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

Percentage Accurate: 97.2% → 97.1%

Time: 13.5s

Alternatives: 18

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: 97.2% 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 96.9%

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

   1. *-commutative 96.9%

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

   2. associate-*r/ 84.1%

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

   3. associate-/l* 96.9%

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

   4. sub-neg 96.9%

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

   5. +-commutative 96.9%

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

   6. neg-sub0 96.9%

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

   7. associate-+l- 96.9%

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

   8. sub0-neg 96.9%

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

   9. neg-mul-1 96.9%

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

   10. associate-/r* 96.9%

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

3. Simplified 96.9%

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

4. Final simplification 96.9%

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

Alternative 2: 65.8% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := y \cdot \frac{t}{y - z}\\ \mathbf{if}\;y \leq -1.9 \cdot 10^{+131}:\\ \;\;\;\;t\\ \mathbf{elif}\;y \leq -2.9 \cdot 10^{-92}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq 2.75 \cdot 10^{-120}:\\ \;\;\;\;\frac{t}{\frac{z}{x}}\\ \mathbf{elif}\;y \leq 9.8 \cdot 10^{+138}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (* y (/ t (- y z)))))
   (if (<= y -1.9e+131)
     t
     (if (<= y -2.9e-92)
       t_1
       (if (<= y 2.75e-120) (/ t (/ z x)) (if (<= y 9.8e+138) 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 <= -1.9e+131) {
		tmp = t;
	} else if (y <= -2.9e-92) {
		tmp = t_1;
	} else if (y <= 2.75e-120) {
		tmp = t / (z / x);
	} else if (y <= 9.8e+138) {
		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 <= (-1.9d+131)) then
        tmp = t
    else if (y <= (-2.9d-92)) then
        tmp = t_1
    else if (y <= 2.75d-120) then
        tmp = t / (z / x)
    else if (y <= 9.8d+138) 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 <= -1.9e+131) {
		tmp = t;
	} else if (y <= -2.9e-92) {
		tmp = t_1;
	} else if (y <= 2.75e-120) {
		tmp = t / (z / x);
	} else if (y <= 9.8e+138) {
		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 <= -1.9e+131:
		tmp = t
	elif y <= -2.9e-92:
		tmp = t_1
	elif y <= 2.75e-120:
		tmp = t / (z / x)
	elif y <= 9.8e+138:
		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 <= -1.9e+131)
		tmp = t;
	elseif (y <= -2.9e-92)
		tmp = t_1;
	elseif (y <= 2.75e-120)
		tmp = Float64(t / Float64(z / x));
	elseif (y <= 9.8e+138)
		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 <= -1.9e+131)
		tmp = t;
	elseif (y <= -2.9e-92)
		tmp = t_1;
	elseif (y <= 2.75e-120)
		tmp = t / (z / x);
	elseif (y <= 9.8e+138)
		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, -1.9e+131], t, If[LessEqual[y, -2.9e-92], t$95$1, If[LessEqual[y, 2.75e-120], N[(t / N[(z / x), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 9.8e+138], t$95$1, t]]]]]

Derivation

1. Split input into 3 regimes

2. if y < -1.9000000000000002e131 or 9.79999999999999966e138 < y

   1. Initial program 99.9%

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

   2. Taylor expanded in y around inf 80.5%

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

   if -1.9000000000000002e131 < y < -2.89999999999999985e-92 or 2.7500000000000001e-120 < y < 9.79999999999999966e138

   1. Initial program 97.0%

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

      1. *-commutative 97.0%

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

      2. associate-*r/ 92.6%

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

      3. associate-/l* 97.1%

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

      4. sub-neg 97.1%

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

      5. +-commutative 97.1%

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

      6. neg-sub0 97.1%

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

      7. associate-+l- 97.1%

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

      8. sub0-neg 97.1%

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

      9. neg-mul-1 97.1%

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

      10. associate-/r* 97.1%

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

   3. Simplified 97.1%

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

   4. Taylor expanded in x around 0 58.0%

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

      1. associate-*l/ 57.9%

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

      2. *-commutative 57.9%

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

   6. Simplified 57.9%

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

   if -2.89999999999999985e-92 < y < 2.7500000000000001e-120

   1. Initial program 94.1%

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

   2. Taylor expanded in y around 0 78.2%

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

      1. associate-/l* 80.4%

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

   4. Simplified 80.4%

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

4. Final simplification 71.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.9 \cdot 10^{+131}:\\ \;\;\;\;t\\ \mathbf{elif}\;y \leq -2.9 \cdot 10^{-92}:\\ \;\;\;\;y \cdot \frac{t}{y - z}\\ \mathbf{elif}\;y \leq 2.75 \cdot 10^{-120}:\\ \;\;\;\;\frac{t}{\frac{z}{x}}\\ \mathbf{elif}\;y \leq 9.8 \cdot 10^{+138}:\\ \;\;\;\;y \cdot \frac{t}{y - z}\\ \mathbf{else}:\\ \;\;\;\;t\\ \end{array} \]

Alternative 3: 66.0% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x \cdot \frac{t}{z - y}\\ \mathbf{if}\;x \leq -6.1 \cdot 10^{+66}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;x \leq 2.8 \cdot 10^{-59}:\\ \;\;\;\;y \cdot \frac{t}{y - z}\\ \mathbf{elif}\;x \leq 1.3 \cdot 10^{-25}:\\ \;\;\;\;t \cdot \frac{x - y}{z}\\ \mathbf{elif}\;x \leq 5 \cdot 10^{+20}:\\ \;\;\;\;t\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (* x (/ t (- z y)))))
   (if (<= x -6.1e+66)
     t_1
     (if (<= x 2.8e-59)
       (* y (/ t (- y z)))
       (if (<= x 1.3e-25) (* t (/ (- x y) z)) (if (<= x 5e+20) t t_1))))))

C

double code(double x, double y, double z, double t) {
	double t_1 = x * (t / (z - y));
	double tmp;
	if (x <= -6.1e+66) {
		tmp = t_1;
	} else if (x <= 2.8e-59) {
		tmp = y * (t / (y - z));
	} else if (x <= 1.3e-25) {
		tmp = t * ((x - y) / z);
	} else if (x <= 5e+20) {
		tmp = t;
	} 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 = x * (t / (z - y))
    if (x <= (-6.1d+66)) then
        tmp = t_1
    else if (x <= 2.8d-59) then
        tmp = y * (t / (y - z))
    else if (x <= 1.3d-25) then
        tmp = t * ((x - y) / z)
    else if (x <= 5d+20) then
        tmp = t
    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 = x * (t / (z - y));
	double tmp;
	if (x <= -6.1e+66) {
		tmp = t_1;
	} else if (x <= 2.8e-59) {
		tmp = y * (t / (y - z));
	} else if (x <= 1.3e-25) {
		tmp = t * ((x - y) / z);
	} else if (x <= 5e+20) {
		tmp = t;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = x * (t / (z - y))
	tmp = 0
	if x <= -6.1e+66:
		tmp = t_1
	elif x <= 2.8e-59:
		tmp = y * (t / (y - z))
	elif x <= 1.3e-25:
		tmp = t * ((x - y) / z)
	elif x <= 5e+20:
		tmp = t
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(x * Float64(t / Float64(z - y)))
	tmp = 0.0
	if (x <= -6.1e+66)
		tmp = t_1;
	elseif (x <= 2.8e-59)
		tmp = Float64(y * Float64(t / Float64(y - z)));
	elseif (x <= 1.3e-25)
		tmp = Float64(t * Float64(Float64(x - y) / z));
	elseif (x <= 5e+20)
		tmp = t;
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = x * (t / (z - y));
	tmp = 0.0;
	if (x <= -6.1e+66)
		tmp = t_1;
	elseif (x <= 2.8e-59)
		tmp = y * (t / (y - z));
	elseif (x <= 1.3e-25)
		tmp = t * ((x - y) / z);
	elseif (x <= 5e+20)
		tmp = t;
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(x * N[(t / N[(z - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[x, -6.1e+66], t$95$1, If[LessEqual[x, 2.8e-59], N[(y * N[(t / N[(y - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 1.3e-25], N[(t * N[(N[(x - y), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 5e+20], t, t$95$1]]]]]

