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

Percentage Accurate: 97.0% → 97.1%

Time: 10.3s

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: 97.0% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Alternative 1: 97.1% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 97.6%

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

   1. associate-*l/ 85.3%

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

   2. associate-*r/ 82.8%

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

3. Simplified 82.8%

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

   1. associate-*r/ 85.3%

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

   2. associate-*l/ 97.6%

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

   3. *-commutative 97.6%

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

   4. clear-num 97.5%

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

   5. un-div-inv 97.6%

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

5. Applied egg-rr 97.6%

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

6. Final simplification 97.6%

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

Alternative 2: 84.3% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(x - y\right) \cdot \frac{t}{z - y}\\ \mathbf{if}\;t \leq -1.2 \cdot 10^{-117}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t \leq 1.05 \cdot 10^{-238}:\\ \;\;\;\;\frac{t \cdot x}{z - y}\\ \mathbf{elif}\;t \leq 3.2 \cdot 10^{-171}:\\ \;\;\;\;t \cdot \frac{y}{y - z}\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (* (- x y) (/ t (- z y)))))
   (if (<= t -1.2e-117)
     t_1
     (if (<= t 1.05e-238)
       (/ (* t x) (- z y))
       (if (<= t 3.2e-171) (* t (/ y (- y z))) t_1)))))

C

double code(double x, double y, double z, double t) {
	double t_1 = (x - y) * (t / (z - y));
	double tmp;
	if (t <= -1.2e-117) {
		tmp = t_1;
	} else if (t <= 1.05e-238) {
		tmp = (t * x) / (z - y);
	} else if (t <= 3.2e-171) {
		tmp = t * (y / (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 = (x - y) * (t / (z - y))
    if (t <= (-1.2d-117)) then
        tmp = t_1
    else if (t <= 1.05d-238) then
        tmp = (t * x) / (z - y)
    else if (t <= 3.2d-171) then
        tmp = t * (y / (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 = (x - y) * (t / (z - y));
	double tmp;
	if (t <= -1.2e-117) {
		tmp = t_1;
	} else if (t <= 1.05e-238) {
		tmp = (t * x) / (z - y);
	} else if (t <= 3.2e-171) {
		tmp = t * (y / (y - z));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = (x - y) * (t / (z - y))
	tmp = 0
	if t <= -1.2e-117:
		tmp = t_1
	elif t <= 1.05e-238:
		tmp = (t * x) / (z - y)
	elif t <= 3.2e-171:
		tmp = t * (y / (y - z))
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(Float64(x - y) * Float64(t / Float64(z - y)))
	tmp = 0.0
	if (t <= -1.2e-117)
		tmp = t_1;
	elseif (t <= 1.05e-238)
		tmp = Float64(Float64(t * x) / Float64(z - y));
	elseif (t <= 3.2e-171)
		tmp = Float64(t * Float64(y / Float64(y - z)));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = (x - y) * (t / (z - y));
	tmp = 0.0;
	if (t <= -1.2e-117)
		tmp = t_1;
	elseif (t <= 1.05e-238)
		tmp = (t * x) / (z - y);
	elseif (t <= 3.2e-171)
		tmp = t * (y / (y - z));
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(N[(x - y), $MachinePrecision] * N[(t / N[(z - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t, -1.2e-117], t$95$1, If[LessEqual[t, 1.05e-238], N[(N[(t * x), $MachinePrecision] / N[(z - y), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 3.2e-171], N[(t * N[(y / N[(y - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if t < -1.20000000000000007e-117 or 3.2000000000000001e-171 < t

   1. Initial program 98.3%

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

      1. associate-*l/ 79.9%

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

      2. associate-*r/ 92.1%

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

   3. Simplified 92.1%

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

   if -1.20000000000000007e-117 < t < 1.0500000000000001e-238

   1. Initial program 94.4%

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

      1. associate-*l/ 99.9%

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

      2. associate-*r/ 56.6%

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

   3. Simplified 56.6%

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

   4. Taylor expanded in x around inf 81.6%

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

   if 1.0500000000000001e-238 < t < 3.2000000000000001e-171

   1. Initial program 100.0%

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

   2. Taylor expanded in x around 0 88.0%

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

      1. neg-mul-1 88.0%

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

      2. distribute-neg-frac 88.0%

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

   4. Simplified 88.0%

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

      1. frac-2neg 88.0%

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

      2. div-inv 87.6%

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

      3. remove-double-neg 87.6%

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

      4. sub-neg 87.6%

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

      5. distribute-neg-in 87.6%

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

      6. remove-double-neg 87.6%

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

   6. Applied egg-rr 87.6%

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

      1. associate-*r/ 88.0%

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

      2. *-rgt-identity 88.0%

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

      3. +-commutative 88.0%

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

      4. unsub-neg 88.0%

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

   8. Simplified 88.0%

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

4. Final simplification 89.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -1.2 \cdot 10^{-117}:\\ \;\;\;\;\left(x - y\right) \cdot \frac{t}{z - y}\\ \mathbf{elif}\;t \leq 1.05 \cdot 10^{-238}:\\ \;\;\;\;\frac{t \cdot x}{z - y}\\ \mathbf{elif}\;t \leq 3.2 \cdot 10^{-171}:\\ \;\;\;\;t \cdot \frac{y}{y - z}\\ \mathbf{else}:\\ \;\;\;\;\left(x - y\right) \cdot \frac{t}{z - y}\\ \end{array} \]

