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

Percentage Accurate: 97.0% → 97.8%

Time: 11.0s

Alternatives: 12

Speedup: 0.4×

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: 97.8% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;\frac{x - y}{z - y} \leq -4 \cdot 10^{+240}:\\ \;\;\;\;x \cdot \frac{t}{z - y}\\ \mathbf{else}:\\ \;\;\;\;t \cdot \left(\frac{x}{z - y} - \frac{y}{z - y}\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= (/ (- x y) (- z y)) -4e+240)
   (* x (/ t (- z y)))
   (* t (- (/ x (- z y)) (/ y (- z y))))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (((x - y) / (z - y)) <= -4e+240) {
		tmp = x * (t / (z - y));
	} else {
		tmp = t * ((x / (z - y)) - (y / (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 (((x - y) / (z - y)) <= (-4d+240)) then
        tmp = x * (t / (z - y))
    else
        tmp = t * ((x / (z - y)) - (y / (z - y)))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if (((x - y) / (z - y)) <= -4e+240) {
		tmp = x * (t / (z - y));
	} else {
		tmp = t * ((x / (z - y)) - (y / (z - y)));
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if ((x - y) / (z - y)) <= -4e+240:
		tmp = x * (t / (z - y))
	else:
		tmp = t * ((x / (z - y)) - (y / (z - y)))
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (Float64(Float64(x - y) / Float64(z - y)) <= -4e+240)
		tmp = Float64(x * Float64(t / Float64(z - y)));
	else
		tmp = Float64(t * Float64(Float64(x / Float64(z - y)) - Float64(y / Float64(z - y))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (((x - y) / (z - y)) <= -4e+240)
		tmp = x * (t / (z - y));
	else
		tmp = t * ((x / (z - y)) - (y / (z - y)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[N[(N[(x - y), $MachinePrecision] / N[(z - y), $MachinePrecision]), $MachinePrecision], -4e+240], N[(x * N[(t / N[(z - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(t * N[(N[(x / N[(z - y), $MachinePrecision]), $MachinePrecision] - N[(y / N[(z - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if (/.f64 (-.f64 x y) (-.f64 z y)) < -4.00000000000000006e240

   1. Initial program 60.7%

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

   3. Taylor expanded in x around inf 99.9%

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

      1. *-commutative 99.9%

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

      2. associate-*r/ 100.0%

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

   5. Simplified 100.0%

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

   if -4.00000000000000006e240 < (/.f64 (-.f64 x y) (-.f64 z y))

   1. Initial program 97.8%

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

      1. div-sub 97.8%

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

   4. Applied egg-rr 97.8%

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

4. Final simplification 97.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{x - y}{z - y} \leq -4 \cdot 10^{+240}:\\ \;\;\;\;x \cdot \frac{t}{z - y}\\ \mathbf{else}:\\ \;\;\;\;t \cdot \left(\frac{x}{z - y} - \frac{y}{z - y}\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 2: 61.1% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -9.5 \cdot 10^{+78}:\\ \;\;\;\;t\\ \mathbf{elif}\;y \leq -850000000:\\ \;\;\;\;\frac{x}{\frac{-y}{t}}\\ \mathbf{elif}\;y \leq 4.7 \cdot 10^{+38}:\\ \;\;\;\;t \cdot \frac{x}{z}\\ \mathbf{else}:\\ \;\;\;\;t\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= y -9.5e+78)
   t
   (if (<= y -850000000.0)
     (/ x (/ (- y) t))
     (if (<= y 4.7e+38) (* t (/ x z)) t))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (y <= -9.5e+78) {
		tmp = t;
	} else if (y <= -850000000.0) {
		tmp = x / (-y / t);
	} else if (y <= 4.7e+38) {
		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 <= (-9.5d+78)) then
        tmp = t
    else if (y <= (-850000000.0d0)) then
        tmp = x / (-y / t)
    else if (y <= 4.7d+38) 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 <= -9.5e+78) {
		tmp = t;
	} else if (y <= -850000000.0) {
		tmp = x / (-y / t);
	} else if (y <= 4.7e+38) {
		tmp = t * (x / z);
	} else {
		tmp = t;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if y <= -9.5e+78:
		tmp = t
	elif y <= -850000000.0:
		tmp = x / (-y / t)
	elif y <= 4.7e+38:
		tmp = t * (x / z)
	else:
		tmp = t
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (y <= -9.5e+78)
		tmp = t;
	elseif (y <= -850000000.0)
		tmp = Float64(x / Float64(Float64(-y) / t));
	elseif (y <= 4.7e+38)
		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 <= -9.5e+78)
		tmp = t;
	elseif (y <= -850000000.0)
		tmp = x / (-y / t);
	elseif (y <= 4.7e+38)
		tmp = t * (x / z);
	else
		tmp = t;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[y, -9.5e+78], t, If[LessEqual[y, -850000000.0], N[(x / N[((-y) / t), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 4.7e+38], N[(t * N[(x / z), $MachinePrecision]), $MachinePrecision], t]]]