Derivation

1. Split input into 4 regimes

2. if x < -6.10000000000000021e66 or 5e20 < x

   1. Initial program 96.4%

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

   2. Taylor expanded in x around inf 77.2%

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

      1. associate-/l* 79.7%

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

   4. Simplified 79.7%

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

      1. associate-/r/ 70.9%

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

   6. Applied egg-rr 70.9%

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

   if -6.10000000000000021e66 < x < 2.79999999999999981e-59

   1. Initial program 96.9%

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

      1. *-commutative 96.9%

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

      2. associate-*r/ 80.0%

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

      3. associate-/l* 97.0%

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

      4. sub-neg 97.0%

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

      5. +-commutative 97.0%

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

      6. neg-sub0 97.0%

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

      7. associate-+l- 97.0%

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

      8. sub0-neg 97.0%

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

      9. neg-mul-1 97.0%

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

      10. associate-/r* 97.0%

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

   3. Simplified 97.0%

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

   4. Taylor expanded in x around 0 71.8%

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

      1. associate-*l/ 73.0%

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

      2. *-commutative 73.0%

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

   6. Simplified 73.0%

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

   if 2.79999999999999981e-59 < x < 1.3e-25

   1. Initial program 99.8%

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

   2. Taylor expanded in z around inf 88.8%

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

   if 1.3e-25 < x < 5e20

   1. Initial program 100.0%

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

   2. Taylor expanded in y around inf 80.9%

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

4. Final simplification 73.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -6.1 \cdot 10^{+66}:\\ \;\;\;\;x \cdot \frac{t}{z - y}\\ \mathbf{elif}\;x \leq 2.8 \cdot 10^{-59}:\\ \;\;\;\;y \cdot \frac{t}{y - z}\\ \mathbf{elif}\;x \leq 1.3 \cdot 10^{-25}:\\ \;\;\;\;t \cdot \frac{x - y}{z}\\ \mathbf{elif}\;x \leq 5 \cdot 10^{+20}:\\ \;\;\;\;t\\ \mathbf{else}:\\ \;\;\;\;x \cdot \frac{t}{z - y}\\ \end{array} \]

Alternative 4: 74.4% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := y \cdot \frac{t}{y - z}\\ t_2 := t \cdot \frac{y - x}{y}\\ \mathbf{if}\;y \leq -1.95 \cdot 10^{+28}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;y \leq -2.8 \cdot 10^{-86}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq 1.7 \cdot 10^{+43}:\\ \;\;\;\;\frac{t}{\frac{z - y}{x}}\\ \mathbf{elif}\;y \leq 3.9 \cdot 10^{+108}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (* y (/ t (- y z)))) (t_2 (* t (/ (- y x) y))))
   (if (<= y -1.95e+28)
     t_2
     (if (<= y -2.8e-86)
       t_1
       (if (<= y 1.7e+43) (/ t (/ (- z y) x)) (if (<= y 3.9e+108) t_1 t_2))))))

C

double code(double x, double y, double z, double t) {
	double t_1 = y * (t / (y - z));
	double t_2 = t * ((y - x) / y);
	double tmp;
	if (y <= -1.95e+28) {
		tmp = t_2;
	} else if (y <= -2.8e-86) {
		tmp = t_1;
	} else if (y <= 1.7e+43) {
		tmp = t / ((z - y) / x);
	} else if (y <= 3.9e+108) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = y * (t / (y - z))
    t_2 = t * ((y - x) / y)
    if (y <= (-1.95d+28)) then
        tmp = t_2
    else if (y <= (-2.8d-86)) then
        tmp = t_1
    else if (y <= 1.7d+43) then
        tmp = t / ((z - y) / x)
    else if (y <= 3.9d+108) then
        tmp = t_1
    else
        tmp = t_2
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double t_1 = y * (t / (y - z));
	double t_2 = t * ((y - x) / y);
	double tmp;
	if (y <= -1.95e+28) {
		tmp = t_2;
	} else if (y <= -2.8e-86) {
		tmp = t_1;
	} else if (y <= 1.7e+43) {
		tmp = t / ((z - y) / x);
	} else if (y <= 3.9e+108) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = y * (t / (y - z))
	t_2 = t * ((y - x) / y)
	tmp = 0
	if y <= -1.95e+28:
		tmp = t_2
	elif y <= -2.8e-86:
		tmp = t_1
	elif y <= 1.7e+43:
		tmp = t / ((z - y) / x)
	elif y <= 3.9e+108:
		tmp = t_1
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(y * Float64(t / Float64(y - z)))
	t_2 = Float64(t * Float64(Float64(y - x) / y))
	tmp = 0.0
	if (y <= -1.95e+28)
		tmp = t_2;
	elseif (y <= -2.8e-86)
		tmp = t_1;
	elseif (y <= 1.7e+43)
		tmp = Float64(t / Float64(Float64(z - y) / x));
	elseif (y <= 3.9e+108)
		tmp = t_1;
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = y * (t / (y - z));
	t_2 = t * ((y - x) / y);
	tmp = 0.0;
	if (y <= -1.95e+28)
		tmp = t_2;
	elseif (y <= -2.8e-86)
		tmp = t_1;
	elseif (y <= 1.7e+43)
		tmp = t / ((z - y) / x);
	elseif (y <= 3.9e+108)
		tmp = t_1;
	else
		tmp = t_2;
	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]}, Block[{t$95$2 = N[(t * N[(N[(y - x), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -1.95e+28], t$95$2, If[LessEqual[y, -2.8e-86], t$95$1, If[LessEqual[y, 1.7e+43], N[(t / N[(N[(z - y), $MachinePrecision] / x), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 3.9e+108], t$95$1, t$95$2]]]]]]

Derivation

1. Split input into 3 regimes

2. if y < -1.9499999999999999e28 or 3.89999999999999985e108 < y

   1. Initial program 99.9%

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

   2. Taylor expanded in z around 0 84.8%

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

      1. associate-*r/ 84.8%

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

      2. neg-mul-1 84.8%

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

      3. neg-sub0 84.8%

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

      4. associate--r- 84.8%

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

      5. neg-sub0 84.8%

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

      6. +-commutative 84.8%

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

      7. sub-neg 84.8%

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

   4. Simplified 84.8%

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

   if -1.9499999999999999e28 < y < -2.80000000000000009e-86 or 1.70000000000000006e43 < y < 3.89999999999999985e108

   1. Initial program 95.7%

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

      1. *-commutative 95.7%

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

      2. associate-*r/ 91.7%

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

      3. associate-/l* 95.6%

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

      4. sub-neg 95.6%

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

      5. +-commutative 95.6%

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

      6. neg-sub0 95.6%

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

      7. associate-+l- 95.6%

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

      8. sub0-neg 95.6%

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

      9. neg-mul-1 95.6%

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

      10. associate-/r* 95.6%

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

   3. Simplified 95.6%

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

   4. Taylor expanded in x around 0 68.6%

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

      1. associate-*l/ 70.6%

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

      2. *-commutative 70.6%

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

   6. Simplified 70.6%

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

   if -2.80000000000000009e-86 < y < 1.70000000000000006e43

   1. Initial program 94.8%

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

   2. Taylor expanded in x around inf 78.1%

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

      1. associate-/l* 80.5%

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

   4. Simplified 80.5%

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

4. Final simplification 80.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.95 \cdot 10^{+28}:\\ \;\;\;\;t \cdot \frac{y - x}{y}\\ \mathbf{elif}\;y \leq -2.8 \cdot 10^{-86}:\\ \;\;\;\;y \cdot \frac{t}{y - z}\\ \mathbf{elif}\;y \leq 1.7 \cdot 10^{+43}:\\ \;\;\;\;\frac{t}{\frac{z - y}{x}}\\ \mathbf{elif}\;y \leq 3.9 \cdot 10^{+108}:\\ \;\;\;\;y \cdot \frac{t}{y - z}\\ \mathbf{else}:\\ \;\;\;\;t \cdot \frac{y - x}{y}\\ \end{array} \]

Alternative 5: 74.4% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := t \cdot \frac{y - x}{y}\\ \mathbf{if}\;y \leq -1 \cdot 10^{+25}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq -2.7 \cdot 10^{-86}:\\ \;\;\;\;\frac{y}{\frac{y - z}{t}}\\ \mathbf{elif}\;y \leq 1.9 \cdot 10^{+43}:\\ \;\;\;\;\frac{t}{\frac{z - y}{x}}\\ \mathbf{elif}\;y \leq 7.6 \cdot 10^{+110}:\\ \;\;\;\;y \cdot \frac{t}{y - z}\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (* t (/ (- y x) y))))
   (if (<= y -1e+25)
     t_1
     (if (<= y -2.7e-86)
       (/ y (/ (- y z) t))
       (if (<= y 1.9e+43)
         (/ t (/ (- z y) x))
         (if (<= y 7.6e+110) (* y (/ t (- y z))) t_1))))))