Alternative 3: 59.3% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -9.5 \cdot 10^{+126}:\\ \;\;\;\;t\\ \mathbf{elif}\;y \leq -2.25 \cdot 10^{-13}:\\ \;\;\;\;\frac{-y}{\frac{z}{t}}\\ \mathbf{elif}\;y \leq -1.85 \cdot 10^{-78}:\\ \;\;\;\;x \cdot \frac{-t}{y}\\ \mathbf{elif}\;y \leq 4.2 \cdot 10^{+58}:\\ \;\;\;\;\frac{t}{\frac{z}{x}}\\ \mathbf{else}:\\ \;\;\;\;t\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= y -9.5e+126)
   t
   (if (<= y -2.25e-13)
     (/ (- y) (/ z t))
     (if (<= y -1.85e-78)
       (* x (/ (- t) y))
       (if (<= y 4.2e+58) (/ t (/ z x)) t)))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (y <= -9.5e+126) {
		tmp = t;
	} else if (y <= -2.25e-13) {
		tmp = -y / (z / t);
	} else if (y <= -1.85e-78) {
		tmp = x * (-t / y);
	} else if (y <= 4.2e+58) {
		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 <= (-9.5d+126)) then
        tmp = t
    else if (y <= (-2.25d-13)) then
        tmp = -y / (z / t)
    else if (y <= (-1.85d-78)) then
        tmp = x * (-t / y)
    else if (y <= 4.2d+58) 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 <= -9.5e+126) {
		tmp = t;
	} else if (y <= -2.25e-13) {
		tmp = -y / (z / t);
	} else if (y <= -1.85e-78) {
		tmp = x * (-t / y);
	} else if (y <= 4.2e+58) {
		tmp = t / (z / x);
	} else {
		tmp = t;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if y <= -9.5e+126:
		tmp = t
	elif y <= -2.25e-13:
		tmp = -y / (z / t)
	elif y <= -1.85e-78:
		tmp = x * (-t / y)
	elif y <= 4.2e+58:
		tmp = t / (z / x)
	else:
		tmp = t
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (y <= -9.5e+126)
		tmp = t;
	elseif (y <= -2.25e-13)
		tmp = Float64(Float64(-y) / Float64(z / t));
	elseif (y <= -1.85e-78)
		tmp = Float64(x * Float64(Float64(-t) / y));
	elseif (y <= 4.2e+58)
		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 <= -9.5e+126)
		tmp = t;
	elseif (y <= -2.25e-13)
		tmp = -y / (z / t);
	elseif (y <= -1.85e-78)
		tmp = x * (-t / y);
	elseif (y <= 4.2e+58)
		tmp = t / (z / x);
	else
		tmp = t;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[y, -9.5e+126], t, If[LessEqual[y, -2.25e-13], N[((-y) / N[(z / t), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, -1.85e-78], N[(x * N[((-t) / y), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 4.2e+58], N[(t / N[(z / x), $MachinePrecision]), $MachinePrecision], t]]]]

Derivation

1. Split input into 4 regimes

2. if y < -9.49999999999999951e126 or 4.20000000000000024e58 < y

   1. Initial program 99.9%

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

      1. associate-*l/ 68.0%

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

      2. associate-*r/ 69.8%

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

   3. Simplified 69.8%

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

   4. Taylor expanded in y around inf 66.0%

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

   if -9.49999999999999951e126 < y < -2.25e-13

   1. Initial program 99.8%

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

   2. Taylor expanded in x around 0 59.4%

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

      1. neg-mul-1 59.4%

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

      2. distribute-neg-frac 59.4%

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

   4. Simplified 59.4%

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

   5. Taylor expanded in y around 0 51.0%

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

      1. mul-1-neg 51.0%

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

      2. associate-/l* 51.0%

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

   7. Simplified 51.0%

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

   if -2.25e-13 < y < -1.85000000000000003e-78

   1. Initial program 99.7%

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

      1. associate-*l/ 99.8%

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

      2. associate-*r/ 99.9%

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

   3. Simplified 99.9%

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

   4. Taylor expanded in x around inf 58.9%

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

      1. associate-/l* 58.7%

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

      2. associate-/r/ 58.9%

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

   6. Applied egg-rr 58.9%

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

   7. Taylor expanded in z around 0 44.6%

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

      1. associate-*r/ 44.6%

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

      2. neg-mul-1 44.6%

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

   9. Simplified 44.6%

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

   if -1.85000000000000003e-78 < y < 4.20000000000000024e58

   1. Initial program 94.8%

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

      1. associate-*l/ 97.6%

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

      2. associate-*r/ 89.9%

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

   3. Simplified 89.9%

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

   4. Taylor expanded in y around 0 68.6%

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

      1. associate-/l* 68.6%

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

   6. Simplified 68.6%

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

4. Final simplification 64.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -9.5 \cdot 10^{+126}:\\ \;\;\;\;t\\ \mathbf{elif}\;y \leq -2.25 \cdot 10^{-13}:\\ \;\;\;\;\frac{-y}{\frac{z}{t}}\\ \mathbf{elif}\;y \leq -1.85 \cdot 10^{-78}:\\ \;\;\;\;x \cdot \frac{-t}{y}\\ \mathbf{elif}\;y \leq 4.2 \cdot 10^{+58}:\\ \;\;\;\;\frac{t}{\frac{z}{x}}\\ \mathbf{else}:\\ \;\;\;\;t\\ \end{array} \]