Derivation

1. Split input into 3 regimes

2. if y < -9.5000000000000006e78 or 4.6999999999999999e38 < y

   1. Initial program 99.8%

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

   3. Taylor expanded in y around inf 72.3%

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

   if -9.5000000000000006e78 < y < -8.5e8

   1. Initial program 99.8%

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

   3. Taylor expanded in x around inf 68.8%

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

      1. *-commutative 68.8%

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

      2. associate-*r/ 68.7%

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

   5. Simplified 68.7%

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

   6. Taylor expanded in z around 0 68.8%

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

      1. mul-1-neg 68.8%

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

      2. *-commutative 68.8%

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

      3. associate-*r/ 68.7%

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

      4. distribute-rgt-neg-in 68.7%

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

      5. distribute-frac-neg 68.7%

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

   8. Simplified 68.7%

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

      1. frac-2neg 68.7%

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

      2. remove-double-neg 68.7%

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

      3. associate-*r/ 68.8%

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

   10. Applied egg-rr 68.8%

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

       1. associate-/l* 68.8%

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

   12. Simplified 68.8%

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

   if -8.5e8 < y < 4.6999999999999999e38

   1. Initial program 93.6%

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

   3. Taylor expanded in y around 0 69.5%

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

4. Final simplification 70.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -9.5 \cdot 10^{+78}:\\ \;\;\;\;t\\ \mathbf{elif}\;y \leq -850000000:\\ \;\;\;\;\frac{x}{\frac{-y}{t}}\\ \mathbf{elif}\;y \leq 4.7 \cdot 10^{+38}:\\ \;\;\;\;t \cdot \frac{x}{z}\\ \mathbf{else}:\\ \;\;\;\;t\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 97.8% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{x - y}{z - y}\\ \mathbf{if}\;t_1 \leq -4 \cdot 10^{+240}:\\ \;\;\;\;x \cdot \frac{t}{z - y}\\ \mathbf{else}:\\ \;\;\;\;t_1 \cdot t\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (/ (- x y) (- z y))))
   (if (<= t_1 -4e+240) (* x (/ t (- z y))) (* t_1 t))))

C

double code(double x, double y, double z, double t) {
	double t_1 = (x - y) / (z - y);
	double tmp;
	if (t_1 <= -4e+240) {
		tmp = x * (t / (z - y));
	} else {
		tmp = t_1 * t;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: t_1
    real(8) :: tmp
    t_1 = (x - y) / (z - y)
    if (t_1 <= (-4d+240)) then
        tmp = x * (t / (z - y))
    else
        tmp = t_1 * t
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double t_1 = (x - y) / (z - y);
	double tmp;
	if (t_1 <= -4e+240) {
		tmp = x * (t / (z - y));
	} else {
		tmp = t_1 * t;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = (x - y) / (z - y)
	tmp = 0
	if t_1 <= -4e+240:
		tmp = x * (t / (z - y))
	else:
		tmp = t_1 * t
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(Float64(x - y) / Float64(z - y))
	tmp = 0.0
	if (t_1 <= -4e+240)
		tmp = Float64(x * Float64(t / Float64(z - y)));
	else
		tmp = Float64(t_1 * t);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = (x - y) / (z - y);
	tmp = 0.0;
	if (t_1 <= -4e+240)
		tmp = x * (t / (z - y));
	else
		tmp = t_1 * t;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(N[(x - y), $MachinePrecision] / N[(z - y), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$1, -4e+240], N[(x * N[(t / N[(z - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(t$95$1 * t), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if (/.f64 (-.f64 x y) (-.f64 z y)) < -4.00000000000000006e240