C

double code(double x, double y, double z, double t) {
	double t_1 = t * ((y - x) / y);
	double tmp;
	if (y <= -1e+25) {
		tmp = t_1;
	} else if (y <= -2.7e-86) {
		tmp = y / ((y - z) / t);
	} else if (y <= 1.9e+43) {
		tmp = t / ((z - y) / x);
	} else if (y <= 7.6e+110) {
		tmp = y * (t / (y - z));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: t_1
    real(8) :: tmp
    t_1 = t * ((y - x) / y)
    if (y <= (-1d+25)) then
        tmp = t_1
    else if (y <= (-2.7d-86)) then
        tmp = y / ((y - z) / t)
    else if (y <= 1.9d+43) then
        tmp = t / ((z - y) / x)
    else if (y <= 7.6d+110) then
        tmp = y * (t / (y - z))
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double t_1 = t * ((y - x) / y);
	double tmp;
	if (y <= -1e+25) {
		tmp = t_1;
	} else if (y <= -2.7e-86) {
		tmp = y / ((y - z) / t);
	} else if (y <= 1.9e+43) {
		tmp = t / ((z - y) / x);
	} else if (y <= 7.6e+110) {
		tmp = y * (t / (y - z));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = t * ((y - x) / y)
	tmp = 0
	if y <= -1e+25:
		tmp = t_1
	elif y <= -2.7e-86:
		tmp = y / ((y - z) / t)
	elif y <= 1.9e+43:
		tmp = t / ((z - y) / x)
	elif y <= 7.6e+110:
		tmp = y * (t / (y - z))
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(t * Float64(Float64(y - x) / y))
	tmp = 0.0
	if (y <= -1e+25)
		tmp = t_1;
	elseif (y <= -2.7e-86)
		tmp = Float64(y / Float64(Float64(y - z) / t));
	elseif (y <= 1.9e+43)
		tmp = Float64(t / Float64(Float64(z - y) / x));
	elseif (y <= 7.6e+110)
		tmp = Float64(y * Float64(t / Float64(y - z)));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = t * ((y - x) / y);
	tmp = 0.0;
	if (y <= -1e+25)
		tmp = t_1;
	elseif (y <= -2.7e-86)
		tmp = y / ((y - z) / t);
	elseif (y <= 1.9e+43)
		tmp = t / ((z - y) / x);
	elseif (y <= 7.6e+110)
		tmp = y * (t / (y - z));
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(t * N[(N[(y - x), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -1e+25], t$95$1, If[LessEqual[y, -2.7e-86], N[(y / N[(N[(y - z), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 1.9e+43], N[(t / N[(N[(z - y), $MachinePrecision] / x), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 7.6e+110], N[(y * N[(t / N[(y - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]]]

Derivation

1. Split input into 4 regimes

2. if y < -1.00000000000000009e25 or 7.59999999999999978e110 < y

   1. Initial program 99.9%

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

   2. Taylor expanded in z around 0 84.8%

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

      1. associate-*r/ 84.8%

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

      2. neg-mul-1 84.8%

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

      3. neg-sub0 84.8%

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

      4. associate--r- 84.8%

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

      5. neg-sub0 84.8%

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

      6. +-commutative 84.8%

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

      7. sub-neg 84.8%

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

   4. Simplified 84.8%

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

   if -1.00000000000000009e25 < y < -2.69999999999999992e-86

   1. Initial program 90.9%

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

      1. *-commutative 90.9%

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

      2. associate-*r/ 95.5%

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

      3. associate-/l* 90.9%

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

      4. sub-neg 90.9%

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

      5. +-commutative 90.9%

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

      6. neg-sub0 90.9%

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

      7. associate-+l- 90.9%

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

      8. sub0-neg 90.9%

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

      9. neg-mul-1 90.9%

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

      10. associate-/r* 90.9%

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

   3. Simplified 90.9%

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

   4. Taylor expanded in x around 0 68.7%

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

      1. associate-*l/ 68.6%

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

      2. *-commutative 68.6%

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

   6. Simplified 68.6%

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

      1. clear-num 68.6%

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

      2. un-div-inv 68.7%

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

   8. Applied egg-rr 68.7%

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

   if -2.69999999999999992e-86 < y < 1.90000000000000004e43

   1. Initial program 94.8%

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

   2. Taylor expanded in x around inf 78.1%

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

      1. associate-/l* 80.5%

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

   4. Simplified 80.5%

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

   if 1.90000000000000004e43 < y < 7.59999999999999978e110

   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/ 88.4%

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

      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 68.4%

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

      1. associate-*l/ 72.2%

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

      2. *-commutative 72.2%

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

   6. Simplified 72.2%

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

4. Final simplification 80.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1 \cdot 10^{+25}:\\ \;\;\;\;t \cdot \frac{y - x}{y}\\ \mathbf{elif}\;y \leq -2.7 \cdot 10^{-86}:\\ \;\;\;\;\frac{y}{\frac{y - z}{t}}\\ \mathbf{elif}\;y \leq 1.9 \cdot 10^{+43}:\\ \;\;\;\;\frac{t}{\frac{z - y}{x}}\\ \mathbf{elif}\;y \leq 7.6 \cdot 10^{+110}:\\ \;\;\;\;y \cdot \frac{t}{y - z}\\ \mathbf{else}:\\ \;\;\;\;t \cdot \frac{y - x}{y}\\ \end{array} \]

Alternative 6: 74.3% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := t \cdot \frac{y - x}{y}\\ \mathbf{if}\;y \leq -4.6 \cdot 10^{+23}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq -2.8 \cdot 10^{-86}:\\ \;\;\;\;\frac{t \cdot y}{y - z}\\ \mathbf{elif}\;y \leq 1.5 \cdot 10^{+47}:\\ \;\;\;\;\frac{t}{\frac{z - y}{x}}\\ \mathbf{elif}\;y \leq 2.25 \cdot 10^{+109}:\\ \;\;\;\;y \cdot \frac{t}{y - z}\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (* t (/ (- y x) y))))
   (if (<= y -4.6e+23)
     t_1
     (if (<= y -2.8e-86)
       (/ (* t y) (- y z))
       (if (<= y 1.5e+47)
         (/ t (/ (- z y) x))
         (if (<= y 2.25e+109) (* y (/ t (- y z))) t_1))))))

C

double code(double x, double y, double z, double t) {
	double t_1 = t * ((y - x) / y);
	double tmp;
	if (y <= -4.6e+23) {
		tmp = t_1;
	} else if (y <= -2.8e-86) {
		tmp = (t * y) / (y - z);
	} else if (y <= 1.5e+47) {
		tmp = t / ((z - y) / x);
	} else if (y <= 2.25e+109) {
		tmp = y * (t / (y - z));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: t_1
    real(8) :: tmp
    t_1 = t * ((y - x) / y)
    if (y <= (-4.6d+23)) then
        tmp = t_1
    else if (y <= (-2.8d-86)) then
        tmp = (t * y) / (y - z)
    else if (y <= 1.5d+47) then
        tmp = t / ((z - y) / x)
    else if (y <= 2.25d+109) then
        tmp = y * (t / (y - z))
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double t_1 = t * ((y - x) / y);
	double tmp;
	if (y <= -4.6e+23) {
		tmp = t_1;
	} else if (y <= -2.8e-86) {
		tmp = (t * y) / (y - z);
	} else if (y <= 1.5e+47) {
		tmp = t / ((z - y) / x);
	} else if (y <= 2.25e+109) {
		tmp = y * (t / (y - z));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = t * ((y - x) / y)
	tmp = 0
	if y <= -4.6e+23:
		tmp = t_1
	elif y <= -2.8e-86:
		tmp = (t * y) / (y - z)
	elif y <= 1.5e+47:
		tmp = t / ((z - y) / x)
	elif y <= 2.25e+109:
		tmp = y * (t / (y - z))
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(t * Float64(Float64(y - x) / y))
	tmp = 0.0
	if (y <= -4.6e+23)
		tmp = t_1;
	elseif (y <= -2.8e-86)
		tmp = Float64(Float64(t * y) / Float64(y - z));
	elseif (y <= 1.5e+47)
		tmp = Float64(t / Float64(Float64(z - y) / x));
	elseif (y <= 2.25e+109)
		tmp = Float64(y * Float64(t / Float64(y - z)));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = t * ((y - x) / y);
	tmp = 0.0;
	if (y <= -4.6e+23)
		tmp = t_1;
	elseif (y <= -2.8e-86)
		tmp = (t * y) / (y - z);
	elseif (y <= 1.5e+47)
		tmp = t / ((z - y) / x);
	elseif (y <= 2.25e+109)
		tmp = y * (t / (y - z));
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(t * N[(N[(y - x), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -4.6e+23], t$95$1, If[LessEqual[y, -2.8e-86], N[(N[(t * y), $MachinePrecision] / N[(y - z), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 1.5e+47], N[(t / N[(N[(z - y), $MachinePrecision] / x), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 2.25e+109], N[(y * N[(t / N[(y - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]]]