Alternative 4: 59.5% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -6.2 \cdot 10^{+126}:\\ \;\;\;\;t\\ \mathbf{elif}\;y \leq -9 \cdot 10^{-25}:\\ \;\;\;\;t \cdot \frac{-y}{z}\\ \mathbf{elif}\;y \leq -7.6 \cdot 10^{-79}:\\ \;\;\;\;x \cdot \frac{-t}{y}\\ \mathbf{elif}\;y \leq 7.2 \cdot 10^{+57}:\\ \;\;\;\;\frac{t}{\frac{z}{x}}\\ \mathbf{else}:\\ \;\;\;\;t\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= y -6.2e+126)
   t
   (if (<= y -9e-25)
     (* t (/ (- y) z))
     (if (<= y -7.6e-79)
       (* x (/ (- t) y))
       (if (<= y 7.2e+57) (/ t (/ z x)) t)))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (y <= -6.2e+126) {
		tmp = t;
	} else if (y <= -9e-25) {
		tmp = t * (-y / z);
	} else if (y <= -7.6e-79) {
		tmp = x * (-t / y);
	} else if (y <= 7.2e+57) {
		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 <= (-6.2d+126)) then
        tmp = t
    else if (y <= (-9d-25)) then
        tmp = t * (-y / z)
    else if (y <= (-7.6d-79)) then
        tmp = x * (-t / y)
    else if (y <= 7.2d+57) 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 <= -6.2e+126) {
		tmp = t;
	} else if (y <= -9e-25) {
		tmp = t * (-y / z);
	} else if (y <= -7.6e-79) {
		tmp = x * (-t / y);
	} else if (y <= 7.2e+57) {
		tmp = t / (z / x);
	} else {
		tmp = t;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if y <= -6.2e+126:
		tmp = t
	elif y <= -9e-25:
		tmp = t * (-y / z)
	elif y <= -7.6e-79:
		tmp = x * (-t / y)
	elif y <= 7.2e+57:
		tmp = t / (z / x)
	else:
		tmp = t
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (y <= -6.2e+126)
		tmp = t;
	elseif (y <= -9e-25)
		tmp = Float64(t * Float64(Float64(-y) / z));
	elseif (y <= -7.6e-79)
		tmp = Float64(x * Float64(Float64(-t) / y));
	elseif (y <= 7.2e+57)
		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 <= -6.2e+126)
		tmp = t;
	elseif (y <= -9e-25)
		tmp = t * (-y / z);
	elseif (y <= -7.6e-79)
		tmp = x * (-t / y);
	elseif (y <= 7.2e+57)
		tmp = t / (z / x);
	else
		tmp = t;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[y, -6.2e+126], t, If[LessEqual[y, -9e-25], N[(t * N[((-y) / z), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, -7.6e-79], N[(x * N[((-t) / y), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 7.2e+57], N[(t / N[(z / x), $MachinePrecision]), $MachinePrecision], t]]]]

Derivation

1. Split input into 4 regimes

2. if y < -6.2e126 or 7.2000000000000005e57 < y

   1. Initial program 99.9%

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

      1. associate-*l/ 68.0%

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

      2. associate-*r/ 69.8%

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

   3. Simplified 69.8%

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

   4. Taylor expanded in y around inf 66.0%

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

   if -6.2e126 < y < -9.0000000000000002e-25

   1. Initial program 99.8%

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

   2. Taylor expanded in x around 0 59.4%

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

      1. neg-mul-1 59.4%

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

      2. distribute-neg-frac 59.4%

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

   4. Simplified 59.4%

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

   5. Taylor expanded in y around 0 51.1%

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

      1. mul-1-neg 51.1%

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

      2. distribute-neg-frac 51.1%

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

   7. Simplified 51.1%

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

   if -9.0000000000000002e-25 < y < -7.6000000000000002e-79

   1. Initial program 99.7%

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

      1. associate-*l/ 99.8%

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

      2. associate-*r/ 99.9%

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

   3. Simplified 99.9%

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

   4. Taylor expanded in x around inf 58.9%

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

      1. associate-/l* 58.7%

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

      2. associate-/r/ 58.9%

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

   6. Applied egg-rr 58.9%

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

   7. Taylor expanded in z around 0 44.6%

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

      1. associate-*r/ 44.6%

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

      2. neg-mul-1 44.6%

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

   9. Simplified 44.6%

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

   if -7.6000000000000002e-79 < y < 7.2000000000000005e57

   1. Initial program 94.8%

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

      1. associate-*l/ 97.6%

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

      2. associate-*r/ 89.9%

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

   3. Simplified 89.9%

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

   4. Taylor expanded in y around 0 68.6%

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

      1. associate-/l* 68.6%

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

   6. Simplified 68.6%

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

4. Final simplification 64.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -6.2 \cdot 10^{+126}:\\ \;\;\;\;t\\ \mathbf{elif}\;y \leq -9 \cdot 10^{-25}:\\ \;\;\;\;t \cdot \frac{-y}{z}\\ \mathbf{elif}\;y \leq -7.6 \cdot 10^{-79}:\\ \;\;\;\;x \cdot \frac{-t}{y}\\ \mathbf{elif}\;y \leq 7.2 \cdot 10^{+57}:\\ \;\;\;\;\frac{t}{\frac{z}{x}}\\ \mathbf{else}:\\ \;\;\;\;t\\ \end{array} \]

