

   3. Simplified 99.9%

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

   4. Taylor expanded in x around 0 81.4%

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

   if -2.10000000000000019e-9 < y < 8.9999999999999998e-26

   1. Initial program 96.2%

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

   2. Taylor expanded in x around inf 80.2%

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

      1. associate-/l* 82.3%

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

   4. Simplified 82.3%

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

   if 8.9999999999999998e-26 < y

   1. Initial program 99.8%

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

   2. Taylor expanded in z around 0 62.5%

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

      1. associate-*r/ 62.5%

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

      2. *-commutative 62.5%

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

      3. neg-mul-1 62.5%

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

      4. distribute-lft-neg-in 62.5%

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

      5. associate-/l* 54.9%

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

      6. neg-sub0 54.9%

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

      7. associate--r- 54.9%

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

      8. neg-sub0 54.9%

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

      9. +-commutative 54.9%

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

      10. sub-neg 54.9%

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

   4. Simplified 54.9%

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

   5. Taylor expanded in y around 0 76.6%

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

      1. mul-1-neg 76.6%

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

      2. unsub-neg 76.6%

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

      3. associate-/l* 76.5%

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

   7. Simplified 76.5%

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

4. Final simplification 80.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -2.1 \cdot 10^{-9}:\\ \;\;\;\;\frac{t}{\frac{y - z}{y}}\\ \mathbf{elif}\;y \leq 9 \cdot 10^{-26}:\\ \;\;\;\;\frac{t}{\frac{z - y}{x}}\\ \mathbf{else}:\\ \;\;\;\;t - \frac{t}{\frac{y}{x}}\\ \end{array} \]

Alternative 10: 60.1% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -1.3 \cdot 10^{+38}:\\ \;\;\;\;t\\ \mathbf{elif}\;y \leq 9.5 \cdot 10^{-26}:\\ \;\;\;\;x \cdot \frac{t}{z}\\ \mathbf{else}:\\ \;\;\;\;t\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= y -1.3e+38) t (if (<= y 9.5e-26) (* x (/ t z)) t)))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (y <= -1.3e+38) {
		tmp = t;
	} else if (y <= 9.5e-26) {
		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 <= (-1.3d+38)) then
        tmp = t
    else if (y <= 9.5d-26) 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 <= -1.3e+38) {
		tmp = t;
	} else if (y <= 9.5e-26) {
		tmp = x * (t / z);
	} else {
		tmp = t;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if y <= -1.3e+38:
		tmp = t
	elif y <= 9.5e-26:
		tmp = x * (t / z)
	else:
		tmp = t
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (y <= -1.3e+38)
		tmp = t;
	elseif (y <= 9.5e-26)
		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 <= -1.3e+38)
		tmp = t;
	elseif (y <= 9.5e-26)
		tmp = x * (t / z);
	else
		tmp = t;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[y, -1.3e+38], t, If[LessEqual[y, 9.5e-26], N[(x * N[(t / z), $MachinePrecision]), $MachinePrecision], t]]

Derivation

1. Split input into 2 regimes

2. if y < -1.3e38 or 9.4999999999999995e-26 < y

   1. Initial program 99.8%

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

   2. Taylor expanded in y around inf 58.4%

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

   if -1.3e38 < y < 9.4999999999999995e-26

   1. Initial program 96.4%

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

   2. Taylor expanded in y around 0 64.2%

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

      1. associate-/l* 65.7%

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

   4. Simplified 65.7%

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

      1. associate-/r/ 64.1%

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

   6. Applied egg-rr 64.1%

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

4. Final simplification 61.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.3 \cdot 10^{+38}:\\ \;\;\;\;t\\ \mathbf{elif}\;y \leq 9.5 \cdot 10^{-26}:\\ \;\;\;\;x \cdot \frac{t}{z}\\ \mathbf{else}:\\ \;\;\;\;t\\ \end{array} \]