Derivation

1. Split input into 4 regimes

2. if y < -4.6000000000000001e23 or 2.2499999999999998e109 < y

   1. Initial program 99.9%

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

   2. Taylor expanded in z around 0 84.1%

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

      1. associate-*r/ 84.1%

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

      2. neg-mul-1 84.1%

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

      3. neg-sub0 84.1%

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

      4. associate--r- 84.1%

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

      5. neg-sub0 84.1%

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

      6. +-commutative 84.1%

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

      7. sub-neg 84.1%

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

   4. Simplified 84.1%

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

   if -4.6000000000000001e23 < y < -2.80000000000000009e-86

   1. Initial program 90.0%

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

      1. *-commutative 90.0%

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

      2. associate-*r/ 95.1%

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

      3. associate-/l* 90.0%

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

      4. sub-neg 90.0%

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

      5. +-commutative 90.0%

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

      6. neg-sub0 90.0%

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

      7. associate-+l- 90.0%

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

      8. sub0-neg 90.0%

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

      9. neg-mul-1 90.0%

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

      10. associate-/r* 90.0%

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

   3. Simplified 90.0%

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

   4. Taylor expanded in x around 0 70.5%

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

   if -2.80000000000000009e-86 < y < 1.5000000000000001e47

   1. Initial program 94.8%

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

   2. Taylor expanded in x around inf 78.1%

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

      1. associate-/l* 80.5%

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

   4. Simplified 80.5%

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

   if 1.5000000000000001e47 < y < 2.2499999999999998e109

   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/ 88.4%

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

      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 68.4%

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

      1. associate-*l/ 72.2%

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

      2. *-commutative 72.2%

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

   6. Simplified 72.2%

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

4. Final simplification 80.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -4.6 \cdot 10^{+23}:\\ \;\;\;\;t \cdot \frac{y - x}{y}\\ \mathbf{elif}\;y \leq -2.8 \cdot 10^{-86}:\\ \;\;\;\;\frac{t \cdot y}{y - z}\\ \mathbf{elif}\;y \leq 1.5 \cdot 10^{+47}:\\ \;\;\;\;\frac{t}{\frac{z - y}{x}}\\ \mathbf{elif}\;y \leq 2.25 \cdot 10^{+109}:\\ \;\;\;\;y \cdot \frac{t}{y - z}\\ \mathbf{else}:\\ \;\;\;\;t \cdot \frac{y - x}{y}\\ \end{array} \]

Alternative 7: 74.2% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := t \cdot \frac{y - x}{y}\\ \mathbf{if}\;y \leq -2.1 \cdot 10^{+18}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq -2.8 \cdot 10^{-86}:\\ \;\;\;\;\frac{t \cdot y}{y - z}\\ \mathbf{elif}\;y \leq 1.52 \cdot 10^{-167}:\\ \;\;\;\;\frac{t}{\frac{z - y}{x}}\\ \mathbf{elif}\;y \leq 8.5 \cdot 10^{-40}:\\ \;\;\;\;\frac{t \cdot \left(x - y\right)}{z}\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (* t (/ (- y x) y))))
   (if (<= y -2.1e+18)
     t_1
     (if (<= y -2.8e-86)
       (/ (* t y) (- y z))
       (if (<= y 1.52e-167)
         (/ t (/ (- z y) x))
         (if (<= y 8.5e-40) (/ (* t (- x y)) z) t_1))))))

C

double code(double x, double y, double z, double t) {
	double t_1 = t * ((y - x) / y);
	double tmp;
	if (y <= -2.1e+18) {
		tmp = t_1;
	} else if (y <= -2.8e-86) {
		tmp = (t * y) / (y - z);
	} else if (y <= 1.52e-167) {
		tmp = t / ((z - y) / x);
	} else if (y <= 8.5e-40) {
		tmp = (t * (x - y)) / z;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: t_1
    real(8) :: tmp
    t_1 = t * ((y - x) / y)
    if (y <= (-2.1d+18)) then
        tmp = t_1
    else if (y <= (-2.8d-86)) then
        tmp = (t * y) / (y - z)
    else if (y <= 1.52d-167) then
        tmp = t / ((z - y) / x)
    else if (y <= 8.5d-40) then
        tmp = (t * (x - y)) / z
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double t_1 = t * ((y - x) / y);
	double tmp;
	if (y <= -2.1e+18) {
		tmp = t_1;
	} else if (y <= -2.8e-86) {
		tmp = (t * y) / (y - z);
	} else if (y <= 1.52e-167) {
		tmp = t / ((z - y) / x);
	} else if (y <= 8.5e-40) {
		tmp = (t * (x - y)) / z;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = t * ((y - x) / y)
	tmp = 0
	if y <= -2.1e+18:
		tmp = t_1
	elif y <= -2.8e-86:
		tmp = (t * y) / (y - z)
	elif y <= 1.52e-167:
		tmp = t / ((z - y) / x)
	elif y <= 8.5e-40:
		tmp = (t * (x - y)) / z
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(t * Float64(Float64(y - x) / y))
	tmp = 0.0
	if (y <= -2.1e+18)
		tmp = t_1;
	elseif (y <= -2.8e-86)
		tmp = Float64(Float64(t * y) / Float64(y - z));
	elseif (y <= 1.52e-167)
		tmp = Float64(t / Float64(Float64(z - y) / x));
	elseif (y <= 8.5e-40)
		tmp = Float64(Float64(t * Float64(x - y)) / z);
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = t * ((y - x) / y);
	tmp = 0.0;
	if (y <= -2.1e+18)
		tmp = t_1;
	elseif (y <= -2.8e-86)
		tmp = (t * y) / (y - z);
	elseif (y <= 1.52e-167)
		tmp = t / ((z - y) / x);
	elseif (y <= 8.5e-40)
		tmp = (t * (x - y)) / z;
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(t * N[(N[(y - x), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -2.1e+18], t$95$1, If[LessEqual[y, -2.8e-86], N[(N[(t * y), $MachinePrecision] / N[(y - z), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 1.52e-167], N[(t / N[(N[(z - y), $MachinePrecision] / x), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 8.5e-40], N[(N[(t * N[(x - y), $MachinePrecision]), $MachinePrecision] / z), $MachinePrecision], t$95$1]]]]]

Derivation

1. Split input into 4 regimes

2. if y < -2.1e18 or 8.4999999999999998e-40 < y

   1. Initial program 99.9%

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

   2. Taylor expanded in z around 0 79.3%

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

      1. associate-*r/ 79.3%

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

      2. neg-mul-1 79.3%

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

      3. neg-sub0 79.3%

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

      4. associate--r- 79.3%

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

      5. neg-sub0 79.3%

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

      6. +-commutative 79.3%

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

      7. sub-neg 79.3%

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

   4. Simplified 79.3%

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

   if -2.1e18 < y < -2.80000000000000009e-86

   1. Initial program 90.0%

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

      1. *-commutative 90.0%

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

      2. associate-*r/ 95.1%

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

      3. associate-/l* 90.0%

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

      4. sub-neg 90.0%

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

      5. +-commutative 90.0%

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

      6. neg-sub0 90.0%

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

      7. associate-+l- 90.0%

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

      8. sub0-neg 90.0%

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

      9. neg-mul-1 90.0%

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

      10. associate-/r* 90.0%

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

   3. Simplified 90.0%

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

   4. Taylor expanded in x around 0 70.5%

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

   if -2.80000000000000009e-86 < y < 1.52e-167

   1. Initial program 93.5%

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

   2. Taylor expanded in x around inf 83.6%

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

      1. associate-/l* 87.3%

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

   4. Simplified 87.3%

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

   if 1.52e-167 < y < 8.4999999999999998e-40

   1. Initial program 95.1%

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

   2. Taylor expanded in z around inf 77.2%

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

4. Final simplification 80.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -2.1 \cdot 10^{+18}:\\ \;\;\;\;t \cdot \frac{y - x}{y}\\ \mathbf{elif}\;y \leq -2.8 \cdot 10^{-86}:\\ \;\;\;\;\frac{t \cdot y}{y - z}\\ \mathbf{elif}\;y \leq 1.52 \cdot 10^{-167}:\\ \;\;\;\;\frac{t}{\frac{z - y}{x}}\\ \mathbf{elif}\;y \leq 8.5 \cdot 10^{-40}:\\ \;\;\;\;\frac{t \cdot \left(x - y\right)}{z}\\ \mathbf{else}:\\ \;\;\;\;t \cdot \frac{y - x}{y}\\ \end{array} \]

