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

Percentage Accurate: 96.8% → 96.7%

Time: 8.3s

Alternatives: 15

Speedup: 1.0×

Specification

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Initial Program: 96.8% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Alternative 1: 96.7% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 97.1%

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

   1. associate-*l/ 82.3%

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

   2. associate-/l* 88.0%

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

3. Simplified 88.0%

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

   1. associate-*r/ 82.3%

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

   2. associate-*l/ 97.1%

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

   3. *-commutative 97.1%

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

   4. clear-num 96.7%

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

   5. un-div-inv 97.4%

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

6. Applied egg-rr 97.4%

   \[\leadsto \color{blue}{\frac{t}{\frac{z - y}{x - y}}} \]
7. Add Preprocessing

Alternative 2: 72.6% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := t - t \cdot \frac{x}{y}\\ \mathbf{if}\;z \leq -1.35 \cdot 10^{-53}:\\ \;\;\;\;\frac{t}{\frac{z}{x - y}}\\ \mathbf{elif}\;z \leq 9.4 \cdot 10^{-26}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq 5.3 \cdot 10^{+54}:\\ \;\;\;\;t \cdot \frac{y}{y - z}\\ \mathbf{elif}\;z \leq 1.35 \cdot 10^{+58}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq 3.5 \cdot 10^{+97}:\\ \;\;\;\;\frac{t}{\frac{z - y}{x}}\\ \mathbf{else}:\\ \;\;\;\;t \cdot \frac{x - y}{z}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (- t (* t (/ x y)))))
   (if (<= z -1.35e-53)
     (/ t (/ z (- x y)))
     (if (<= z 9.4e-26)
       t_1
       (if (<= z 5.3e+54)
         (* t (/ y (- y z)))
         (if (<= z 1.35e+58)
           t_1
           (if (<= z 3.5e+97) (/ t (/ (- z y) x)) (* t (/ (- x y) z)))))))))

C

double code(double x, double y, double z, double t) {
	double t_1 = t - (t * (x / y));
	double tmp;
	if (z <= -1.35e-53) {
		tmp = t / (z / (x - y));
	} else if (z <= 9.4e-26) {
		tmp = t_1;
	} else if (z <= 5.3e+54) {
		tmp = t * (y / (y - z));
	} else if (z <= 1.35e+58) {
		tmp = t_1;
	} else if (z <= 3.5e+97) {
		tmp = t / ((z - y) / x);
	} 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) :: t_1
    real(8) :: tmp
    t_1 = t - (t * (x / y))
    if (z <= (-1.35d-53)) then
        tmp = t / (z / (x - y))
    else if (z <= 9.4d-26) then
        tmp = t_1
    else if (z <= 5.3d+54) then
        tmp = t * (y / (y - z))
    else if (z <= 1.35d+58) then
        tmp = t_1
    else if (z <= 3.5d+97) then
        tmp = t / ((z - y) / x)
    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 t_1 = t - (t * (x / y));
	double tmp;
	if (z <= -1.35e-53) {
		tmp = t / (z / (x - y));
	} else if (z <= 9.4e-26) {
		tmp = t_1;
	} else if (z <= 5.3e+54) {
		tmp = t * (y / (y - z));
	} else if (z <= 1.35e+58) {
		tmp = t_1;
	} else if (z <= 3.5e+97) {
		tmp = t / ((z - y) / x);
	} else {
		tmp = t * ((x - y) / z);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = t - (t * (x / y))
	tmp = 0
	if z <= -1.35e-53:
		tmp = t / (z / (x - y))
	elif z <= 9.4e-26:
		tmp = t_1
	elif z <= 5.3e+54:
		tmp = t * (y / (y - z))
	elif z <= 1.35e+58:
		tmp = t_1
	elif z <= 3.5e+97:
		tmp = t / ((z - y) / x)
	else:
		tmp = t * ((x - y) / z)
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(t - Float64(t * Float64(x / y)))
	tmp = 0.0
	if (z <= -1.35e-53)
		tmp = Float64(t / Float64(z / Float64(x - y)));
	elseif (z <= 9.4e-26)
		tmp = t_1;
	elseif (z <= 5.3e+54)
		tmp = Float64(t * Float64(y / Float64(y - z)));
	elseif (z <= 1.35e+58)
		tmp = t_1;
	elseif (z <= 3.5e+97)
		tmp = Float64(t / Float64(Float64(z - y) / x));
	else
		tmp = Float64(t * Float64(Float64(x - y) / z));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = t - (t * (x / y));
	tmp = 0.0;
	if (z <= -1.35e-53)
		tmp = t / (z / (x - y));
	elseif (z <= 9.4e-26)
		tmp = t_1;
	elseif (z <= 5.3e+54)
		tmp = t * (y / (y - z));
	elseif (z <= 1.35e+58)
		tmp = t_1;
	elseif (z <= 3.5e+97)
		tmp = t / ((z - y) / x);
	else
		tmp = t * ((x - y) / z);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(t - N[(t * N[(x / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -1.35e-53], N[(t / N[(z / N[(x - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 9.4e-26], t$95$1, If[LessEqual[z, 5.3e+54], N[(t * N[(y / N[(y - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 1.35e+58], t$95$1, If[LessEqual[z, 3.5e+97], N[(t / N[(N[(z - y), $MachinePrecision] / x), $MachinePrecision]), $MachinePrecision], N[(t * N[(N[(x - y), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision]]]]]]]

Derivation

1. Split input into 5 regimes

2. if z < -1.35e-53

   1. Initial program 99.7%

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

      1. associate-*l/ 81.1%

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

      2. associate-/l* 86.3%

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

   3. Simplified 86.3%

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

      1. associate-*r/ 81.1%

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

      2. associate-*l/ 99.7%

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

      3. *-commutative 99.7%

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

      4. clear-num 99.6%

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

      5. un-div-inv 99.8%

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

   6. Applied egg-rr 99.8%

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

   7. Taylor expanded in z around inf 79.3%

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

   if -1.35e-53 < z < 9.39999999999999979e-26 or 5.30000000000000018e54 < z < 1.3500000000000001e58