Alternative 5: 73.9% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -3.4 \cdot 10^{-132} \lor \neg \left(x \leq 2.4 \cdot 10^{+34}\right):\\ \;\;\;\;t \cdot \frac{x}{z - y}\\ \mathbf{else}:\\ \;\;\;\;t \cdot \frac{y}{y - z}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= x -3.4e-132) (not (<= x 2.4e+34)))
   (* t (/ x (- z y)))
   (* t (/ y (- y z)))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((x <= -3.4e-132) || !(x <= 2.4e+34)) {
		tmp = t * (x / (z - y));
	} else {
		tmp = t * (y / (y - z));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if ((x <= (-3.4d-132)) .or. (.not. (x <= 2.4d+34))) then
        tmp = t * (x / (z - y))
    else
        tmp = t * (y / (y - z))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if ((x <= -3.4e-132) || !(x <= 2.4e+34)) {
		tmp = t * (x / (z - y));
	} else {
		tmp = t * (y / (y - z));
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (x <= -3.4e-132) or not (x <= 2.4e+34):
		tmp = t * (x / (z - y))
	else:
		tmp = t * (y / (y - z))
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((x <= -3.4e-132) || !(x <= 2.4e+34))
		tmp = Float64(t * Float64(x / Float64(z - y)));
	else
		tmp = Float64(t * Float64(y / Float64(y - z)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((x <= -3.4e-132) || ~((x <= 2.4e+34)))
		tmp = t * (x / (z - y));
	else
		tmp = t * (y / (y - z));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[x, -3.4e-132], N[Not[LessEqual[x, 2.4e+34]], $MachinePrecision]], N[(t * N[(x / N[(z - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(t * N[(y / N[(y - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < -3.39999999999999983e-132 or 2.39999999999999987e34 < x

   1. Initial program 97.1%

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

   2. Taylor expanded in x around inf 77.0%

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

   if -3.39999999999999983e-132 < x < 2.39999999999999987e34

   1. Initial program 98.2%

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

   2. Taylor expanded in x around 0 85.1%

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

      1. neg-mul-1 85.1%

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

      2. distribute-neg-frac 85.1%

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

   4. Simplified 85.1%

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

      1. frac-2neg 85.1%

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

      2. div-inv 84.9%

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

      3. remove-double-neg 84.9%

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

      4. sub-neg 84.9%

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

      5. distribute-neg-in 84.9%

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

      6. remove-double-neg 84.9%

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

   6. Applied egg-rr 84.9%

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

      1. associate-*r/ 85.1%

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

      2. *-rgt-identity 85.1%

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

      3. +-commutative 85.1%

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

      4. unsub-neg 85.1%

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

   8. Simplified 85.1%

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

4. Final simplification 80.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -3.4 \cdot 10^{-132} \lor \neg \left(x \leq 2.4 \cdot 10^{+34}\right):\\ \;\;\;\;t \cdot \frac{x}{z - y}\\ \mathbf{else}:\\ \;\;\;\;t \cdot \frac{y}{y - z}\\ \end{array} \]

Alternative 6: 74.1% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -3.4 \cdot 10^{-132} \lor \neg \left(x \leq 10^{+33}\right):\\ \;\;\;\;\frac{t}{\frac{z - y}{x}}\\ \mathbf{else}:\\ \;\;\;\;t \cdot \frac{y}{y - z}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= x -3.4e-132) (not (<= x 1e+33)))
   (/ t (/ (- z y) x))
   (* t (/ y (- y z)))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((x <= -3.4e-132) || !(x <= 1e+33)) {
		tmp = t / ((z - y) / x);
	} else {
		tmp = t * (y / (y - z));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if ((x <= (-3.4d-132)) .or. (.not. (x <= 1d+33))) then
        tmp = t / ((z - y) / x)
    else
        tmp = t * (y / (y - z))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if ((x <= -3.4e-132) || !(x <= 1e+33)) {
		tmp = t / ((z - y) / x);
	} else {
		tmp = t * (y / (y - z));
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (x <= -3.4e-132) or not (x <= 1e+33):
		tmp = t / ((z - y) / x)
	else:
		tmp = t * (y / (y - z))
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((x <= -3.4e-132) || !(x <= 1e+33))
		tmp = Float64(t / Float64(Float64(z - y) / x));
	else
		tmp = Float64(t * Float64(y / Float64(y - z)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((x <= -3.4e-132) || ~((x <= 1e+33)))
		tmp = t / ((z - y) / x);
	else
		tmp = t * (y / (y - z));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[x, -3.4e-132], N[Not[LessEqual[x, 1e+33]], $MachinePrecision]], N[(t / N[(N[(z - y), $MachinePrecision] / x), $MachinePrecision]), $MachinePrecision], N[(t * N[(y / N[(y - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < -3.39999999999999983e-132 or 9.9999999999999995e32 < x