Alternative 11: 61.0% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -3.25 \cdot 10^{+38}:\\ \;\;\;\;t\\ \mathbf{elif}\;y \leq 3 \cdot 10^{-26}:\\ \;\;\;\;t \cdot \frac{x}{z}\\ \mathbf{else}:\\ \;\;\;\;t\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= y -3.25e+38) t (if (<= y 3e-26) (* t (/ x z)) t)))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (y <= -3.25e+38) {
		tmp = t;
	} else if (y <= 3e-26) {
		tmp = t * (x / z);
	} else {
		tmp = t;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if (y <= (-3.25d+38)) then
        tmp = t
    else if (y <= 3d-26) then
        tmp = t * (x / z)
    else
        tmp = t
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if (y <= -3.25e+38) {
		tmp = t;
	} else if (y <= 3e-26) {
		tmp = t * (x / z);
	} else {
		tmp = t;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if y <= -3.25e+38:
		tmp = t
	elif y <= 3e-26:
		tmp = t * (x / z)
	else:
		tmp = t
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (y <= -3.25e+38)
		tmp = t;
	elseif (y <= 3e-26)
		tmp = Float64(t * Float64(x / z));
	else
		tmp = t;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (y <= -3.25e+38)
		tmp = t;
	elseif (y <= 3e-26)
		tmp = t * (x / z);
	else
		tmp = t;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[y, -3.25e+38], t, If[LessEqual[y, 3e-26], N[(t * N[(x / z), $MachinePrecision]), $MachinePrecision], t]]

Derivation

1. Split input into 2 regimes

2. if y < -3.25e38 or 3.00000000000000012e-26 < y

   1. Initial program 99.8%

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

   2. Taylor expanded in y around inf 58.4%

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

   if -3.25e38 < y < 3.00000000000000012e-26

   1. Initial program 96.4%

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

   2. Taylor expanded in y around 0 65.5%

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

4. Final simplification 62.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -3.25 \cdot 10^{+38}:\\ \;\;\;\;t\\ \mathbf{elif}\;y \leq 3 \cdot 10^{-26}:\\ \;\;\;\;t \cdot \frac{x}{z}\\ \mathbf{else}:\\ \;\;\;\;t\\ \end{array} \]

Alternative 12: 61.0% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -2.5 \cdot 10^{+38}:\\ \;\;\;\;t\\ \mathbf{elif}\;y \leq 6 \cdot 10^{-26}:\\ \;\;\;\;\frac{t}{\frac{z}{x}}\\ \mathbf{else}:\\ \;\;\;\;t\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= y -2.5e+38) t (if (<= y 6e-26) (/ t (/ z x)) t)))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (y <= -2.5e+38) {
		tmp = t;
	} else if (y <= 6e-26) {
		tmp = t / (z / x);
	} else {
		tmp = t;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if (y <= (-2.5d+38)) then
        tmp = t
    else if (y <= 6d-26) then
        tmp = t / (z / x)
    else
        tmp = t
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if (y <= -2.5e+38) {
		tmp = t;
	} else if (y <= 6e-26) {
		tmp = t / (z / x);
	} else {
		tmp = t;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if y <= -2.5e+38:
		tmp = t
	elif y <= 6e-26:
		tmp = t / (z / x)
	else:
		tmp = t
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (y <= -2.5e+38)
		tmp = t;
	elseif (y <= 6e-26)
		tmp = Float64(t / Float64(z / x));
	else
		tmp = t;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (y <= -2.5e+38)
		tmp = t;
	elseif (y <= 6e-26)
		tmp = t / (z / x);
	else
		tmp = t;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[y, -2.5e+38], t, If[LessEqual[y, 6e-26], N[(t / N[(z / x), $MachinePrecision]), $MachinePrecision], t]]

Derivation

1. Split input into 2 regimes

2. if y < -2.49999999999999985e38 or 6.00000000000000023e-26 < y

   1. Initial program 99.8%

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

   2. Taylor expanded in y around inf 58.4%

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

   if -2.49999999999999985e38 < y < 6.00000000000000023e-26

   1. Initial program 96.4%

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

   2. Taylor expanded in y around 0 64.2%

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

      1. associate-/l* 65.7%

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

   4. Simplified 65.7%

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

4. Final simplification 62.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -2.5 \cdot 10^{+38}:\\ \;\;\;\;t\\ \mathbf{elif}\;y \leq 6 \cdot 10^{-26}:\\ \;\;\;\;\frac{t}{\frac{z}{x}}\\ \mathbf{else}:\\ \;\;\;\;t\\ \end{array} \]

Alternative 13: 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 98.0%

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

2. Final simplification 98.0%

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

Alternative 14: 34.8% accurate, 9.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 98.0%

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

2. Taylor expanded in y around inf 33.5%

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

3. Final simplification 33.5%

   \[\leadsto t \]

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 2023290 
(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))