   1. Initial program 95.9%

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

      1. associate-*l/ 81.7%

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

      2. associate-/l* 86.9%

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

   3. Simplified 86.9%

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

   5. Taylor expanded in z around 0 78.1%

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

      1. associate-*r/ 78.1%

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

      2. neg-mul-1 78.1%

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

   7. Simplified 78.1%

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

   8. Taylor expanded in x around 0 85.7%

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

      1. mul-1-neg 85.7%

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

      2. unsub-neg 85.7%

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

      3. associate-/l* 87.9%

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

   10. Simplified 87.9%

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

   if 9.39999999999999979e-26 < z < 5.30000000000000018e54

   1. Initial program 100.0%

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

   3. Taylor expanded in x around 0 87.3%

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

      1. neg-mul-1 87.3%

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

      2. distribute-neg-frac2 87.3%

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

   5. Simplified 87.3%

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

   6. Taylor expanded in t around 0 68.9%

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

      1. associate-/l* 87.3%

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

   8. Simplified 87.3%

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

   if 1.3500000000000001e58 < z < 3.5000000000000001e97

   1. Initial program 99.7%

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

      1. associate-*l/ 99.7%

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

      2. associate-/l* 95.8%

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

   3. Simplified 95.8%

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

      1. associate-*r/ 99.7%

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

      2. associate-*l/ 99.7%

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

      3. *-commutative 99.7%

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

      4. clear-num 99.7%

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

      5. un-div-inv 100.0%

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

   6. Applied egg-rr 100.0%

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

   7. Taylor expanded in x around inf 100.0%

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

   if 3.5000000000000001e97 < z

   1. Initial program 95.4%

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

   3. Taylor expanded in z around inf 87.2%

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

4. Final simplification 85.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.35 \cdot 10^{-53}:\\ \;\;\;\;\frac{t}{\frac{z}{x - y}}\\ \mathbf{elif}\;z \leq 9.4 \cdot 10^{-26}:\\ \;\;\;\;t - t \cdot \frac{x}{y}\\ \mathbf{elif}\;z \leq 5.3 \cdot 10^{+54}:\\ \;\;\;\;t \cdot \frac{y}{y - z}\\ \mathbf{elif}\;z \leq 1.35 \cdot 10^{+58}:\\ \;\;\;\;t - t \cdot \frac{x}{y}\\ \mathbf{elif}\;z \leq 3.5 \cdot 10^{+97}:\\ \;\;\;\;\frac{t}{\frac{z - y}{x}}\\ \mathbf{else}:\\ \;\;\;\;t \cdot \frac{x - y}{z}\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 72.5% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := t - t \cdot \frac{x}{y}\\ \mathbf{if}\;z \leq -3.4 \cdot 10^{-54}:\\ \;\;\;\;\frac{t}{\frac{z}{x - y}}\\ \mathbf{elif}\;z \leq 8.5 \cdot 10^{-24}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq 7.8 \cdot 10^{+52}:\\ \;\;\;\;t \cdot \frac{y}{y - z}\\ \mathbf{elif}\;z \leq 3.3 \cdot 10^{+58}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq 4 \cdot 10^{+97}:\\ \;\;\;\;t \cdot \frac{x}{z - y}\\ \mathbf{else}:\\ \;\;\;\;t \cdot \frac{x - y}{z}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (- t (* t (/ x y)))))
   (if (<= z -3.4e-54)
     (/ t (/ z (- x y)))
     (if (<= z 8.5e-24)
       t_1
       (if (<= z 7.8e+52)
         (* t (/ y (- y z)))
         (if (<= z 3.3e+58)
           t_1
           (if (<= z 4e+97) (* t (/ x (- z y))) (* t (/ (- x y) z)))))))))

C

double code(double x, double y, double z, double t) {
	double t_1 = t - (t * (x / y));
	double tmp;
	if (z <= -3.4e-54) {
		tmp = t / (z / (x - y));
	} else if (z <= 8.5e-24) {
		tmp = t_1;
	} else if (z <= 7.8e+52) {
		tmp = t * (y / (y - z));
	} else if (z <= 3.3e+58) {
		tmp = t_1;
	} else if (z <= 4e+97) {
		tmp = t * (x / (z - 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) :: t_1
    real(8) :: tmp
    t_1 = t - (t * (x / y))
    if (z <= (-3.4d-54)) then
        tmp = t / (z / (x - y))
    else if (z <= 8.5d-24) then
        tmp = t_1
    else if (z <= 7.8d+52) then
        tmp = t * (y / (y - z))
    else if (z <= 3.3d+58) then
        tmp = t_1
    else if (z <= 4d+97) then
        tmp = t * (x / (z - 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 t_1 = t - (t * (x / y));
	double tmp;
	if (z <= -3.4e-54) {
		tmp = t / (z / (x - y));
	} else if (z <= 8.5e-24) {
		tmp = t_1;
	} else if (z <= 7.8e+52) {
		tmp = t * (y / (y - z));
	} else if (z <= 3.3e+58) {
		tmp = t_1;
	} else if (z <= 4e+97) {
		tmp = t * (x / (z - y));
	} else {
		tmp = t * ((x - y) / z);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = t - (t * (x / y))
	tmp = 0
	if z <= -3.4e-54:
		tmp = t / (z / (x - y))
	elif z <= 8.5e-24:
		tmp = t_1
	elif z <= 7.8e+52:
		tmp = t * (y / (y - z))
	elif z <= 3.3e+58:
		tmp = t_1
	elif z <= 4e+97:
		tmp = t * (x / (z - y))
	else:
		tmp = t * ((x - y) / z)
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(t - Float64(t * Float64(x / y)))
	tmp = 0.0
	if (z <= -3.4e-54)
		tmp = Float64(t / Float64(z / Float64(x - y)));
	elseif (z <= 8.5e-24)
		tmp = t_1;
	elseif (z <= 7.8e+52)
		tmp = Float64(t * Float64(y / Float64(y - z)));
	elseif (z <= 3.3e+58)
		tmp = t_1;
	elseif (z <= 4e+97)
		tmp = Float64(t * Float64(x / Float64(z - y)));
	else
		tmp = Float64(t * Float64(Float64(x - y) / z));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = t - (t * (x / y));
	tmp = 0.0;
	if (z <= -3.4e-54)
		tmp = t / (z / (x - y));
	elseif (z <= 8.5e-24)
		tmp = t_1;
	elseif (z <= 7.8e+52)
		tmp = t * (y / (y - z));
	elseif (z <= 3.3e+58)
		tmp = t_1;
	elseif (z <= 4e+97)
		tmp = t * (x / (z - y));
	else
		tmp = t * ((x - y) / z);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(t - N[(t * N[(x / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -3.4e-54], N[(t / N[(z / N[(x - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 8.5e-24], t$95$1, If[LessEqual[z, 7.8e+52], N[(t * N[(y / N[(y - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 3.3e+58], t$95$1, If[LessEqual[z, 4e+97], N[(t * N[(x / N[(z - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(t * N[(N[(x - y), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision]]]]]]]

Derivation

1. Split input into 5 regimes

2. if z < -3.39999999999999987e-54

   1. Initial program 99.7%

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

      1. associate-*l/ 81.1%

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

      2. associate-/l* 86.3%

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

   3. Simplified 86.3%

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

      1. associate-*r/ 81.1%

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

      2. associate-*l/ 99.7%

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

      3. *-commutative 99.7%

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

      4. clear-num 99.6%

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

      5. un-div-inv 99.8%

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

   6. Applied egg-rr 99.8%

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

   7. Taylor expanded in z around inf 79.3%

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

   if -3.39999999999999987e-54 < z < 8.5000000000000002e-24 or 7.7999999999999999e52 < z < 3.29999999999999983e58