   1. Initial program 60.7%

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

   3. Taylor expanded in x around inf 99.9%

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

      1. *-commutative 99.9%

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

      2. associate-*r/ 100.0%

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

   5. Simplified 100.0%

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

   if -4.00000000000000006e240 < (/.f64 (-.f64 x y) (-.f64 z y))

   1. Initial program 97.8%

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

4. Final simplification 97.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{x - y}{z - y} \leq -4 \cdot 10^{+240}:\\ \;\;\;\;x \cdot \frac{t}{z - y}\\ \mathbf{else}:\\ \;\;\;\;\frac{x - y}{z - y} \cdot t\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 75.3% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -6.5 \cdot 10^{+46} \lor \neg \left(y \leq 1.45 \cdot 10^{+37}\right):\\ \;\;\;\;t \cdot \left(1 - \frac{x}{y}\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \frac{t}{z - y}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= y -6.5e+46) (not (<= y 1.45e+37)))
   (* t (- 1.0 (/ x y)))
   (* x (/ t (- z y)))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((y <= -6.5e+46) || !(y <= 1.45e+37)) {
		tmp = t * (1.0 - (x / y));
	} else {
		tmp = x * (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 <= (-6.5d+46)) .or. (.not. (y <= 1.45d+37))) then
        tmp = t * (1.0d0 - (x / y))
    else
        tmp = x * (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 <= -6.5e+46) || !(y <= 1.45e+37)) {
		tmp = t * (1.0 - (x / y));
	} else {
		tmp = x * (t / (z - y));
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (y <= -6.5e+46) or not (y <= 1.45e+37):
		tmp = t * (1.0 - (x / y))
	else:
		tmp = x * (t / (z - y))
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((y <= -6.5e+46) || !(y <= 1.45e+37))
		tmp = Float64(t * Float64(1.0 - Float64(x / y)));
	else
		tmp = Float64(x * Float64(t / Float64(z - y)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((y <= -6.5e+46) || ~((y <= 1.45e+37)))
		tmp = t * (1.0 - (x / y));
	else
		tmp = x * (t / (z - y));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[y, -6.5e+46], N[Not[LessEqual[y, 1.45e+37]], $MachinePrecision]], N[(t * N[(1.0 - N[(x / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x * N[(t / N[(z - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -6.50000000000000008e46 or 1.44999999999999989e37 < y