   1. Initial program 97.1%

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

      1. associate-*l/ 86.5%

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

      2. associate-*r/ 79.8%

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

   3. Simplified 79.8%

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

      1. associate-*r/ 86.5%

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

      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 97.0%

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

      5. un-div-inv 97.2%

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

   5. Applied egg-rr 97.2%

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

   6. Taylor expanded in x around inf 77.1%

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

   if -3.39999999999999983e-132 < x < 9.9999999999999995e32

   1. Initial program 98.2%

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

   2. Taylor expanded in x around 0 85.1%

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

      1. neg-mul-1 85.1%

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

      2. distribute-neg-frac 85.1%

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

   4. Simplified 85.1%

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

      1. frac-2neg 85.1%

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

      2. div-inv 84.9%

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

      3. remove-double-neg 84.9%

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

      4. sub-neg 84.9%

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

      5. distribute-neg-in 84.9%

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

      6. remove-double-neg 84.9%

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

   6. Applied egg-rr 84.9%

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

      1. associate-*r/ 85.1%

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

      2. *-rgt-identity 85.1%

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

      3. +-commutative 85.1%

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

      4. unsub-neg 85.1%

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

   8. Simplified 85.1%

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

4. Final simplification 80.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -3.4 \cdot 10^{-132} \lor \neg \left(x \leq 10^{+33}\right):\\ \;\;\;\;\frac{t}{\frac{z - y}{x}}\\ \mathbf{else}:\\ \;\;\;\;t \cdot \frac{y}{y - z}\\ \end{array} \]

Alternative 7: 68.1% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -7.5 \cdot 10^{+126}:\\ \;\;\;\;t\\ \mathbf{elif}\;y \leq 1.5 \cdot 10^{+58}:\\ \;\;\;\;x \cdot \frac{t}{z - y}\\ \mathbf{else}:\\ \;\;\;\;t\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= y -7.5e+126) t (if (<= y 1.5e+58) (* x (/ t (- z y))) t)))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (y <= -7.5e+126) {
		tmp = t;
	} else if (y <= 1.5e+58) {
		tmp = x * (t / (z - y));
	} else {
		tmp = t;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if (y <= (-7.5d+126)) then
        tmp = t
    else if (y <= 1.5d+58) then
        tmp = x * (t / (z - y))
    else
        tmp = t
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if (y <= -7.5e+126) {
		tmp = t;
	} else if (y <= 1.5e+58) {
		tmp = x * (t / (z - y));
	} else {
		tmp = t;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if y <= -7.5e+126:
		tmp = t
	elif y <= 1.5e+58:
		tmp = x * (t / (z - y))
	else:
		tmp = t
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (y <= -7.5e+126)
		tmp = t;
	elseif (y <= 1.5e+58)
		tmp = Float64(x * Float64(t / Float64(z - y)));
	else
		tmp = t;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (y <= -7.5e+126)
		tmp = t;
	elseif (y <= 1.5e+58)
		tmp = x * (t / (z - y));
	else
		tmp = t;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[y, -7.5e+126], t, If[LessEqual[y, 1.5e+58], N[(x * N[(t / N[(z - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t]]

Derivation

1. Split input into 2 regimes

2. if y < -7.5000000000000006e126 or 1.5000000000000001e58 < y

   1. Initial program 99.9%

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

      1. associate-*l/ 68.0%

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

      2. associate-*r/ 69.8%

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

   3. Simplified 69.8%

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

   4. Taylor expanded in y around inf 66.0%

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

   if -7.5000000000000006e126 < y < 1.5000000000000001e58

   1. Initial program 96.1%

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

      1. associate-*l/ 96.3%

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

      2. associate-*r/ 91.2%

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

   3. Simplified 91.2%

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

   4. Taylor expanded in x around inf 73.5%

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

      1. associate-*l/ 68.7%

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

      2. *-commutative 68.7%

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

   6. Simplified 68.7%

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

4. Final simplification 67.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -7.5 \cdot 10^{+126}:\\ \;\;\;\;t\\ \mathbf{elif}\;y \leq 1.5 \cdot 10^{+58}:\\ \;\;\;\;x \cdot \frac{t}{z - y}\\ \mathbf{else}:\\ \;\;\;\;t\\ \end{array} \]

Alternative 8: 65.7% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -7 \cdot 10^{+126}:\\ \;\;\;\;t\\ \mathbf{elif}\;y \leq 4.8 \cdot 10^{+58}:\\ \;\;\;\;\left(x - y\right) \cdot \frac{t}{z}\\ \mathbf{else}:\\ \;\;\;\;t\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= y -7e+126) t (if (<= y 4.8e+58) (* (- x y) (/ t z)) t)))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (y <= -7e+126) {
		tmp = t;
	} else if (y <= 4.8e+58) {
		tmp = (x - y) * (t / z);
	} else {
		tmp = t;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if (y <= (-7d+126)) then
        tmp = t
    else if (y <= 4.8d+58) then
        tmp = (x - y) * (t / z)
    else
        tmp = t
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if (y <= -7e+126) {
		tmp = t;
	} else if (y <= 4.8e+58) {
		tmp = (x - y) * (t / z);
	} else {
		tmp = t;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if y <= -7e+126:
		tmp = t
	elif y <= 4.8e+58:
		tmp = (x - y) * (t / z)
	else:
		tmp = t
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (y <= -7e+126)
		tmp = t;
	elseif (y <= 4.8e+58)
		tmp = Float64(Float64(x - y) * Float64(t / z));
	else
		tmp = t;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (y <= -7e+126)
		tmp = t;
	elseif (y <= 4.8e+58)
		tmp = (x - y) * (t / z);
	else
		tmp = t;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[y, -7e+126], t, If[LessEqual[y, 4.8e+58], N[(N[(x - y), $MachinePrecision] * N[(t / z), $MachinePrecision]), $MachinePrecision], t]]