   1. Initial program 95.9%

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

      1. associate-*l/ 81.7%

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

      2. associate-/l* 86.9%

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

   3. Simplified 86.9%

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

   5. Taylor expanded in z around 0 78.1%

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

      1. associate-*r/ 78.1%

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

      2. neg-mul-1 78.1%

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

   7. Simplified 78.1%

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

   8. Taylor expanded in x around 0 85.7%

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

      1. mul-1-neg 85.7%

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

      2. unsub-neg 85.7%

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

      3. associate-/l* 87.9%

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

   10. Simplified 87.9%

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

   if 8.5000000000000002e-24 < z < 7.7999999999999999e52

   1. Initial program 100.0%

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

   3. Taylor expanded in x around 0 87.3%

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

      1. neg-mul-1 87.3%

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

      2. distribute-neg-frac2 87.3%

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

   5. Simplified 87.3%

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

   6. Taylor expanded in t around 0 68.9%

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

      1. associate-/l* 87.3%

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

   8. Simplified 87.3%

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

   if 3.29999999999999983e58 < z < 4.0000000000000003e97

   1. Initial program 99.7%

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

   3. Taylor expanded in x around inf 99.7%

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

   if 4.0000000000000003e97 < z

   1. Initial program 95.4%

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

   3. Taylor expanded in z around inf 87.2%

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

4. Final simplification 85.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -3.4 \cdot 10^{-54}:\\ \;\;\;\;\frac{t}{\frac{z}{x - y}}\\ \mathbf{elif}\;z \leq 8.5 \cdot 10^{-24}:\\ \;\;\;\;t - t \cdot \frac{x}{y}\\ \mathbf{elif}\;z \leq 7.8 \cdot 10^{+52}:\\ \;\;\;\;t \cdot \frac{y}{y - z}\\ \mathbf{elif}\;z \leq 3.3 \cdot 10^{+58}:\\ \;\;\;\;t - t \cdot \frac{x}{y}\\ \mathbf{elif}\;z \leq 4 \cdot 10^{+97}:\\ \;\;\;\;t \cdot \frac{x}{z - y}\\ \mathbf{else}:\\ \;\;\;\;t \cdot \frac{x - y}{z}\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 72.6% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := t - t \cdot \frac{x}{y}\\ t_2 := t \cdot \frac{x - y}{z}\\ \mathbf{if}\;z \leq -1 \cdot 10^{-55}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;z \leq 4.5 \cdot 10^{-25}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq 1.05 \cdot 10^{+54}:\\ \;\;\;\;t \cdot \frac{y}{y - z}\\ \mathbf{elif}\;z \leq 1.92 \cdot 10^{+58}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq 3.5 \cdot 10^{+97}:\\ \;\;\;\;t \cdot \frac{x}{z - y}\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (- t (* t (/ x y)))) (t_2 (* t (/ (- x y) z))))
   (if (<= z -1e-55)
     t_2
     (if (<= z 4.5e-25)
       t_1
       (if (<= z 1.05e+54)
         (* t (/ y (- y z)))
         (if (<= z 1.92e+58)
           t_1
           (if (<= z 3.5e+97) (* t (/ x (- z y))) t_2)))))))

C

double code(double x, double y, double z, double t) {
	double t_1 = t - (t * (x / y));
	double t_2 = t * ((x - y) / z);
	double tmp;
	if (z <= -1e-55) {
		tmp = t_2;
	} else if (z <= 4.5e-25) {
		tmp = t_1;
	} else if (z <= 1.05e+54) {
		tmp = t * (y / (y - z));
	} else if (z <= 1.92e+58) {
		tmp = t_1;
	} else if (z <= 3.5e+97) {
		tmp = t * (x / (z - y));
	} 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 = t - (t * (x / y))
    t_2 = t * ((x - y) / z)
    if (z <= (-1d-55)) then
        tmp = t_2
    else if (z <= 4.5d-25) then
        tmp = t_1
    else if (z <= 1.05d+54) then
        tmp = t * (y / (y - z))
    else if (z <= 1.92d+58) then
        tmp = t_1
    else if (z <= 3.5d+97) then
        tmp = t * (x / (z - y))
    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 = t - (t * (x / y));
	double t_2 = t * ((x - y) / z);
	double tmp;
	if (z <= -1e-55) {
		tmp = t_2;
	} else if (z <= 4.5e-25) {
		tmp = t_1;
	} else if (z <= 1.05e+54) {
		tmp = t * (y / (y - z));
	} else if (z <= 1.92e+58) {
		tmp = t_1;
	} else if (z <= 3.5e+97) {
		tmp = t * (x / (z - y));
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = t - (t * (x / y))
	t_2 = t * ((x - y) / z)
	tmp = 0
	if z <= -1e-55:
		tmp = t_2
	elif z <= 4.5e-25:
		tmp = t_1
	elif z <= 1.05e+54:
		tmp = t * (y / (y - z))
	elif z <= 1.92e+58:
		tmp = t_1
	elif z <= 3.5e+97:
		tmp = t * (x / (z - y))
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(t - Float64(t * Float64(x / y)))
	t_2 = Float64(t * Float64(Float64(x - y) / z))
	tmp = 0.0
	if (z <= -1e-55)
		tmp = t_2;
	elseif (z <= 4.5e-25)
		tmp = t_1;
	elseif (z <= 1.05e+54)
		tmp = Float64(t * Float64(y / Float64(y - z)));
	elseif (z <= 1.92e+58)
		tmp = t_1;
	elseif (z <= 3.5e+97)
		tmp = Float64(t * Float64(x / Float64(z - y)));
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = t - (t * (x / y));
	t_2 = t * ((x - y) / z);
	tmp = 0.0;
	if (z <= -1e-55)
		tmp = t_2;
	elseif (z <= 4.5e-25)
		tmp = t_1;
	elseif (z <= 1.05e+54)
		tmp = t * (y / (y - z));
	elseif (z <= 1.92e+58)
		tmp = t_1;
	elseif (z <= 3.5e+97)
		tmp = t * (x / (z - y));
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(t - N[(t * N[(x / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(t * N[(N[(x - y), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -1e-55], t$95$2, If[LessEqual[z, 4.5e-25], t$95$1, If[LessEqual[z, 1.05e+54], N[(t * N[(y / N[(y - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 1.92e+58], t$95$1, If[LessEqual[z, 3.5e+97], N[(t * N[(x / N[(z - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$2]]]]]]]

Derivation

1. Split input into 4 regimes

2. if z < -9.99999999999999995e-56 or 3.5000000000000001e97 < z

   1. Initial program 97.9%

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

   3. Taylor expanded in z around inf 82.6%

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

   if -9.99999999999999995e-56 < z < 4.5000000000000001e-25 or 1.04999999999999993e54 < z < 1.92000000000000004e58