   1. Initial program 99.9%

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

      1. div-sub 99.9%

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

   4. Applied egg-rr 99.9%

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

   5. Taylor expanded in z around 0 81.4%

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

      1. mul-1-neg 81.4%

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

      2. unsub-neg 81.4%

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

   7. Simplified 81.4%

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

   if -6.50000000000000008e46 < y < 1.44999999999999989e37

   1. Initial program 93.8%

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

   3. Taylor expanded in x around inf 79.0%

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

      1. *-commutative 79.0%

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

      2. associate-*r/ 77.1%

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

   5. Simplified 77.1%

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

4. Final simplification 78.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -6.5 \cdot 10^{+46} \lor \neg \left(y \leq 1.45 \cdot 10^{+37}\right):\\ \;\;\;\;t \cdot \left(1 - \frac{x}{y}\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \frac{t}{z - y}\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 75.9% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -8.2 \cdot 10^{+48} \lor \neg \left(y \leq 8.2 \cdot 10^{+37}\right):\\ \;\;\;\;t \cdot \left(1 - \frac{x}{y}\right)\\ \mathbf{else}:\\ \;\;\;\;t \cdot \frac{x}{z - y}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= y -8.2e+48) (not (<= y 8.2e+37)))
   (* t (- 1.0 (/ x y)))
   (* t (/ x (- z y)))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((y <= -8.2e+48) || !(y <= 8.2e+37)) {
		tmp = t * (1.0 - (x / y));
	} else {
		tmp = t * (x / (z - y));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if ((y <= (-8.2d+48)) .or. (.not. (y <= 8.2d+37))) then
        tmp = t * (1.0d0 - (x / y))
    else
        tmp = t * (x / (z - y))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if ((y <= -8.2e+48) || !(y <= 8.2e+37)) {
		tmp = t * (1.0 - (x / y));
	} else {
		tmp = t * (x / (z - y));
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (y <= -8.2e+48) or not (y <= 8.2e+37):
		tmp = t * (1.0 - (x / y))
	else:
		tmp = t * (x / (z - y))
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((y <= -8.2e+48) || !(y <= 8.2e+37))
		tmp = Float64(t * Float64(1.0 - Float64(x / y)));
	else
		tmp = Float64(t * Float64(x / Float64(z - y)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((y <= -8.2e+48) || ~((y <= 8.2e+37)))
		tmp = t * (1.0 - (x / y));
	else
		tmp = t * (x / (z - y));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[y, -8.2e+48], N[Not[LessEqual[y, 8.2e+37]], $MachinePrecision]], N[(t * N[(1.0 - N[(x / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(t * N[(x / N[(z - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -8.2000000000000005e48 or 8.1999999999999996e37 < y

   1. Initial program 99.9%

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

      1. div-sub 99.9%

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

   4. Applied egg-rr 99.9%

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

   5. Taylor expanded in z around 0 81.4%

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

      1. mul-1-neg 81.4%

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

      2. unsub-neg 81.4%

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

   7. Simplified 81.4%

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

   if -8.2000000000000005e48 < y < 8.1999999999999996e37

   1. Initial program 93.8%

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

   3. Taylor expanded in x around inf 77.7%

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

4. Final simplification 79.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -8.2 \cdot 10^{+48} \lor \neg \left(y \leq 8.2 \cdot 10^{+37}\right):\\ \;\;\;\;t \cdot \left(1 - \frac{x}{y}\right)\\ \mathbf{else}:\\ \;\;\;\;t \cdot \frac{x}{z - y}\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 68.7% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -2.75 \cdot 10^{+79}:\\ \;\;\;\;t\\ \mathbf{elif}\;y \leq 3.7 \cdot 10^{+38}:\\ \;\;\;\;x \cdot \frac{t}{z - y}\\ \mathbf{else}:\\ \;\;\;\;t\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= y -2.75e+79) t (if (<= y 3.7e+38) (* x (/ t (- z y))) t)))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (y <= -2.75e+79) {
		tmp = t;
	} else if (y <= 3.7e+38) {
		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 <= (-2.75d+79)) then
        tmp = t
    else if (y <= 3.7d+38) 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 <= -2.75e+79) {
		tmp = t;
	} else if (y <= 3.7e+38) {
		tmp = x * (t / (z - y));
	} else {
		tmp = t;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if y <= -2.75e+79:
		tmp = t
	elif y <= 3.7e+38:
		tmp = x * (t / (z - y))
	else:
		tmp = t
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (y <= -2.75e+79)
		tmp = t;
	elseif (y <= 3.7e+38)
		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 <= -2.75e+79)
		tmp = t;
	elseif (y <= 3.7e+38)
		tmp = x * (t / (z - y));
	else
		tmp = t;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[y, -2.75e+79], t, If[LessEqual[y, 3.7e+38], N[(x * N[(t / N[(z - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t]]