Derivation

1. Split input into 2 regimes

2. if y < -7.0000000000000005e126 or 4.8e58 < y

   1. Initial program 99.9%

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

      1. associate-*l/ 68.0%

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

      2. associate-*r/ 69.8%

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

   3. Simplified 69.8%

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

   4. Taylor expanded in y around inf 66.0%

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

   if -7.0000000000000005e126 < y < 4.8e58

   1. Initial program 96.1%

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

      1. associate-*l/ 96.3%

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

      2. associate-*r/ 91.2%

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

   3. Simplified 91.2%

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

   4. Taylor expanded in z around inf 69.4%

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

4. Final simplification 68.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -7 \cdot 10^{+126}:\\ \;\;\;\;t\\ \mathbf{elif}\;y \leq 4.8 \cdot 10^{+58}:\\ \;\;\;\;\left(x - y\right) \cdot \frac{t}{z}\\ \mathbf{else}:\\ \;\;\;\;t\\ \end{array} \]

Alternative 9: 68.8% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -4.4 \cdot 10^{+145}:\\ \;\;\;\;t\\ \mathbf{elif}\;y \leq 1.9 \cdot 10^{+119}:\\ \;\;\;\;t \cdot \frac{x}{z - y}\\ \mathbf{else}:\\ \;\;\;\;t\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= y -4.4e+145) t (if (<= y 1.9e+119) (* t (/ x (- z y))) t)))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (y <= -4.4e+145) {
		tmp = t;
	} else if (y <= 1.9e+119) {
		tmp = t * (x / (z - y));
	} else {
		tmp = t;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if (y <= (-4.4d+145)) then
        tmp = t
    else if (y <= 1.9d+119) then
        tmp = t * (x / (z - y))
    else
        tmp = t
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if (y <= -4.4e+145) {
		tmp = t;
	} else if (y <= 1.9e+119) {
		tmp = t * (x / (z - y));
	} else {
		tmp = t;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if y <= -4.4e+145:
		tmp = t
	elif y <= 1.9e+119:
		tmp = t * (x / (z - y))
	else:
		tmp = t
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (y <= -4.4e+145)
		tmp = t;
	elseif (y <= 1.9e+119)
		tmp = Float64(t * Float64(x / Float64(z - y)));
	else
		tmp = t;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (y <= -4.4e+145)
		tmp = t;
	elseif (y <= 1.9e+119)
		tmp = t * (x / (z - y));
	else
		tmp = t;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[y, -4.4e+145], t, If[LessEqual[y, 1.9e+119], N[(t * N[(x / N[(z - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t]]

Derivation

1. Split input into 2 regimes

2. if y < -4.40000000000000017e145 or 1.89999999999999995e119 < y

   1. Initial program 99.9%

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

      1. associate-*l/ 62.3%

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

      2. associate-*r/ 70.5%

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

   3. Simplified 70.5%

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

   4. Taylor expanded in y around inf 70.7%

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

   if -4.40000000000000017e145 < y < 1.89999999999999995e119

   1. Initial program 96.5%

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

   2. Taylor expanded in x around inf 70.8%

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

4. Final simplification 70.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -4.4 \cdot 10^{+145}:\\ \;\;\;\;t\\ \mathbf{elif}\;y \leq 1.9 \cdot 10^{+119}:\\ \;\;\;\;t \cdot \frac{x}{z - y}\\ \mathbf{else}:\\ \;\;\;\;t\\ \end{array} \]

Alternative 10: 72.9% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -3.4 \cdot 10^{-132}:\\ \;\;\;\;\frac{t \cdot x}{z - y}\\ \mathbf{elif}\;x \leq 8 \cdot 10^{+32}:\\ \;\;\;\;t \cdot \frac{y}{y - z}\\ \mathbf{else}:\\ \;\;\;\;\frac{t}{\frac{z - y}{x}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= x -3.4e-132)
   (/ (* t x) (- z y))
   (if (<= x 8e+32) (* t (/ y (- y z))) (/ t (/ (- z y) x)))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (x <= -3.4e-132) {
		tmp = (t * x) / (z - y);
	} else if (x <= 8e+32) {
		tmp = t * (y / (y - z));
	} else {
		tmp = t / ((z - y) / x);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if (x <= (-3.4d-132)) then
        tmp = (t * x) / (z - y)
    else if (x <= 8d+32) then
        tmp = t * (y / (y - z))
    else
        tmp = t / ((z - y) / x)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if (x <= -3.4e-132) {
		tmp = (t * x) / (z - y);
	} else if (x <= 8e+32) {
		tmp = t * (y / (y - z));
	} else {
		tmp = t / ((z - y) / x);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if x <= -3.4e-132:
		tmp = (t * x) / (z - y)
	elif x <= 8e+32:
		tmp = t * (y / (y - z))
	else:
		tmp = t / ((z - y) / x)
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (x <= -3.4e-132)
		tmp = Float64(Float64(t * x) / Float64(z - y));
	elseif (x <= 8e+32)
		tmp = Float64(t * Float64(y / Float64(y - z)));
	else
		tmp = Float64(t / Float64(Float64(z - y) / x));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (x <= -3.4e-132)
		tmp = (t * x) / (z - y);
	elseif (x <= 8e+32)
		tmp = t * (y / (y - z));
	else
		tmp = t / ((z - y) / x);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[x, -3.4e-132], N[(N[(t * x), $MachinePrecision] / N[(z - y), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 8e+32], N[(t * N[(y / N[(y - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(t / N[(N[(z - y), $MachinePrecision] / x), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if x < -3.39999999999999983e-132