   1. Initial program 95.9%

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

      1. associate-*l/ 81.7%

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

      2. associate-/l* 86.9%

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

   3. Simplified 86.9%

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

   5. Taylor expanded in z around 0 78.1%

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

      1. associate-*r/ 78.1%

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

      2. neg-mul-1 78.1%

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

   7. Simplified 78.1%

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

   8. Taylor expanded in x around 0 85.7%

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

      1. mul-1-neg 85.7%

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

      2. unsub-neg 85.7%

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

      3. associate-/l* 87.9%

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

   10. Simplified 87.9%

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

   if 4.5000000000000001e-25 < z < 1.04999999999999993e54

   1. Initial program 100.0%

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

   3. Taylor expanded in x around 0 87.3%

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

      1. neg-mul-1 87.3%

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

      2. distribute-neg-frac2 87.3%

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

   5. Simplified 87.3%

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

   6. Taylor expanded in t around 0 68.9%

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

      1. associate-/l* 87.3%

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

   8. Simplified 87.3%

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

   if 1.92000000000000004e58 < z < 3.5000000000000001e97

   1. Initial program 99.7%

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

   3. Taylor expanded in x around inf 99.7%

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

4. Final simplification 85.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1 \cdot 10^{-55}:\\ \;\;\;\;t \cdot \frac{x - y}{z}\\ \mathbf{elif}\;z \leq 4.5 \cdot 10^{-25}:\\ \;\;\;\;t - t \cdot \frac{x}{y}\\ \mathbf{elif}\;z \leq 1.05 \cdot 10^{+54}:\\ \;\;\;\;t \cdot \frac{y}{y - z}\\ \mathbf{elif}\;z \leq 1.92 \cdot 10^{+58}:\\ \;\;\;\;t - t \cdot \frac{x}{y}\\ \mathbf{elif}\;z \leq 3.5 \cdot 10^{+97}:\\ \;\;\;\;t \cdot \frac{x}{z - y}\\ \mathbf{else}:\\ \;\;\;\;t \cdot \frac{x - y}{z}\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 70.3% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := t \cdot \frac{y}{y - z}\\ \mathbf{if}\;y \leq -3.4 \cdot 10^{-119}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y \leq -7.2 \cdot 10^{-140}:\\ \;\;\;\;\frac{t \cdot x}{-y}\\ \mathbf{elif}\;y \leq -7 \cdot 10^{-140}:\\ \;\;\;\;t\\ \mathbf{elif}\;y \leq 1.05 \cdot 10^{-252}:\\ \;\;\;\;\frac{t \cdot x}{z}\\ \mathbf{elif}\;y \leq 1.8 \cdot 10^{+52}:\\ \;\;\;\;\left(x - y\right) \cdot \frac{t}{z}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (* t (/ y (- y z)))))
   (if (<= y -3.4e-119)
     t_1
     (if (<= y -7.2e-140)
       (/ (* t x) (- y))
       (if (<= y -7e-140)
         t
         (if (<= y 1.05e-252)
           (/ (* t x) z)
           (if (<= y 1.8e+52) (* (- x y) (/ t z)) t_1)))))))

C

double code(double x, double y, double z, double t) {
	double t_1 = t * (y / (y - z));
	double tmp;
	if (y <= -3.4e-119) {
		tmp = t_1;
	} else if (y <= -7.2e-140) {
		tmp = (t * x) / -y;
	} else if (y <= -7e-140) {
		tmp = t;
	} else if (y <= 1.05e-252) {
		tmp = (t * x) / z;
	} else if (y <= 1.8e+52) {
		tmp = (x - y) * (t / 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 / (y - z))
    if (y <= (-3.4d-119)) then
        tmp = t_1
    else if (y <= (-7.2d-140)) then
        tmp = (t * x) / -y
    else if (y <= (-7d-140)) then
        tmp = t
    else if (y <= 1.05d-252) then
        tmp = (t * x) / z
    else if (y <= 1.8d+52) then
        tmp = (x - y) * (t / 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 / (y - z));
	double tmp;
	if (y <= -3.4e-119) {
		tmp = t_1;
	} else if (y <= -7.2e-140) {
		tmp = (t * x) / -y;
	} else if (y <= -7e-140) {
		tmp = t;
	} else if (y <= 1.05e-252) {
		tmp = (t * x) / z;
	} else if (y <= 1.8e+52) {
		tmp = (x - y) * (t / z);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = t * (y / (y - z))
	tmp = 0
	if y <= -3.4e-119:
		tmp = t_1
	elif y <= -7.2e-140:
		tmp = (t * x) / -y
	elif y <= -7e-140:
		tmp = t
	elif y <= 1.05e-252:
		tmp = (t * x) / z
	elif y <= 1.8e+52:
		tmp = (x - y) * (t / z)
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(t * Float64(y / Float64(y - z)))
	tmp = 0.0
	if (y <= -3.4e-119)
		tmp = t_1;
	elseif (y <= -7.2e-140)
		tmp = Float64(Float64(t * x) / Float64(-y));
	elseif (y <= -7e-140)
		tmp = t;
	elseif (y <= 1.05e-252)
		tmp = Float64(Float64(t * x) / z);
	elseif (y <= 1.8e+52)
		tmp = Float64(Float64(x - y) * Float64(t / z));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = t * (y / (y - z));
	tmp = 0.0;
	if (y <= -3.4e-119)
		tmp = t_1;
	elseif (y <= -7.2e-140)
		tmp = (t * x) / -y;
	elseif (y <= -7e-140)
		tmp = t;
	elseif (y <= 1.05e-252)
		tmp = (t * x) / z;
	elseif (y <= 1.8e+52)
		tmp = (x - y) * (t / z);
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(t * N[(y / N[(y - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -3.4e-119], t$95$1, If[LessEqual[y, -7.2e-140], N[(N[(t * x), $MachinePrecision] / (-y)), $MachinePrecision], If[LessEqual[y, -7e-140], t, If[LessEqual[y, 1.05e-252], N[(N[(t * x), $MachinePrecision] / z), $MachinePrecision], If[LessEqual[y, 1.8e+52], N[(N[(x - y), $MachinePrecision] * N[(t / z), $MachinePrecision]), $MachinePrecision], t$95$1]]]]]]