Derivation

1. Split input into 2 regimes

2. if y < -2.75000000000000003e79 or 3.7000000000000001e38 < y

   1. Initial program 99.8%

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

   3. Taylor expanded in y around inf 72.3%

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

   if -2.75000000000000003e79 < y < 3.7000000000000001e38

   1. Initial program 94.1%

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

   3. Taylor expanded in x around inf 78.2%

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

      1. *-commutative 78.2%

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

      2. associate-*r/ 76.4%

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

   5. Simplified 76.4%

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

4. Final simplification 75.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -2.75 \cdot 10^{+79}:\\ \;\;\;\;t\\ \mathbf{elif}\;y \leq 3.7 \cdot 10^{+38}:\\ \;\;\;\;x \cdot \frac{t}{z - y}\\ \mathbf{else}:\\ \;\;\;\;t\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 75.5% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -2.15 \cdot 10^{+49}:\\ \;\;\;\;t \cdot \left(1 - \frac{x}{y}\right)\\ \mathbf{elif}\;y \leq 3.2 \cdot 10^{+38}:\\ \;\;\;\;t \cdot \frac{x}{z - y}\\ \mathbf{else}:\\ \;\;\;\;\frac{t}{1 - \frac{z}{y}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= y -2.15e+49)
   (* t (- 1.0 (/ x y)))
   (if (<= y 3.2e+38) (* t (/ x (- z y))) (/ t (- 1.0 (/ z y))))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (y <= -2.15e+49) {
		tmp = t * (1.0 - (x / y));
	} else if (y <= 3.2e+38) {
		tmp = t * (x / (z - y));
	} else {
		tmp = t / (1.0 - (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 <= (-2.15d+49)) then
        tmp = t * (1.0d0 - (x / y))
    else if (y <= 3.2d+38) then
        tmp = t * (x / (z - y))
    else
        tmp = t / (1.0d0 - (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 <= -2.15e+49) {
		tmp = t * (1.0 - (x / y));
	} else if (y <= 3.2e+38) {
		tmp = t * (x / (z - y));
	} else {
		tmp = t / (1.0 - (z / y));
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if y <= -2.15e+49:
		tmp = t * (1.0 - (x / y))
	elif y <= 3.2e+38:
		tmp = t * (x / (z - y))
	else:
		tmp = t / (1.0 - (z / y))
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (y <= -2.15e+49)
		tmp = Float64(t * Float64(1.0 - Float64(x / y)));
	elseif (y <= 3.2e+38)
		tmp = Float64(t * Float64(x / Float64(z - y)));
	else
		tmp = Float64(t / Float64(1.0 - Float64(z / y)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (y <= -2.15e+49)
		tmp = t * (1.0 - (x / y));
	elseif (y <= 3.2e+38)
		tmp = t * (x / (z - y));
	else
		tmp = t / (1.0 - (z / y));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[y, -2.15e+49], N[(t * N[(1.0 - N[(x / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 3.2e+38], N[(t * N[(x / N[(z - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(t / N[(1.0 - N[(z / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if y < -2.15e49

   1. Initial program 99.9%

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

      1. div-sub 99.9%

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

   4. Applied egg-rr 99.9%

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

   5. Taylor expanded in z around 0 87.4%

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

      1. mul-1-neg 87.4%

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

      2. unsub-neg 87.4%

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

   7. Simplified 87.4%

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

   if -2.15e49 < y < 3.19999999999999985e38

   1. Initial program 93.8%

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

   3. Taylor expanded in x around inf 77.8%

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

   if 3.19999999999999985e38 < y

   1. Initial program 99.8%

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

   3. Taylor expanded in x around 0 64.1%

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

      1. mul-1-neg 64.1%

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

      2. associate-/l* 84.0%

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

      3. distribute-neg-frac 84.0%

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

      4. div-sub 84.0%

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

      5. *-inverses 84.0%

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

   5. Simplified 84.0%

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

      1. frac-2neg 84.0%

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

      2. div-inv 83.9%

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

      3. remove-double-neg 83.9%

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

      4. sub-neg 83.9%

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

      5. metadata-eval 83.9%

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

      6. distribute-neg-in 83.9%

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

      7. metadata-eval 83.9%

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

   7. Applied egg-rr 83.9%

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

      1. associate-*r/ 84.0%

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

      2. *-rgt-identity 84.0%

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

      3. +-commutative 84.0%

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

      4. unsub-neg 84.0%

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

   9. Simplified 84.0%

      \[\leadsto \color{blue}{\frac{t}{1 - \frac{z}{y}}} \]
3. Recombined 3 regimes into one program.