Alternative 8: 59.3% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := y \cdot \frac{-t}{z}\\ \mathbf{if}\;y \leq -3 \cdot 10^{-54}:\\ \;\;\;\;t\\ \mathbf{elif}\;y \leq -1.3 \cdot 10^{-86}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq 2.3 \cdot 10^{-124}:\\ \;\;\;\;\frac{t}{\frac{z}{x}}\\ \mathbf{elif}\;y \leq 1.15 \cdot 10^{+52}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (* y (/ (- t) z))))
   (if (<= y -3e-54)
     t
     (if (<= y -1.3e-86)
       t_1
       (if (<= y 2.3e-124) (/ t (/ z x)) (if (<= y 1.15e+52) t_1 t))))))

C

double code(double x, double y, double z, double t) {
	double t_1 = y * (-t / z);
	double tmp;
	if (y <= -3e-54) {
		tmp = t;
	} else if (y <= -1.3e-86) {
		tmp = t_1;
	} else if (y <= 2.3e-124) {
		tmp = t / (z / x);
	} else if (y <= 1.15e+52) {
		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 / z)
    if (y <= (-3d-54)) then
        tmp = t
    else if (y <= (-1.3d-86)) then
        tmp = t_1
    else if (y <= 2.3d-124) then
        tmp = t / (z / x)
    else if (y <= 1.15d+52) 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 / z);
	double tmp;
	if (y <= -3e-54) {
		tmp = t;
	} else if (y <= -1.3e-86) {
		tmp = t_1;
	} else if (y <= 2.3e-124) {
		tmp = t / (z / x);
	} else if (y <= 1.15e+52) {
		tmp = t_1;
	} else {
		tmp = t;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = y * (-t / z)
	tmp = 0
	if y <= -3e-54:
		tmp = t
	elif y <= -1.3e-86:
		tmp = t_1
	elif y <= 2.3e-124:
		tmp = t / (z / x)
	elif y <= 1.15e+52:
		tmp = t_1
	else:
		tmp = t
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(y * Float64(Float64(-t) / z))
	tmp = 0.0
	if (y <= -3e-54)
		tmp = t;
	elseif (y <= -1.3e-86)
		tmp = t_1;
	elseif (y <= 2.3e-124)
		tmp = Float64(t / Float64(z / x));
	elseif (y <= 1.15e+52)
		tmp = t_1;
	else
		tmp = t;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = y * (-t / z);
	tmp = 0.0;
	if (y <= -3e-54)
		tmp = t;
	elseif (y <= -1.3e-86)
		tmp = t_1;
	elseif (y <= 2.3e-124)
		tmp = t / (z / x);
	elseif (y <= 1.15e+52)
		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) / z), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -3e-54], t, If[LessEqual[y, -1.3e-86], t$95$1, If[LessEqual[y, 2.3e-124], N[(t / N[(z / x), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 1.15e+52], t$95$1, t]]]]]

Derivation

1. Split input into 3 regimes

2. if y < -3.00000000000000009e-54 or 1.15e52 < y

   1. Initial program 99.2%

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

   2. Taylor expanded in y around inf 63.2%

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

   if -3.00000000000000009e-54 < y < -1.3000000000000001e-86 or 2.30000000000000012e-124 < y < 1.15e52

   1. Initial program 94.9%

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

      1. *-commutative 94.9%

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

      2. associate-*r/ 99.8%

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

      3. associate-/l* 94.9%

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

      4. sub-neg 94.9%

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

      5. +-commutative 94.9%

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

      6. neg-sub0 94.9%

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

      7. associate-+l- 94.9%

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

      8. sub0-neg 94.9%

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

      9. neg-mul-1 94.9%

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

      10. associate-/r* 94.9%

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

   3. Simplified 94.9%

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

   4. Taylor expanded in x around 0 63.1%

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

      1. associate-*l/ 60.6%

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

      2. *-commutative 60.6%

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

   6. Simplified 60.6%

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

   7. Taylor expanded in y around 0 58.1%

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

      1. associate-*r/ 58.1%

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

      2. neg-mul-1 58.1%

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

   9. Simplified 58.1%

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

   if -1.3000000000000001e-86 < y < 2.30000000000000012e-124

   1. Initial program 94.2%

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

   2. Taylor expanded in y around 0 76.4%

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

      1. associate-/l* 78.5%

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

   4. Simplified 78.5%

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

4. Final simplification 67.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -3 \cdot 10^{-54}:\\ \;\;\;\;t\\ \mathbf{elif}\;y \leq -1.3 \cdot 10^{-86}:\\ \;\;\;\;y \cdot \frac{-t}{z}\\ \mathbf{elif}\;y \leq 2.3 \cdot 10^{-124}:\\ \;\;\;\;\frac{t}{\frac{z}{x}}\\ \mathbf{elif}\;y \leq 1.15 \cdot 10^{+52}:\\ \;\;\;\;y \cdot \frac{-t}{z}\\ \mathbf{else}:\\ \;\;\;\;t\\ \end{array} \]

Alternative 9: 60.5% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -1 \cdot 10^{-51}:\\ \;\;\;\;t\\ \mathbf{elif}\;y \leq -2.8 \cdot 10^{-86}:\\ \;\;\;\;y \cdot \frac{-t}{z}\\ \mathbf{elif}\;y \leq 4.3 \cdot 10^{-56}:\\ \;\;\;\;\frac{t}{\frac{z}{x}}\\ \mathbf{elif}\;y \leq 3.7 \cdot 10^{+43}:\\ \;\;\;\;t \cdot \left(-\frac{x}{y}\right)\\ \mathbf{else}:\\ \;\;\;\;t\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= y -1e-51)
   t
   (if (<= y -2.8e-86)
     (* y (/ (- t) z))
     (if (<= y 4.3e-56)
       (/ t (/ z x))
       (if (<= y 3.7e+43) (* t (- (/ x y))) t)))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (y <= -1e-51) {
		tmp = t;
	} else if (y <= -2.8e-86) {
		tmp = y * (-t / z);
	} else if (y <= 4.3e-56) {
		tmp = t / (z / x);
	} else if (y <= 3.7e+43) {
		tmp = t * -(x / y);
	} else {
		tmp = t;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if (y <= (-1d-51)) then
        tmp = t
    else if (y <= (-2.8d-86)) then
        tmp = y * (-t / z)
    else if (y <= 4.3d-56) then
        tmp = t / (z / x)
    else if (y <= 3.7d+43) then
        tmp = t * -(x / y)
    else
        tmp = t
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if (y <= -1e-51) {
		tmp = t;
	} else if (y <= -2.8e-86) {
		tmp = y * (-t / z);
	} else if (y <= 4.3e-56) {
		tmp = t / (z / x);
	} else if (y <= 3.7e+43) {
		tmp = t * -(x / y);
	} else {
		tmp = t;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if y <= -1e-51:
		tmp = t
	elif y <= -2.8e-86:
		tmp = y * (-t / z)
	elif y <= 4.3e-56:
		tmp = t / (z / x)
	elif y <= 3.7e+43:
		tmp = t * -(x / y)
	else:
		tmp = t
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (y <= -1e-51)
		tmp = t;
	elseif (y <= -2.8e-86)
		tmp = Float64(y * Float64(Float64(-t) / z));
	elseif (y <= 4.3e-56)
		tmp = Float64(t / Float64(z / x));
	elseif (y <= 3.7e+43)
		tmp = Float64(t * Float64(-Float64(x / y)));
	else
		tmp = t;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (y <= -1e-51)
		tmp = t;
	elseif (y <= -2.8e-86)
		tmp = y * (-t / z);
	elseif (y <= 4.3e-56)
		tmp = t / (z / x);
	elseif (y <= 3.7e+43)
		tmp = t * -(x / y);
	else
		tmp = t;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[y, -1e-51], t, If[LessEqual[y, -2.8e-86], N[(y * N[((-t) / z), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 4.3e-56], N[(t / N[(z / x), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 3.7e+43], N[(t * (-N[(x / y), $MachinePrecision])), $MachinePrecision], t]]]]