Derivation

1. Split input into 5 regimes

2. if y < -3.40000000000000024e-119 or 1.8e52 < y

   1. Initial program 98.7%

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

   3. Taylor expanded in x around 0 75.6%

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

      1. neg-mul-1 75.6%

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

      2. distribute-neg-frac2 75.6%

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

   5. Simplified 75.6%

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

   6. Taylor expanded in t around 0 57.0%

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

      1. associate-/l* 75.6%

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

   8. Simplified 75.6%

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

   if -3.40000000000000024e-119 < y < -7.2000000000000001e-140

   1. Initial program 99.7%

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

      1. associate-*l/ 100.0%

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

      2. associate-/l* 99.7%

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

   3. Simplified 99.7%

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

      1. associate-*r/ 100.0%

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

      2. associate-*l/ 99.7%

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

      3. *-commutative 99.7%

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

      4. clear-num 99.7%

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

      5. un-div-inv 99.7%

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

   6. Applied egg-rr 99.7%

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

   7. Taylor expanded in x around inf 99.7%

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

   8. Taylor expanded in z around 0 100.0%

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

      1. associate-*r/ 100.0%

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

      2. neg-mul-1 100.0%

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

      3. distribute-rgt-neg-in 100.0%

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

   10. Simplified 100.0%

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

   if -7.2000000000000001e-140 < y < -6.9999999999999996e-140

   1. Initial program 100.0%

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

      1. associate-*l/ 5.4%

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

      2. associate-/l* 100.0%

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

   3. Simplified 100.0%

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

   5. Taylor expanded in y around inf 100.0%

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

   if -6.9999999999999996e-140 < y < 1.05e-252

   1. Initial program 93.8%

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

      1. associate-*l/ 95.1%

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

      2. associate-/l* 92.0%

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

   3. Simplified 92.0%

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

   5. Taylor expanded in y around 0 88.1%

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

   if 1.05e-252 < y < 1.8e52

   1. Initial program 95.5%

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

      1. associate-*l/ 88.9%

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

      2. associate-/l* 97.7%

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

   3. Simplified 97.7%

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

   5. Taylor expanded in z around inf 62.0%

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

      1. *-commutative 62.0%

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

      2. associate-/l* 72.5%

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

   7. Simplified 72.5%

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

4. Final simplification 77.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -3.4 \cdot 10^{-119}:\\ \;\;\;\;t \cdot \frac{y}{y - z}\\ \mathbf{elif}\;y \leq -7.2 \cdot 10^{-140}:\\ \;\;\;\;\frac{t \cdot x}{-y}\\ \mathbf{elif}\;y \leq -7 \cdot 10^{-140}:\\ \;\;\;\;t\\ \mathbf{elif}\;y \leq 1.05 \cdot 10^{-252}:\\ \;\;\;\;\frac{t \cdot x}{z}\\ \mathbf{elif}\;y \leq 1.8 \cdot 10^{+52}:\\ \;\;\;\;\left(x - y\right) \cdot \frac{t}{z}\\ \mathbf{else}:\\ \;\;\;\;t \cdot \frac{y}{y - z}\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 68.0% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := t \cdot \frac{y}{y - z}\\ \mathbf{if}\;y \leq -2.85 \cdot 10^{-117}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y \leq -7.2 \cdot 10^{-140}:\\ \;\;\;\;\frac{t \cdot x}{-y}\\ \mathbf{elif}\;y \leq -7 \cdot 10^{-140}:\\ \;\;\;\;t\\ \mathbf{elif}\;y \leq 1.8 \cdot 10^{-157}:\\ \;\;\;\;\frac{t}{\frac{z}{x}}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (* t (/ y (- y z)))))
   (if (<= y -2.85e-117)
     t_1
     (if (<= y -7.2e-140)
       (/ (* t x) (- y))
       (if (<= y -7e-140) t (if (<= y 1.8e-157) (/ t (/ z x)) t_1))))))

C

double code(double x, double y, double z, double t) {
	double t_1 = t * (y / (y - z));
	double tmp;
	if (y <= -2.85e-117) {
		tmp = t_1;
	} else if (y <= -7.2e-140) {
		tmp = (t * x) / -y;
	} else if (y <= -7e-140) {
		tmp = t;
	} else if (y <= 1.8e-157) {
		tmp = t / (z / x);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: t_1
    real(8) :: tmp
    t_1 = t * (y / (y - z))
    if (y <= (-2.85d-117)) then
        tmp = t_1
    else if (y <= (-7.2d-140)) then
        tmp = (t * x) / -y
    else if (y <= (-7d-140)) then
        tmp = t
    else if (y <= 1.8d-157) then
        tmp = t / (z / x)
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double t_1 = t * (y / (y - z));
	double tmp;
	if (y <= -2.85e-117) {
		tmp = t_1;
	} else if (y <= -7.2e-140) {
		tmp = (t * x) / -y;
	} else if (y <= -7e-140) {
		tmp = t;
	} else if (y <= 1.8e-157) {
		tmp = t / (z / x);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = t * (y / (y - z))
	tmp = 0
	if y <= -2.85e-117:
		tmp = t_1
	elif y <= -7.2e-140:
		tmp = (t * x) / -y
	elif y <= -7e-140:
		tmp = t
	elif y <= 1.8e-157:
		tmp = t / (z / x)
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(t * Float64(y / Float64(y - z)))
	tmp = 0.0
	if (y <= -2.85e-117)
		tmp = t_1;
	elseif (y <= -7.2e-140)
		tmp = Float64(Float64(t * x) / Float64(-y));
	elseif (y <= -7e-140)
		tmp = t;
	elseif (y <= 1.8e-157)
		tmp = Float64(t / Float64(z / x));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = t * (y / (y - z));
	tmp = 0.0;
	if (y <= -2.85e-117)
		tmp = t_1;
	elseif (y <= -7.2e-140)
		tmp = (t * x) / -y;
	elseif (y <= -7e-140)
		tmp = t;
	elseif (y <= 1.8e-157)
		tmp = t / (z / x);
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(t * N[(y / N[(y - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -2.85e-117], t$95$1, If[LessEqual[y, -7.2e-140], N[(N[(t * x), $MachinePrecision] / (-y)), $MachinePrecision], If[LessEqual[y, -7e-140], t, If[LessEqual[y, 1.8e-157], N[(t / N[(z / x), $MachinePrecision]), $MachinePrecision], t$95$1]]]]]

Derivation

1. Split input into 4 regimes

2. if y < -2.85e-117 or 1.8e-157 < y

   1. Initial program 98.1%

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

   3. Taylor expanded in x around 0 70.3%

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

      1. neg-mul-1 70.3%

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

      2. distribute-neg-frac2 70.3%

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

   5. Simplified 70.3%

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

   6. Taylor expanded in t around 0 55.6%

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

      1. associate-/l* 70.3%

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

   8. Simplified 70.3%

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

   if -2.85e-117 < y < -7.2000000000000001e-140

   1. Initial program 99.7%

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

      1. associate-*l/ 100.0%

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

      2. associate-/l* 99.7%

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

   3. Simplified 99.7%

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

      1. associate-*r/ 100.0%

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

      2. associate-*l/ 99.7%

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

      3. *-commutative 99.7%

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

      4. clear-num 99.7%

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

      5. un-div-inv 99.7%

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

   6. Applied egg-rr 99.7%

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

   7. Taylor expanded in x around inf 99.7%

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

   8. Taylor expanded in z around 0 100.0%

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

      1. associate-*r/ 100.0%

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

      2. neg-mul-1 100.0%

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

      3. distribute-rgt-neg-in 100.0%

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

   10. Simplified 100.0%

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

   if -7.2000000000000001e-140 < y < -6.9999999999999996e-140

   1. Initial program 100.0%

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

      1. associate-*l/ 5.4%

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

      2. associate-/l* 100.0%

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

   3. Simplified 100.0%

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

   5. Taylor expanded in y around inf 100.0%

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

   if -6.9999999999999996e-140 < y < 1.8e-157

   1. Initial program 93.9%

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

      1. associate-*l/ 89.9%

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

      2. associate-/l* 94.1%

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

   3. Simplified 94.1%

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

      1. associate-*r/ 89.9%

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

      2. associate-*l/ 93.9%

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

      3. *-commutative 93.9%

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

      4. clear-num 93.8%

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

      5. un-div-inv 95.2%

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

   6. Applied egg-rr 95.2%

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

   7. Taylor expanded in y around 0 84.7%

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

4. Final simplification 74.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -2.85 \cdot 10^{-117}:\\ \;\;\;\;t \cdot \frac{y}{y - z}\\ \mathbf{elif}\;y \leq -7.2 \cdot 10^{-140}:\\ \;\;\;\;\frac{t \cdot x}{-y}\\ \mathbf{elif}\;y \leq -7 \cdot 10^{-140}:\\ \;\;\;\;t\\ \mathbf{elif}\;y \leq 1.8 \cdot 10^{-157}:\\ \;\;\;\;\frac{t}{\frac{z}{x}}\\ \mathbf{else}:\\ \;\;\;\;t \cdot \frac{y}{y - z}\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 74.4% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := t \cdot \frac{y}{y - z}\\ \mathbf{if}\;y \leq -7.2 \cdot 10^{-27}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y \leq 4.3 \cdot 10^{-153}:\\ \;\;\;\;t \cdot \frac{x}{z - y}\\ \mathbf{elif}\;y \leq 2.8 \cdot 10^{+88}:\\ \;\;\;\;t \cdot \frac{x - y}{z}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (* t (/ y (- y z)))))
   (if (<= y -7.2e-27)
     t_1
     (if (<= y 4.3e-153)
       (* t (/ x (- z y)))
       (if (<= y 2.8e+88) (* t (/ (- x y) z)) t_1)))))