   1. Initial program 97.3%

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

      1. associate-*l/ 89.3%

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

      2. associate-*r/ 77.3%

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

   3. Simplified 77.3%

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

   4. Taylor expanded in x around inf 77.0%

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

   if -3.39999999999999983e-132 < x < 8.00000000000000043e32

   1. Initial program 98.2%

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

   2. Taylor expanded in x around 0 85.1%

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

      1. neg-mul-1 85.1%

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

      2. distribute-neg-frac 85.1%

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

   4. Simplified 85.1%

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

      1. frac-2neg 85.1%

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

      2. div-inv 84.9%

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

      3. remove-double-neg 84.9%

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

      4. sub-neg 84.9%

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

      5. distribute-neg-in 84.9%

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

      6. remove-double-neg 84.9%

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

   6. Applied egg-rr 84.9%

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

      1. associate-*r/ 85.1%

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

      2. *-rgt-identity 85.1%

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

      3. +-commutative 85.1%

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

      4. unsub-neg 85.1%

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

   8. Simplified 85.1%

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

   if 8.00000000000000043e32 < x

   1. Initial program 96.9%

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

      1. associate-*l/ 83.5%

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

      2. associate-*r/ 82.5%

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

   3. Simplified 82.5%

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

      1. associate-*r/ 83.5%

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

      2. associate-*l/ 96.9%

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

      3. *-commutative 96.9%

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

      4. clear-num 96.9%

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

      5. un-div-inv 97.0%

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

   5. Applied egg-rr 97.0%

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

   6. Taylor expanded in x around inf 78.2%

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

4. Final simplification 80.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -3.4 \cdot 10^{-132}:\\ \;\;\;\;\frac{t \cdot x}{z - y}\\ \mathbf{elif}\;x \leq 8 \cdot 10^{+32}:\\ \;\;\;\;t \cdot \frac{y}{y - z}\\ \mathbf{else}:\\ \;\;\;\;\frac{t}{\frac{z - y}{x}}\\ \end{array} \]

Alternative 11: 58.5% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -7.5 \cdot 10^{+126}:\\ \;\;\;\;t\\ \mathbf{elif}\;y \leq 1.55 \cdot 10^{+58}:\\ \;\;\;\;x \cdot \frac{t}{z}\\ \mathbf{else}:\\ \;\;\;\;t\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= y -7.5e+126) t (if (<= y 1.55e+58) (* x (/ t z)) t)))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (y <= -7.5e+126) {
		tmp = t;
	} else if (y <= 1.55e+58) {
		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 <= (-7.5d+126)) then
        tmp = t
    else if (y <= 1.55d+58) 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 <= -7.5e+126) {
		tmp = t;
	} else if (y <= 1.55e+58) {
		tmp = x * (t / z);
	} else {
		tmp = t;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if y <= -7.5e+126:
		tmp = t
	elif y <= 1.55e+58:
		tmp = x * (t / z)
	else:
		tmp = t
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (y <= -7.5e+126)
		tmp = t;
	elseif (y <= 1.55e+58)
		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 <= -7.5e+126)
		tmp = t;
	elseif (y <= 1.55e+58)
		tmp = x * (t / z);
	else
		tmp = t;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[y, -7.5e+126], t, If[LessEqual[y, 1.55e+58], N[(x * N[(t / z), $MachinePrecision]), $MachinePrecision], t]]

Derivation

1. Split input into 2 regimes

2. if y < -7.5000000000000006e126 or 1.55e58 < y

   1. Initial program 99.9%

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

      1. associate-*l/ 68.0%

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

      2. associate-*r/ 69.8%

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

   3. Simplified 69.8%

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

   4. Taylor expanded in y around inf 66.0%

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

   if -7.5000000000000006e126 < y < 1.55e58

   1. Initial program 96.1%

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

      1. associate-*l/ 96.3%

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

      2. associate-*r/ 91.2%

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

   3. Simplified 91.2%

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

      1. associate-*r/ 96.3%

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

      2. associate-*l/ 96.1%

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

      3. *-commutative 96.1%

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

      4. clear-num 95.9%

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

      5. un-div-inv 96.1%

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

   5. Applied egg-rr 96.1%

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

   6. Taylor expanded in y around 0 58.8%

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

      1. associate-*l/ 54.5%

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

      2. *-commutative 54.5%

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

   8. Simplified 54.5%

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

4. Final simplification 59.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -7.5 \cdot 10^{+126}:\\ \;\;\;\;t\\ \mathbf{elif}\;y \leq 1.55 \cdot 10^{+58}:\\ \;\;\;\;x \cdot \frac{t}{z}\\ \mathbf{else}:\\ \;\;\;\;t\\ \end{array} \]