4. Final simplification 80.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -2.15 \cdot 10^{+49}:\\ \;\;\;\;t \cdot \left(1 - \frac{x}{y}\right)\\ \mathbf{elif}\;y \leq 3.2 \cdot 10^{+38}:\\ \;\;\;\;t \cdot \frac{x}{z - y}\\ \mathbf{else}:\\ \;\;\;\;\frac{t}{1 - \frac{z}{y}}\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 74.8% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -5.5 \cdot 10^{+46}:\\ \;\;\;\;t \cdot \left(1 - \frac{x}{y}\right)\\ \mathbf{elif}\;y \leq 3.9 \cdot 10^{+38}:\\ \;\;\;\;\frac{x \cdot t}{z - y}\\ \mathbf{else}:\\ \;\;\;\;\frac{t}{1 - \frac{z}{y}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= y -5.5e+46)
   (* t (- 1.0 (/ x y)))
   (if (<= y 3.9e+38) (/ (* x t) (- z y)) (/ t (- 1.0 (/ z y))))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (y <= -5.5e+46) {
		tmp = t * (1.0 - (x / y));
	} else if (y <= 3.9e+38) {
		tmp = (x * t) / (z - y);
	} else {
		tmp = t / (1.0 - (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 <= (-5.5d+46)) then
        tmp = t * (1.0d0 - (x / y))
    else if (y <= 3.9d+38) then
        tmp = (x * t) / (z - y)
    else
        tmp = t / (1.0d0 - (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 <= -5.5e+46) {
		tmp = t * (1.0 - (x / y));
	} else if (y <= 3.9e+38) {
		tmp = (x * t) / (z - y);
	} else {
		tmp = t / (1.0 - (z / y));
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if y <= -5.5e+46:
		tmp = t * (1.0 - (x / y))
	elif y <= 3.9e+38:
		tmp = (x * t) / (z - y)
	else:
		tmp = t / (1.0 - (z / y))
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (y <= -5.5e+46)
		tmp = Float64(t * Float64(1.0 - Float64(x / y)));
	elseif (y <= 3.9e+38)
		tmp = Float64(Float64(x * t) / Float64(z - y));
	else
		tmp = Float64(t / Float64(1.0 - Float64(z / y)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (y <= -5.5e+46)
		tmp = t * (1.0 - (x / y));
	elseif (y <= 3.9e+38)
		tmp = (x * t) / (z - y);
	else
		tmp = t / (1.0 - (z / y));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[y, -5.5e+46], N[(t * N[(1.0 - N[(x / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 3.9e+38], N[(N[(x * t), $MachinePrecision] / N[(z - y), $MachinePrecision]), $MachinePrecision], N[(t / N[(1.0 - N[(z / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if y < -5.4999999999999998e46

   1. Initial program 99.9%

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

      1. div-sub 99.9%

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

   4. Applied egg-rr 99.9%

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

   5. Taylor expanded in z around 0 87.4%

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

      1. mul-1-neg 87.4%

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

      2. unsub-neg 87.4%

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

   7. Simplified 87.4%

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

   if -5.4999999999999998e46 < y < 3.90000000000000023e38

   1. Initial program 93.8%

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

   3. Taylor expanded in x around inf 79.1%

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

   if 3.90000000000000023e38 < y

   1. Initial program 99.8%

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

   3. Taylor expanded in x around 0 64.1%

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

      1. mul-1-neg 64.1%

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

      2. associate-/l* 84.0%

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

      3. distribute-neg-frac 84.0%

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

      4. div-sub 84.0%

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

      5. *-inverses 84.0%

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

   5. Simplified 84.0%

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

      1. frac-2neg 84.0%

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

      2. div-inv 83.9%

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

      3. remove-double-neg 83.9%

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

      4. sub-neg 83.9%

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

      5. metadata-eval 83.9%

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

      6. distribute-neg-in 83.9%

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

      7. metadata-eval 83.9%

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

   7. Applied egg-rr 83.9%

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

      1. associate-*r/ 84.0%

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

      2. *-rgt-identity 84.0%

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

      3. +-commutative 84.0%

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

      4. unsub-neg 84.0%

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

   9. Simplified 84.0%

      \[\leadsto \color{blue}{\frac{t}{1 - \frac{z}{y}}} \]
3. Recombined 3 regimes into one program.