C

double code(double x, double y, double z, double t) {
	double t_1 = t * (y / (y - z));
	double tmp;
	if (y <= -7.2e-27) {
		tmp = t_1;
	} else if (y <= 4.3e-153) {
		tmp = t * (x / (z - y));
	} else if (y <= 2.8e+88) {
		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 / (y - z))
    if (y <= (-7.2d-27)) then
        tmp = t_1
    else if (y <= 4.3d-153) then
        tmp = t * (x / (z - y))
    else if (y <= 2.8d+88) 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 / (y - z));
	double tmp;
	if (y <= -7.2e-27) {
		tmp = t_1;
	} else if (y <= 4.3e-153) {
		tmp = t * (x / (z - y));
	} else if (y <= 2.8e+88) {
		tmp = t * ((x - y) / z);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = t * (y / (y - z))
	tmp = 0
	if y <= -7.2e-27:
		tmp = t_1
	elif y <= 4.3e-153:
		tmp = t * (x / (z - y))
	elif y <= 2.8e+88:
		tmp = t * ((x - y) / z)
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(t * Float64(y / Float64(y - z)))
	tmp = 0.0
	if (y <= -7.2e-27)
		tmp = t_1;
	elseif (y <= 4.3e-153)
		tmp = Float64(t * Float64(x / Float64(z - y)));
	elseif (y <= 2.8e+88)
		tmp = Float64(t * Float64(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 / (y - z));
	tmp = 0.0;
	if (y <= -7.2e-27)
		tmp = t_1;
	elseif (y <= 4.3e-153)
		tmp = t * (x / (z - y));
	elseif (y <= 2.8e+88)
		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[(y / N[(y - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -7.2e-27], t$95$1, If[LessEqual[y, 4.3e-153], N[(t * N[(x / N[(z - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 2.8e+88], N[(t * N[(N[(x - y), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if y < -7.1999999999999997e-27 or 2.79999999999999989e88 < y

   1. Initial program 99.8%

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

   3. Taylor expanded in x around 0 79.3%

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

      1. neg-mul-1 79.3%

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

      2. distribute-neg-frac2 79.3%

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

   5. Simplified 79.3%

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

   6. Taylor expanded in t around 0 58.3%

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

      1. associate-/l* 79.3%

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

   8. Simplified 79.3%

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

   if -7.1999999999999997e-27 < y < 4.3e-153

   1. Initial program 93.4%

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

   3. Taylor expanded in x around inf 85.0%

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

   if 4.3e-153 < y < 2.79999999999999989e88

   1. Initial program 97.3%

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

   3. Taylor expanded in z around inf 73.2%

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

4. Final simplification 80.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -7.2 \cdot 10^{-27}:\\ \;\;\;\;t \cdot \frac{y}{y - z}\\ \mathbf{elif}\;y \leq 4.3 \cdot 10^{-153}:\\ \;\;\;\;t \cdot \frac{x}{z - y}\\ \mathbf{elif}\;y \leq 2.8 \cdot 10^{+88}:\\ \;\;\;\;t \cdot \frac{x - y}{z}\\ \mathbf{else}:\\ \;\;\;\;t \cdot \frac{y}{y - z}\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 74.7% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := t \cdot \frac{y}{y - z}\\ \mathbf{if}\;y \leq -4.1 \cdot 10^{-29}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y \leq 8.4 \cdot 10^{-153}:\\ \;\;\;\;t \cdot \frac{x}{z - y}\\ \mathbf{elif}\;y \leq 1.8 \cdot 10^{+52}:\\ \;\;\;\;\left(x - y\right) \cdot \frac{t}{z}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (* t (/ y (- y z)))))
   (if (<= y -4.1e-29)
     t_1
     (if (<= y 8.4e-153)
       (* t (/ x (- z y)))
       (if (<= y 1.8e+52) (* (- x y) (/ t z)) t_1)))))

C

double code(double x, double y, double z, double t) {
	double t_1 = t * (y / (y - z));
	double tmp;
	if (y <= -4.1e-29) {
		tmp = t_1;
	} else if (y <= 8.4e-153) {
		tmp = t * (x / (z - y));
	} else if (y <= 1.8e+52) {
		tmp = (x - y) * (t / 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 / (y - z))
    if (y <= (-4.1d-29)) then
        tmp = t_1
    else if (y <= 8.4d-153) then
        tmp = t * (x / (z - y))
    else if (y <= 1.8d+52) then
        tmp = (x - y) * (t / 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 / (y - z));
	double tmp;
	if (y <= -4.1e-29) {
		tmp = t_1;
	} else if (y <= 8.4e-153) {
		tmp = t * (x / (z - y));
	} else if (y <= 1.8e+52) {
		tmp = (x - y) * (t / z);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = t * (y / (y - z))
	tmp = 0
	if y <= -4.1e-29:
		tmp = t_1
	elif y <= 8.4e-153:
		tmp = t * (x / (z - y))
	elif y <= 1.8e+52:
		tmp = (x - y) * (t / z)
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(t * Float64(y / Float64(y - z)))
	tmp = 0.0
	if (y <= -4.1e-29)
		tmp = t_1;
	elseif (y <= 8.4e-153)
		tmp = Float64(t * Float64(x / Float64(z - y)));
	elseif (y <= 1.8e+52)
		tmp = Float64(Float64(x - y) * Float64(t / z));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = t * (y / (y - z));
	tmp = 0.0;
	if (y <= -4.1e-29)
		tmp = t_1;
	elseif (y <= 8.4e-153)
		tmp = t * (x / (z - y));
	elseif (y <= 1.8e+52)
		tmp = (x - y) * (t / z);
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(t * N[(y / N[(y - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -4.1e-29], t$95$1, If[LessEqual[y, 8.4e-153], N[(t * N[(x / N[(z - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 1.8e+52], N[(N[(x - y), $MachinePrecision] * N[(t / z), $MachinePrecision]), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if y < -4.0999999999999998e-29 or 1.8e52 < y