Derivation

1. Split input into 4 regimes

2. if y < -1e-51 or 3.7000000000000001e43 < y

   1. Initial program 99.2%

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

   2. Taylor expanded in y around inf 62.4%

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

   if -1e-51 < y < -2.80000000000000009e-86

   1. Initial program 83.8%

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

      1. *-commutative 83.8%

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

      2. associate-*r/ 100.0%

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

      3. associate-/l* 83.8%

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

      4. sub-neg 83.8%

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

      5. +-commutative 83.8%

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

      6. neg-sub0 83.8%

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

      7. associate-+l- 83.8%

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

      8. sub0-neg 83.8%

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

      9. neg-mul-1 83.8%

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

      10. associate-/r* 83.8%

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

   3. Simplified 83.8%

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

   4. Taylor expanded in x around 0 100.0%

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

      1. associate-*l/ 99.7%

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

      2. *-commutative 99.7%

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

   6. Simplified 99.7%

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

   7. Taylor expanded in y around 0 96.4%

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

      1. associate-*r/ 96.4%

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

      2. neg-mul-1 96.4%

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

   9. Simplified 96.4%

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

   if -2.80000000000000009e-86 < y < 4.3000000000000001e-56

   1. Initial program 94.7%

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

   2. Taylor expanded in y around 0 74.3%

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

      1. associate-/l* 76.2%

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

   4. Simplified 76.2%

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

   if 4.3000000000000001e-56 < y < 3.7000000000000001e43

   1. Initial program 95.1%

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

   2. Taylor expanded in x around inf 72.0%

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

      1. associate-/l* 71.9%

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

   4. Simplified 71.9%

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

   5. Taylor expanded in z around 0 61.6%

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

      1. metadata-eval 61.6%

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

      2. times-frac 61.6%

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

      3. associate-*r* 61.6%

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

      4. neg-mul-1 61.6%

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

      5. times-frac 61.7%

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

      6. distribute-neg-frac 61.7%

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

      7. /-rgt-identity 61.7%

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

   7. Simplified 61.7%

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

4. Final simplification 68.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1 \cdot 10^{-51}:\\ \;\;\;\;t\\ \mathbf{elif}\;y \leq -2.8 \cdot 10^{-86}:\\ \;\;\;\;y \cdot \frac{-t}{z}\\ \mathbf{elif}\;y \leq 4.3 \cdot 10^{-56}:\\ \;\;\;\;\frac{t}{\frac{z}{x}}\\ \mathbf{elif}\;y \leq 3.7 \cdot 10^{+43}:\\ \;\;\;\;t \cdot \left(-\frac{x}{y}\right)\\ \mathbf{else}:\\ \;\;\;\;t\\ \end{array} \]

Alternative 10: 60.4% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -5 \cdot 10^{-52}:\\ \;\;\;\;t\\ \mathbf{elif}\;y \leq -9.5 \cdot 10^{-91}:\\ \;\;\;\;\frac{t \cdot \left(-y\right)}{z}\\ \mathbf{elif}\;y \leq 1.6 \cdot 10^{-60}:\\ \;\;\;\;\frac{t}{\frac{z}{x}}\\ \mathbf{elif}\;y \leq 4 \cdot 10^{+46}:\\ \;\;\;\;t \cdot \left(-\frac{x}{y}\right)\\ \mathbf{else}:\\ \;\;\;\;t\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= y -5e-52)
   t
   (if (<= y -9.5e-91)
     (/ (* t (- y)) z)
     (if (<= y 1.6e-60) (/ t (/ z x)) (if (<= y 4e+46) (* t (- (/ x y))) t)))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (y <= -5e-52) {
		tmp = t;
	} else if (y <= -9.5e-91) {
		tmp = (t * -y) / z;
	} else if (y <= 1.6e-60) {
		tmp = t / (z / x);
	} else if (y <= 4e+46) {
		tmp = t * -(x / y);
	} else {
		tmp = t;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if (y <= (-5d-52)) then
        tmp = t
    else if (y <= (-9.5d-91)) then
        tmp = (t * -y) / z
    else if (y <= 1.6d-60) then
        tmp = t / (z / x)
    else if (y <= 4d+46) then
        tmp = t * -(x / y)
    else
        tmp = t
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if (y <= -5e-52) {
		tmp = t;
	} else if (y <= -9.5e-91) {
		tmp = (t * -y) / z;
	} else if (y <= 1.6e-60) {
		tmp = t / (z / x);
	} else if (y <= 4e+46) {
		tmp = t * -(x / y);
	} else {
		tmp = t;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if y <= -5e-52:
		tmp = t
	elif y <= -9.5e-91:
		tmp = (t * -y) / z
	elif y <= 1.6e-60:
		tmp = t / (z / x)
	elif y <= 4e+46:
		tmp = t * -(x / y)
	else:
		tmp = t
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (y <= -5e-52)
		tmp = t;
	elseif (y <= -9.5e-91)
		tmp = Float64(Float64(t * Float64(-y)) / z);
	elseif (y <= 1.6e-60)
		tmp = Float64(t / Float64(z / x));
	elseif (y <= 4e+46)
		tmp = Float64(t * Float64(-Float64(x / y)));
	else
		tmp = t;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (y <= -5e-52)
		tmp = t;
	elseif (y <= -9.5e-91)
		tmp = (t * -y) / z;
	elseif (y <= 1.6e-60)
		tmp = t / (z / x);
	elseif (y <= 4e+46)
		tmp = t * -(x / y);
	else
		tmp = t;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[y, -5e-52], t, If[LessEqual[y, -9.5e-91], N[(N[(t * (-y)), $MachinePrecision] / z), $MachinePrecision], If[LessEqual[y, 1.6e-60], N[(t / N[(z / x), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 4e+46], N[(t * (-N[(x / y), $MachinePrecision])), $MachinePrecision], t]]]]

Derivation

1. Split input into 4 regimes

2. if y < -5e-52 or 4e46 < y

   1. Initial program 99.2%

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

   2. Taylor expanded in y around inf 62.4%

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

   if -5e-52 < y < -9.5e-91

   1. Initial program 87.6%

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

      1. *-commutative 87.6%

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

      2. associate-*r/ 99.8%

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

      3. associate-/l* 87.6%

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

      4. sub-neg 87.6%

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

      5. +-commutative 87.6%

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

      6. neg-sub0 87.6%

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

      7. associate-+l- 87.6%

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

      8. sub0-neg 87.6%

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

      9. neg-mul-1 87.6%

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

      10. associate-/r* 87.6%

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

   3. Simplified 87.6%

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

   4. Taylor expanded in x around 0 76.1%

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

      1. associate-*l/ 75.9%

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

      2. *-commutative 75.9%

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

   6. Simplified 75.9%

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

   7. Taylor expanded in y around 0 72.6%

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

      1. associate-*r/ 72.6%

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

      2. *-commutative 72.6%

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

      3. neg-mul-1 72.6%

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

      4. distribute-rgt-neg-in 72.6%

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

   9. Simplified 72.6%

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

   if -9.5e-91 < y < 1.6000000000000001e-60

   1. Initial program 94.6%

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

   2. Taylor expanded in y around 0 76.0%

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

      1. associate-/l* 77.9%

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

   4. Simplified 77.9%

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

   if 1.6000000000000001e-60 < y < 4e46

   1. Initial program 95.1%

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

   2. Taylor expanded in x around inf 72.0%

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

      1. associate-/l* 71.9%

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

   4. Simplified 71.9%

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

   5. Taylor expanded in z around 0 61.6%

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

      1. metadata-eval 61.6%

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

      2. times-frac 61.6%

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

      3. associate-*r* 61.6%

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

      4. neg-mul-1 61.6%

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

      5. times-frac 61.7%

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

      6. distribute-neg-frac 61.7%

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

      7. /-rgt-identity 61.7%

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

   7. Simplified 61.7%

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

4. Final simplification 68.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -5 \cdot 10^{-52}:\\ \;\;\;\;t\\ \mathbf{elif}\;y \leq -9.5 \cdot 10^{-91}:\\ \;\;\;\;\frac{t \cdot \left(-y\right)}{z}\\ \mathbf{elif}\;y \leq 1.6 \cdot 10^{-60}:\\ \;\;\;\;\frac{t}{\frac{z}{x}}\\ \mathbf{elif}\;y \leq 4 \cdot 10^{+46}:\\ \;\;\;\;t \cdot \left(-\frac{x}{y}\right)\\ \mathbf{else}:\\ \;\;\;\;t\\ \end{array} \]