Alternative 12: 60.2% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -6.8 \cdot 10^{+127}:\\ \;\;\;\;t\\ \mathbf{elif}\;y \leq 2.3 \cdot 10^{+58}:\\ \;\;\;\;t \cdot \frac{x}{z}\\ \mathbf{else}:\\ \;\;\;\;t\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= y -6.8e+127) t (if (<= y 2.3e+58) (* t (/ x z)) t)))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (y <= -6.8e+127) {
		tmp = t;
	} else if (y <= 2.3e+58) {
		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+127)) then
        tmp = t
    else if (y <= 2.3d+58) 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+127) {
		tmp = t;
	} else if (y <= 2.3e+58) {
		tmp = t * (x / z);
	} else {
		tmp = t;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if y <= -6.8e+127:
		tmp = t
	elif y <= 2.3e+58:
		tmp = t * (x / z)
	else:
		tmp = t
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (y <= -6.8e+127)
		tmp = t;
	elseif (y <= 2.3e+58)
		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+127)
		tmp = t;
	elseif (y <= 2.3e+58)
		tmp = t * (x / z);
	else
		tmp = t;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[y, -6.8e+127], t, If[LessEqual[y, 2.3e+58], N[(t * N[(x / z), $MachinePrecision]), $MachinePrecision], t]]

Derivation

1. Split input into 2 regimes

2. if y < -6.79999999999999955e127 or 2.30000000000000002e58 < y

   1. Initial program 99.9%

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

      1. associate-*l/ 67.4%

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

      2. associate-*r/ 70.1%

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

   3. Simplified 70.1%

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

   4. Taylor expanded in y around inf 66.3%

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

   if -6.79999999999999955e127 < y < 2.30000000000000002e58

   1. Initial program 96.1%

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

   2. Taylor expanded in y around 0 59.9%

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

4. Final simplification 62.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -6.8 \cdot 10^{+127}:\\ \;\;\;\;t\\ \mathbf{elif}\;y \leq 2.3 \cdot 10^{+58}:\\ \;\;\;\;t \cdot \frac{x}{z}\\ \mathbf{else}:\\ \;\;\;\;t\\ \end{array} \]

Alternative 13: 60.2% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -3.5 \cdot 10^{+129}:\\ \;\;\;\;t\\ \mathbf{elif}\;y \leq 1.55 \cdot 10^{+58}:\\ \;\;\;\;\frac{t}{\frac{z}{x}}\\ \mathbf{else}:\\ \;\;\;\;t\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= y -3.5e+129) t (if (<= y 1.55e+58) (/ t (/ z x)) t)))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (y <= -3.5e+129) {
		tmp = t;
	} else if (y <= 1.55e+58) {
		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 <= (-3.5d+129)) then
        tmp = t
    else if (y <= 1.55d+58) 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 <= -3.5e+129) {
		tmp = t;
	} else if (y <= 1.55e+58) {
		tmp = t / (z / x);
	} else {
		tmp = t;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if y <= -3.5e+129:
		tmp = t
	elif y <= 1.55e+58:
		tmp = t / (z / x)
	else:
		tmp = t
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (y <= -3.5e+129)
		tmp = t;
	elseif (y <= 1.55e+58)
		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 <= -3.5e+129)
		tmp = t;
	elseif (y <= 1.55e+58)
		tmp = t / (z / x);
	else
		tmp = t;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[y, -3.5e+129], t, If[LessEqual[y, 1.55e+58], N[(t / N[(z / x), $MachinePrecision]), $MachinePrecision], t]]

Derivation

1. Split input into 2 regimes

2. if y < -3.4999999999999998e129 or 1.55e58 < y

   1. Initial program 99.9%

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

      1. associate-*l/ 67.4%

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

      2. associate-*r/ 70.1%

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

   3. Simplified 70.1%

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

   4. Taylor expanded in y around inf 66.3%

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

   if -3.4999999999999998e129 < y < 1.55e58

   1. Initial program 96.1%

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

      1. associate-*l/ 96.4%

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

      2. associate-*r/ 90.7%

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

   3. Simplified 90.7%

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

   4. Taylor expanded in y around 0 58.7%

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

      1. associate-/l* 59.9%

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

   6. Simplified 59.9%

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

4. Final simplification 62.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -3.5 \cdot 10^{+129}:\\ \;\;\;\;t\\ \mathbf{elif}\;y \leq 1.55 \cdot 10^{+58}:\\ \;\;\;\;\frac{t}{\frac{z}{x}}\\ \mathbf{else}:\\ \;\;\;\;t\\ \end{array} \]

Alternative 14: 97.0% 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 97.6%

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

2. Final simplification 97.6%

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

Alternative 15: 35.8% accurate, 9.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 97.6%

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

   1. associate-*l/ 85.3%

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

   2. associate-*r/ 82.8%

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

3. Simplified 82.8%

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

4. Taylor expanded in y around inf 32.8%

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

5. Final simplification 32.8%

   \[\leadsto t \]

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 2023196 
(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))