   1. Initial program 99.8%

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

   3. Taylor expanded in x around 0 80.1%

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

      1. neg-mul-1 80.1%

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

      2. distribute-neg-frac2 80.1%

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

   5. Simplified 80.1%

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

   6. Taylor expanded in t around 0 59.3%

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

      1. associate-/l* 80.1%

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

   8. Simplified 80.1%

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

   if -4.0999999999999998e-29 < y < 8.40000000000000017e-153

   1. Initial program 93.4%

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

   3. Taylor expanded in x around inf 85.0%

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

   if 8.40000000000000017e-153 < y < 1.8e52

   1. Initial program 97.0%

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

      1. associate-*l/ 94.5%

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

      2. associate-/l* 96.6%

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

   3. Simplified 96.6%

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

   5. Taylor expanded in z around inf 64.6%

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

      1. *-commutative 64.6%

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

      2. associate-/l* 69.3%

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

   7. Simplified 69.3%

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

4. Final simplification 80.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -4.1 \cdot 10^{-29}:\\ \;\;\;\;t \cdot \frac{y}{y - z}\\ \mathbf{elif}\;y \leq 8.4 \cdot 10^{-153}:\\ \;\;\;\;t \cdot \frac{x}{z - y}\\ \mathbf{elif}\;y \leq 1.8 \cdot 10^{+52}:\\ \;\;\;\;\left(x - y\right) \cdot \frac{t}{z}\\ \mathbf{else}:\\ \;\;\;\;t \cdot \frac{y}{y - z}\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 59.0% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -2.8 \cdot 10^{-5}:\\ \;\;\;\;t\\ \mathbf{elif}\;y \leq 5.1 \cdot 10^{-103}:\\ \;\;\;\;\frac{t}{\frac{z}{x}}\\ \mathbf{elif}\;y \leq 5.4 \cdot 10^{+126}:\\ \;\;\;\;t \cdot \frac{y}{-z}\\ \mathbf{else}:\\ \;\;\;\;t\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= y -2.8e-5)
   t
   (if (<= y 5.1e-103)
     (/ t (/ z x))
     (if (<= y 5.4e+126) (* t (/ y (- z))) t))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (y <= -2.8e-5) {
		tmp = t;
	} else if (y <= 5.1e-103) {
		tmp = t / (z / x);
	} else if (y <= 5.4e+126) {
		tmp = t * (y / -z);
	} else {
		tmp = t;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if (y <= (-2.8d-5)) then
        tmp = t
    else if (y <= 5.1d-103) then
        tmp = t / (z / x)
    else if (y <= 5.4d+126) then
        tmp = t * (y / -z)
    else
        tmp = t
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if (y <= -2.8e-5) {
		tmp = t;
	} else if (y <= 5.1e-103) {
		tmp = t / (z / x);
	} else if (y <= 5.4e+126) {
		tmp = t * (y / -z);
	} else {
		tmp = t;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if y <= -2.8e-5:
		tmp = t
	elif y <= 5.1e-103:
		tmp = t / (z / x)
	elif y <= 5.4e+126:
		tmp = t * (y / -z)
	else:
		tmp = t
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (y <= -2.8e-5)
		tmp = t;
	elseif (y <= 5.1e-103)
		tmp = Float64(t / Float64(z / x));
	elseif (y <= 5.4e+126)
		tmp = Float64(t * Float64(y / Float64(-z)));
	else
		tmp = t;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (y <= -2.8e-5)
		tmp = t;
	elseif (y <= 5.1e-103)
		tmp = t / (z / x);
	elseif (y <= 5.4e+126)
		tmp = t * (y / -z);
	else
		tmp = t;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[y, -2.8e-5], t, If[LessEqual[y, 5.1e-103], N[(t / N[(z / x), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 5.4e+126], N[(t * N[(y / (-z)), $MachinePrecision]), $MachinePrecision], t]]]

Derivation

1. Split input into 3 regimes

2. if y < -2.79999999999999996e-5 or 5.40000000000000005e126 < y

   1. Initial program 99.9%

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

      1. associate-*l/ 71.9%

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

      2. associate-/l* 80.1%

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

   3. Simplified 80.1%

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

   5. Taylor expanded in y around inf 68.6%

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

   if -2.79999999999999996e-5 < y < 5.0999999999999998e-103

   1. Initial program 94.1%

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

      1. associate-*l/ 90.0%

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

      2. associate-/l* 93.2%

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

   3. Simplified 93.2%

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

      1. associate-*r/ 90.0%

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

      2. associate-*l/ 94.1%

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

      3. *-commutative 94.1%

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

      4. clear-num 93.3%

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

      5. un-div-inv 94.1%

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

   6. Applied egg-rr 94.1%

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

   7. Taylor expanded in y around 0 68.1%

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

   if 5.0999999999999998e-103 < y < 5.40000000000000005e126

   1. Initial program 97.3%

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

      1. associate-*l/ 90.7%

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

      2. associate-/l* 95.8%

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

   3. Simplified 95.8%

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

   5. Taylor expanded in z around inf 59.5%

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

      1. *-commutative 59.5%

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

      2. associate-/l* 64.7%

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

   7. Simplified 64.7%

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

   8. Taylor expanded in x around 0 46.2%

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

      1. mul-1-neg 46.2%

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

      2. associate-/l* 50.6%

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

      3. distribute-rgt-neg-in 50.6%

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

   10. Simplified 50.6%

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

4. Final simplification 65.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -2.8 \cdot 10^{-5}:\\ \;\;\;\;t\\ \mathbf{elif}\;y \leq 5.1 \cdot 10^{-103}:\\ \;\;\;\;\frac{t}{\frac{z}{x}}\\ \mathbf{elif}\;y \leq 5.4 \cdot 10^{+126}:\\ \;\;\;\;t \cdot \frac{y}{-z}\\ \mathbf{else}:\\ \;\;\;\;t\\ \end{array} \]
5. Add Preprocessing

Alternative 10: 60.3% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -1.1 \cdot 10^{-5}:\\ \;\;\;\;t\\ \mathbf{elif}\;y \leq 3.05 \cdot 10^{+91}:\\ \;\;\;\;\frac{t}{\frac{z}{x}}\\ \mathbf{else}:\\ \;\;\;\;t\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= y -1.1e-5) t (if (<= y 3.05e+91) (/ t (/ z x)) t)))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (y <= -1.1e-5) {
		tmp = t;
	} else if (y <= 3.05e+91) {
		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 <= (-1.1d-5)) then
        tmp = t
    else if (y <= 3.05d+91) 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 <= -1.1e-5) {
		tmp = t;
	} else if (y <= 3.05e+91) {
		tmp = t / (z / x);
	} else {
		tmp = t;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if y <= -1.1e-5:
		tmp = t
	elif y <= 3.05e+91:
		tmp = t / (z / x)
	else:
		tmp = t
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (y <= -1.1e-5)
		tmp = t;
	elseif (y <= 3.05e+91)
		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 <= -1.1e-5)
		tmp = t;
	elseif (y <= 3.05e+91)
		tmp = t / (z / x);
	else
		tmp = t;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[y, -1.1e-5], t, If[LessEqual[y, 3.05e+91], N[(t / N[(z / x), $MachinePrecision]), $MachinePrecision], t]]