Alternative 11: 75.3% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{t}{\frac{z - y}{x}}\\ \mathbf{if}\;x \leq -1.16 \cdot 10^{+67}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;x \leq 8.5 \cdot 10^{-27}:\\ \;\;\;\;\frac{-t}{\frac{z}{y} + -1}\\ \mathbf{elif}\;x \leq 1.85 \cdot 10^{+72}:\\ \;\;\;\;t \cdot \frac{y - x}{y}\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (/ t (/ (- z y) x))))
   (if (<= x -1.16e+67)
     t_1
     (if (<= x 8.5e-27)
       (/ (- t) (+ (/ z y) -1.0))
       (if (<= x 1.85e+72) (* t (/ (- y x) y)) t_1)))))

C

double code(double x, double y, double z, double t) {
	double t_1 = t / ((z - y) / x);
	double tmp;
	if (x <= -1.16e+67) {
		tmp = t_1;
	} else if (x <= 8.5e-27) {
		tmp = -t / ((z / y) + -1.0);
	} else if (x <= 1.85e+72) {
		tmp = t * ((y - x) / 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 / ((z - y) / x)
    if (x <= (-1.16d+67)) then
        tmp = t_1
    else if (x <= 8.5d-27) then
        tmp = -t / ((z / y) + (-1.0d0))
    else if (x <= 1.85d+72) then
        tmp = t * ((y - x) / 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 / ((z - y) / x);
	double tmp;
	if (x <= -1.16e+67) {
		tmp = t_1;
	} else if (x <= 8.5e-27) {
		tmp = -t / ((z / y) + -1.0);
	} else if (x <= 1.85e+72) {
		tmp = t * ((y - x) / y);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = t / ((z - y) / x)
	tmp = 0
	if x <= -1.16e+67:
		tmp = t_1
	elif x <= 8.5e-27:
		tmp = -t / ((z / y) + -1.0)
	elif x <= 1.85e+72:
		tmp = t * ((y - x) / y)
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(t / Float64(Float64(z - y) / x))
	tmp = 0.0
	if (x <= -1.16e+67)
		tmp = t_1;
	elseif (x <= 8.5e-27)
		tmp = Float64(Float64(-t) / Float64(Float64(z / y) + -1.0));
	elseif (x <= 1.85e+72)
		tmp = Float64(t * Float64(Float64(y - x) / y));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = t / ((z - y) / x);
	tmp = 0.0;
	if (x <= -1.16e+67)
		tmp = t_1;
	elseif (x <= 8.5e-27)
		tmp = -t / ((z / y) + -1.0);
	elseif (x <= 1.85e+72)
		tmp = t * ((y - x) / y);
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(t / N[(N[(z - y), $MachinePrecision] / x), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[x, -1.16e+67], t$95$1, If[LessEqual[x, 8.5e-27], N[((-t) / N[(N[(z / y), $MachinePrecision] + -1.0), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 1.85e+72], N[(t * N[(N[(y - x), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if x < -1.15999999999999994e67 or 1.8500000000000001e72 < x

   1. Initial program 95.9%

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

   2. Taylor expanded in x around inf 81.1%

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

      1. associate-/l* 83.9%

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

   4. Simplified 83.9%

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

   if -1.15999999999999994e67 < x < 8.50000000000000033e-27

   1. Initial program 97.1%

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

   2. Taylor expanded in x around 0 71.0%

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

      1. mul-1-neg 71.0%

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

      2. associate-/l* 84.0%

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

      3. distribute-neg-frac 84.0%

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

      4. div-sub 84.0%

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

      5. *-inverses 84.0%

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

   4. Simplified 84.0%

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

   if 8.50000000000000033e-27 < x < 1.8500000000000001e72

   1. Initial program 99.9%

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

   2. Taylor expanded in z around 0 83.0%

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

      1. associate-*r/ 83.0%

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

      2. neg-mul-1 83.0%

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

      3. neg-sub0 83.0%

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

      4. associate--r- 83.0%

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

      5. neg-sub0 83.0%

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

      6. +-commutative 83.0%

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

      7. sub-neg 83.0%

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

   4. Simplified 83.0%

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

4. Final simplification 83.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -1.16 \cdot 10^{+67}:\\ \;\;\;\;\frac{t}{\frac{z - y}{x}}\\ \mathbf{elif}\;x \leq 8.5 \cdot 10^{-27}:\\ \;\;\;\;\frac{-t}{\frac{z}{y} + -1}\\ \mathbf{elif}\;x \leq 1.85 \cdot 10^{+72}:\\ \;\;\;\;t \cdot \frac{y - x}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{t}{\frac{z - y}{x}}\\ \end{array} \]

Alternative 12: 66.4% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -5.8 \cdot 10^{+66} \lor \neg \left(x \leq 1450000000\right):\\ \;\;\;\;x \cdot \frac{t}{z - y}\\ \mathbf{else}:\\ \;\;\;\;y \cdot \frac{t}{y - z}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= x -5.8e+66) (not (<= x 1450000000.0)))
   (* x (/ t (- z y)))
   (* y (/ t (- y z)))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((x <= -5.8e+66) || !(x <= 1450000000.0)) {
		tmp = x * (t / (z - y));
	} else {
		tmp = y * (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 ((x <= (-5.8d+66)) .or. (.not. (x <= 1450000000.0d0))) then
        tmp = x * (t / (z - y))
    else
        tmp = y * (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 ((x <= -5.8e+66) || !(x <= 1450000000.0)) {
		tmp = x * (t / (z - y));
	} else {
		tmp = y * (t / (y - z));
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (x <= -5.8e+66) or not (x <= 1450000000.0):
		tmp = x * (t / (z - y))
	else:
		tmp = y * (t / (y - z))
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((x <= -5.8e+66) || !(x <= 1450000000.0))
		tmp = Float64(x * Float64(t / Float64(z - y)));
	else
		tmp = Float64(y * Float64(t / Float64(y - z)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((x <= -5.8e+66) || ~((x <= 1450000000.0)))
		tmp = x * (t / (z - y));
	else
		tmp = y * (t / (y - z));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[x, -5.8e+66], N[Not[LessEqual[x, 1450000000.0]], $MachinePrecision]], N[(x * N[(t / N[(z - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(y * N[(t / N[(y - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < -5.79999999999999972e66 or 1.45e9 < x

   1. Initial program 96.5%

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

   2. Taylor expanded in x around inf 76.1%

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

      1. associate-/l* 78.5%

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

   4. Simplified 78.5%

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

      1. associate-/r/ 69.9%

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

   6. Applied egg-rr 69.9%

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

   if -5.79999999999999972e66 < x < 1.45e9

   1. Initial program 97.3%

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

      1. *-commutative 97.3%

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

      2. associate-*r/ 80.8%

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

      3. associate-/l* 97.3%

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

      4. sub-neg 97.3%

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

      5. +-commutative 97.3%

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

      6. neg-sub0 97.3%

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

      7. associate-+l- 97.3%

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

      8. sub0-neg 97.3%

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

      9. neg-mul-1 97.3%

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

      10. associate-/r* 97.3%

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

   3. Simplified 97.3%

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

   4. Taylor expanded in x around 0 70.0%

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

      1. associate-*l/ 71.1%

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

      2. *-commutative 71.1%

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

   6. Simplified 71.1%

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

4. Final simplification 70.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -5.8 \cdot 10^{+66} \lor \neg \left(x \leq 1450000000\right):\\ \;\;\;\;x \cdot \frac{t}{z - y}\\ \mathbf{else}:\\ \;\;\;\;y \cdot \frac{t}{y - z}\\ \end{array} \]

Alternative 13: 74.9% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -6.2 \cdot 10^{-35} \lor \neg \left(y \leq 8.5 \cdot 10^{-40}\right):\\ \;\;\;\;t \cdot \frac{y - x}{y}\\ \mathbf{else}:\\ \;\;\;\;t \cdot \frac{x - y}{z}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= y -6.2e-35) (not (<= y 8.5e-40)))
   (* t (/ (- y x) y))
   (* t (/ (- x y) z))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((y <= -6.2e-35) || !(y <= 8.5e-40)) {
		tmp = t * ((y - x) / y);
	} else {
		tmp = t * ((x - y) / z);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if ((y <= (-6.2d-35)) .or. (.not. (y <= 8.5d-40))) then
        tmp = t * ((y - x) / y)
    else
        tmp = t * ((x - y) / z)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if ((y <= -6.2e-35) || !(y <= 8.5e-40)) {
		tmp = t * ((y - x) / y);
	} else {
		tmp = t * ((x - y) / z);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (y <= -6.2e-35) or not (y <= 8.5e-40):
		tmp = t * ((y - x) / y)
	else:
		tmp = t * ((x - y) / z)
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((y <= -6.2e-35) || !(y <= 8.5e-40))
		tmp = Float64(t * Float64(Float64(y - x) / y));
	else
		tmp = Float64(t * Float64(Float64(x - y) / z));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((y <= -6.2e-35) || ~((y <= 8.5e-40)))
		tmp = t * ((y - x) / y);
	else
		tmp = t * ((x - y) / z);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[y, -6.2e-35], N[Not[LessEqual[y, 8.5e-40]], $MachinePrecision]], N[(t * N[(N[(y - x), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision], N[(t * N[(N[(x - y), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -6.20000000000000024e-35 or 8.4999999999999998e-40 < y