Derivation

1. Split input into 2 regimes

2. if y < -1.1e-5 or 3.05e91 < y

   1. Initial program 99.8%

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

      1. associate-*l/ 72.7%

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

      2. associate-/l* 81.3%

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

   3. Simplified 81.3%

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

   5. Taylor expanded in y around inf 66.3%

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

   if -1.1e-5 < y < 3.05e91

   1. Initial program 94.8%

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

      1. associate-*l/ 90.4%

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

      2. associate-/l* 93.7%

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

   3. Simplified 93.7%

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

      1. associate-*r/ 90.4%

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

      2. associate-*l/ 94.8%

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

      3. *-commutative 94.8%

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

      4. clear-num 94.2%

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

      5. un-div-inv 95.4%

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

   6. Applied egg-rr 95.4%

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

   7. Taylor expanded in y around 0 60.0%

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

Alternative 11: 60.3% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -3.4 \cdot 10^{-7}:\\ \;\;\;\;t\\ \mathbf{elif}\;y \leq 2.9 \cdot 10^{+91}:\\ \;\;\;\;t \cdot \frac{x}{z}\\ \mathbf{else}:\\ \;\;\;\;t\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= y -3.4e-7) t (if (<= y 2.9e+91) (* t (/ x z)) t)))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (y <= -3.4e-7) {
		tmp = t;
	} else if (y <= 2.9e+91) {
		tmp = t * (x / z);
	} else {
		tmp = t;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if (y <= (-3.4d-7)) then
        tmp = t
    else if (y <= 2.9d+91) then
        tmp = t * (x / z)
    else
        tmp = t
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if (y <= -3.4e-7) {
		tmp = t;
	} else if (y <= 2.9e+91) {
		tmp = t * (x / z);
	} else {
		tmp = t;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if y <= -3.4e-7:
		tmp = t
	elif y <= 2.9e+91:
		tmp = t * (x / z)
	else:
		tmp = t
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (y <= -3.4e-7)
		tmp = t;
	elseif (y <= 2.9e+91)
		tmp = Float64(t * Float64(x / z));
	else
		tmp = t;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (y <= -3.4e-7)
		tmp = t;
	elseif (y <= 2.9e+91)
		tmp = t * (x / z);
	else
		tmp = t;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[y, -3.4e-7], t, If[LessEqual[y, 2.9e+91], N[(t * N[(x / z), $MachinePrecision]), $MachinePrecision], t]]

Derivation

1. Split input into 2 regimes

2. if y < -3.39999999999999974e-7 or 2.90000000000000014e91 < y

   1. Initial program 99.8%

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

      1. associate-*l/ 72.7%

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

      2. associate-/l* 81.3%

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

   3. Simplified 81.3%

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

   5. Taylor expanded in y around inf 66.3%

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

   if -3.39999999999999974e-7 < y < 2.90000000000000014e91

   1. Initial program 94.8%

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

   3. Taylor expanded in y around 0 59.8%

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

4. Final simplification 62.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -3.4 \cdot 10^{-7}:\\ \;\;\;\;t\\ \mathbf{elif}\;y \leq 2.9 \cdot 10^{+91}:\\ \;\;\;\;t \cdot \frac{x}{z}\\ \mathbf{else}:\\ \;\;\;\;t\\ \end{array} \]
5. Add Preprocessing

Alternative 12: 59.1% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -5.8 \cdot 10^{-7}:\\ \;\;\;\;t\\ \mathbf{elif}\;y \leq 2.9 \cdot 10^{+91}:\\ \;\;\;\;x \cdot \frac{t}{z}\\ \mathbf{else}:\\ \;\;\;\;t\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= y -5.8e-7) t (if (<= y 2.9e+91) (* x (/ t z)) t)))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (y <= -5.8e-7) {
		tmp = t;
	} else if (y <= 2.9e+91) {
		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 <= (-5.8d-7)) then
        tmp = t
    else if (y <= 2.9d+91) 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 <= -5.8e-7) {
		tmp = t;
	} else if (y <= 2.9e+91) {
		tmp = x * (t / z);
	} else {
		tmp = t;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if y <= -5.8e-7:
		tmp = t
	elif y <= 2.9e+91:
		tmp = x * (t / z)
	else:
		tmp = t
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (y <= -5.8e-7)
		tmp = t;
	elseif (y <= 2.9e+91)
		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 <= -5.8e-7)
		tmp = t;
	elseif (y <= 2.9e+91)
		tmp = x * (t / z);
	else
		tmp = t;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[y, -5.8e-7], t, If[LessEqual[y, 2.9e+91], N[(x * N[(t / z), $MachinePrecision]), $MachinePrecision], t]]

Derivation

1. Split input into 2 regimes

2. if y < -5.7999999999999995e-7 or 2.90000000000000014e91 < y

   1. Initial program 99.8%

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

      1. associate-*l/ 72.7%

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

      2. associate-/l* 81.3%

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

   3. Simplified 81.3%

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

   5. Taylor expanded in y around inf 66.3%

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

   if -5.7999999999999995e-7 < y < 2.90000000000000014e91

   1. Initial program 94.8%

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

      1. associate-*l/ 90.4%

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

      2. associate-/l* 93.7%

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

   3. Simplified 93.7%

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

   5. Taylor expanded in y around 0 56.5%

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

      1. *-commutative 56.5%

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

      2. associate-/l* 58.5%

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

   7. Simplified 58.5%

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

Alternative 13: 87.2% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -4 \cdot 10^{+166}:\\ \;\;\;\;t - t \cdot \frac{x}{y}\\ \mathbf{else}:\\ \;\;\;\;\left(x - y\right) \cdot \frac{t}{z - y}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= y -4e+166) (- t (* t (/ x y))) (* (- x y) (/ t (- z y)))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (y <= -4e+166) {
		tmp = t - (t * (x / y));
	} else {
		tmp = (x - y) * (t / (z - y));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if (y <= (-4d+166)) then
        tmp = t - (t * (x / y))
    else
        tmp = (x - y) * (t / (z - y))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if (y <= -4e+166) {
		tmp = t - (t * (x / y));
	} else {
		tmp = (x - y) * (t / (z - y));
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if y <= -4e+166:
		tmp = t - (t * (x / y))
	else:
		tmp = (x - y) * (t / (z - y))
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (y <= -4e+166)
		tmp = Float64(t - Float64(t * Float64(x / y)));
	else
		tmp = Float64(Float64(x - y) * Float64(t / Float64(z - y)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (y <= -4e+166)
		tmp = t - (t * (x / y));
	else
		tmp = (x - y) * (t / (z - y));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[y, -4e+166], N[(t - N[(t * N[(x / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(x - y), $MachinePrecision] * N[(t / N[(z - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -3.99999999999999976e166

   1. Initial program 99.9%

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

      1. associate-*l/ 64.6%

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

      2. associate-/l* 67.1%

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

   3. Simplified 67.1%

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

   5. Taylor expanded in z around 0 64.5%

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

      1. associate-*r/ 64.5%

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

      2. neg-mul-1 64.5%

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

   7. Simplified 64.5%

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

   8. Taylor expanded in x around 0 82.4%

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

      1. mul-1-neg 82.4%

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

      2. unsub-neg 82.4%

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

      3. associate-/l* 92.2%

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

   10. Simplified 92.2%

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

   if -3.99999999999999976e166 < y

   1. Initial program 96.6%

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

      1. associate-*l/ 85.3%

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

      2. associate-/l* 91.5%

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

   3. Simplified 91.5%

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

Alternative 14: 96.8% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 97.1%

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

3. Final simplification 97.1%

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

Alternative 15: 35.3% accurate, 9.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 97.1%

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

   1. associate-*l/ 82.3%

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

   2. associate-/l* 88.0%

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

3. Simplified 88.0%

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

5. Taylor expanded in y around inf 35.3%

   \[\leadsto \color{blue}{t} \]
6. Add Preprocessing

Developer target: 96.7% 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 2024100 
(FPCore (x y z t)
  :name "Numeric.Signal.Multichannel:$cput from hsignal-0.2.7.1"
  :precision binary64

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

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