   1. Initial program 99.9%

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

   2. Taylor expanded in z around 0 78.0%

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

      1. associate-*r/ 78.0%

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

      2. neg-mul-1 78.0%

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

      3. neg-sub0 78.0%

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

      4. associate--r- 78.0%

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

      5. neg-sub0 78.0%

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

      6. +-commutative 78.0%

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

      7. sub-neg 78.0%

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

   4. Simplified 78.0%

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

   if -6.20000000000000024e-35 < y < 8.4999999999999998e-40

   1. Initial program 92.6%

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

   2. Taylor expanded in z around inf 79.5%

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

4. Final simplification 78.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -6.2 \cdot 10^{-35} \lor \neg \left(y \leq 8.5 \cdot 10^{-40}\right):\\ \;\;\;\;t \cdot \frac{y - x}{y}\\ \mathbf{else}:\\ \;\;\;\;t \cdot \frac{x - y}{z}\\ \end{array} \]

Alternative 14: 60.3% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -7 \cdot 10^{-40}:\\ \;\;\;\;t\\ \mathbf{elif}\;y \leq 2.8 \cdot 10^{+45}:\\ \;\;\;\;x \cdot \frac{t}{z}\\ \mathbf{else}:\\ \;\;\;\;t\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= y -7e-40) t (if (<= y 2.8e+45) (* x (/ t z)) t)))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (y <= -7e-40) {
		tmp = t;
	} else if (y <= 2.8e+45) {
		tmp = x * (t / z);
	} else {
		tmp = t;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if (y <= (-7d-40)) then
        tmp = t
    else if (y <= 2.8d+45) then
        tmp = x * (t / z)
    else
        tmp = t
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if (y <= -7e-40) {
		tmp = t;
	} else if (y <= 2.8e+45) {
		tmp = x * (t / z);
	} else {
		tmp = t;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if y <= -7e-40:
		tmp = t
	elif y <= 2.8e+45:
		tmp = x * (t / z)
	else:
		tmp = t
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (y <= -7e-40)
		tmp = t;
	elseif (y <= 2.8e+45)
		tmp = Float64(x * Float64(t / z));
	else
		tmp = t;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (y <= -7e-40)
		tmp = t;
	elseif (y <= 2.8e+45)
		tmp = x * (t / z);
	else
		tmp = t;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[y, -7e-40], t, If[LessEqual[y, 2.8e+45], N[(x * N[(t / z), $MachinePrecision]), $MachinePrecision], t]]

Derivation

1. Split input into 2 regimes

2. if y < -7.0000000000000003e-40 or 2.7999999999999999e45 < y

   1. Initial program 99.9%

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

   2. Taylor expanded in y around inf 63.9%

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

   if -7.0000000000000003e-40 < y < 2.7999999999999999e45

   1. Initial program 93.6%

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

   2. Taylor expanded in x around inf 73.6%

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

      1. associate-/l* 75.8%

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

   4. Simplified 75.8%

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

      1. associate-/r/ 73.7%

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

   6. Applied egg-rr 73.7%

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

   7. Taylor expanded in z around inf 61.1%

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

4. Final simplification 62.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -7 \cdot 10^{-40}:\\ \;\;\;\;t\\ \mathbf{elif}\;y \leq 2.8 \cdot 10^{+45}:\\ \;\;\;\;x \cdot \frac{t}{z}\\ \mathbf{else}:\\ \;\;\;\;t\\ \end{array} \]

Alternative 15: 61.8% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -6.8 \cdot 10^{-39}:\\ \;\;\;\;t\\ \mathbf{elif}\;y \leq 2.5 \cdot 10^{+43}:\\ \;\;\;\;t \cdot \frac{x}{z}\\ \mathbf{else}:\\ \;\;\;\;t\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= y -6.8e-39) t (if (<= y 2.5e+43) (* t (/ x z)) t)))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (y <= -6.8e-39) {
		tmp = t;
	} else if (y <= 2.5e+43) {
		tmp = t * (x / z);
	} else {
		tmp = t;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if (y <= (-6.8d-39)) then
        tmp = t
    else if (y <= 2.5d+43) then
        tmp = t * (x / z)
    else
        tmp = t
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if (y <= -6.8e-39) {
		tmp = t;
	} else if (y <= 2.5e+43) {
		tmp = t * (x / z);
	} else {
		tmp = t;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if y <= -6.8e-39:
		tmp = t
	elif y <= 2.5e+43:
		tmp = t * (x / z)
	else:
		tmp = t
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (y <= -6.8e-39)
		tmp = t;
	elseif (y <= 2.5e+43)
		tmp = Float64(t * Float64(x / z));
	else
		tmp = t;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (y <= -6.8e-39)
		tmp = t;
	elseif (y <= 2.5e+43)
		tmp = t * (x / z);
	else
		tmp = t;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[y, -6.8e-39], t, If[LessEqual[y, 2.5e+43], N[(t * N[(x / z), $MachinePrecision]), $MachinePrecision], t]]

Derivation

1. Split input into 2 regimes

2. if y < -6.7999999999999998e-39 or 2.5000000000000002e43 < y

   1. Initial program 99.9%

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

   2. Taylor expanded in y around inf 63.9%

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

   if -6.7999999999999998e-39 < y < 2.5000000000000002e43

   1. Initial program 93.6%

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

   2. Taylor expanded in y around 0 63.8%

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

4. Final simplification 63.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -6.8 \cdot 10^{-39}:\\ \;\;\;\;t\\ \mathbf{elif}\;y \leq 2.5 \cdot 10^{+43}:\\ \;\;\;\;t \cdot \frac{x}{z}\\ \mathbf{else}:\\ \;\;\;\;t\\ \end{array} \]

Alternative 16: 61.9% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -1.45 \cdot 10^{-32}:\\ \;\;\;\;t\\ \mathbf{elif}\;y \leq 1.75 \cdot 10^{+43}:\\ \;\;\;\;\frac{t}{\frac{z}{x}}\\ \mathbf{else}:\\ \;\;\;\;t\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= y -1.45e-32) t (if (<= y 1.75e+43) (/ t (/ z x)) t)))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (y <= -1.45e-32) {
		tmp = t;
	} else if (y <= 1.75e+43) {
		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 <= (-1.45d-32)) then
        tmp = t
    else if (y <= 1.75d+43) 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 <= -1.45e-32) {
		tmp = t;
	} else if (y <= 1.75e+43) {
		tmp = t / (z / x);
	} else {
		tmp = t;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if y <= -1.45e-32:
		tmp = t
	elif y <= 1.75e+43:
		tmp = t / (z / x)
	else:
		tmp = t
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (y <= -1.45e-32)
		tmp = t;
	elseif (y <= 1.75e+43)
		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 <= -1.45e-32)
		tmp = t;
	elseif (y <= 1.75e+43)
		tmp = t / (z / x);
	else
		tmp = t;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[y, -1.45e-32], t, If[LessEqual[y, 1.75e+43], N[(t / N[(z / x), $MachinePrecision]), $MachinePrecision], t]]

Derivation

1. Split input into 2 regimes

2. if y < -1.44999999999999998e-32 or 1.7500000000000001e43 < y

   1. Initial program 99.9%

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

   2. Taylor expanded in y around inf 63.9%

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

   if -1.44999999999999998e-32 < y < 1.7500000000000001e43

   1. Initial program 93.6%

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

   2. Taylor expanded in y around 0 61.6%

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

      1. associate-/l* 63.8%

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

   4. Simplified 63.8%

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

4. Final simplification 63.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.45 \cdot 10^{-32}:\\ \;\;\;\;t\\ \mathbf{elif}\;y \leq 1.75 \cdot 10^{+43}:\\ \;\;\;\;\frac{t}{\frac{z}{x}}\\ \mathbf{else}:\\ \;\;\;\;t\\ \end{array} \]

Alternative 17: 97.2% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 96.9%

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

2. Final simplification 96.9%

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

Alternative 18: 35.7% accurate, 9.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 96.9%

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

2. Taylor expanded in y around inf 38.1%

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

3. Final simplification 38.1%

   \[\leadsto t \]

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 2023274 
(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))