4. Final simplification 81.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -5.5 \cdot 10^{+46}:\\ \;\;\;\;t \cdot \left(1 - \frac{x}{y}\right)\\ \mathbf{elif}\;y \leq 3.9 \cdot 10^{+38}:\\ \;\;\;\;\frac{x \cdot t}{z - y}\\ \mathbf{else}:\\ \;\;\;\;\frac{t}{1 - \frac{z}{y}}\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 38.9% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -5.4 \cdot 10^{-118}:\\ \;\;\;\;t\\ \mathbf{elif}\;y \leq 6.5 \cdot 10^{-142}:\\ \;\;\;\;t \cdot \frac{y}{z}\\ \mathbf{else}:\\ \;\;\;\;t\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= y -5.4e-118) t (if (<= y 6.5e-142) (* t (/ y z)) t)))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (y <= -5.4e-118) {
		tmp = t;
	} else if (y <= 6.5e-142) {
		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 <= (-5.4d-118)) then
        tmp = t
    else if (y <= 6.5d-142) 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 <= -5.4e-118) {
		tmp = t;
	} else if (y <= 6.5e-142) {
		tmp = t * (y / z);
	} else {
		tmp = t;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if y <= -5.4e-118:
		tmp = t
	elif y <= 6.5e-142:
		tmp = t * (y / z)
	else:
		tmp = t
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (y <= -5.4e-118)
		tmp = t;
	elseif (y <= 6.5e-142)
		tmp = Float64(t * Float64(y / z));
	else
		tmp = t;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (y <= -5.4e-118)
		tmp = t;
	elseif (y <= 6.5e-142)
		tmp = t * (y / z);
	else
		tmp = t;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[y, -5.4e-118], t, If[LessEqual[y, 6.5e-142], N[(t * N[(y / z), $MachinePrecision]), $MachinePrecision], t]]

Derivation

1. Split input into 2 regimes

2. if y < -5.39999999999999988e-118 or 6.50000000000000027e-142 < y

   1. Initial program 98.1%

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

   3. Taylor expanded in y around inf 46.8%

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

   if -5.39999999999999988e-118 < y < 6.50000000000000027e-142

   1. Initial program 92.1%

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

   3. Taylor expanded in z around inf 85.2%

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

   4. Taylor expanded in x around 0 29.6%

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

      1. associate-*r/ 29.6%

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

      2. associate-*r* 29.6%

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

      3. neg-mul-1 29.6%

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

   6. Simplified 29.6%

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

      1. expm1-log1p-u 27.1%

         \[\leadsto \color{blue}{\mathsf{expm1}\left(\mathsf{log1p}\left(\frac{\left(-t\right) \cdot y}{z}\right)\right)} \]

      2. expm1-udef 24.8%

         \[\leadsto \color{blue}{e^{\mathsf{log1p}\left(\frac{\left(-t\right) \cdot y}{z}\right)} - 1} \]

      3. associate-/l* 24.8%

         \[\leadsto e^{\mathsf{log1p}\left(\color{blue}{\frac{-t}{\frac{z}{y}}}\right)} - 1 \]

      4. add-sqr-sqrt 13.5%

         \[\leadsto e^{\mathsf{log1p}\left(\frac{\color{blue}{\sqrt{-t} \cdot \sqrt{-t}}}{\frac{z}{y}}\right)} - 1 \]

      5. sqrt-unprod 24.7%

         \[\leadsto e^{\mathsf{log1p}\left(\frac{\color{blue}{\sqrt{\left(-t\right) \cdot \left(-t\right)}}}{\frac{z}{y}}\right)} - 1 \]

      6. sqr-neg 24.7%

         \[\leadsto e^{\mathsf{log1p}\left(\frac{\sqrt{\color{blue}{t \cdot t}}}{\frac{z}{y}}\right)} - 1 \]

      7. sqrt-unprod 11.3%

         \[\leadsto e^{\mathsf{log1p}\left(\frac{\color{blue}{\sqrt{t} \cdot \sqrt{t}}}{\frac{z}{y}}\right)} - 1 \]

      8. add-sqr-sqrt 24.8%

         \[\leadsto e^{\mathsf{log1p}\left(\frac{\color{blue}{t}}{\frac{z}{y}}\right)} - 1 \]

   8. Applied egg-rr 24.8%

      \[\leadsto \color{blue}{e^{\mathsf{log1p}\left(\frac{t}{\frac{z}{y}}\right)} - 1} \]
   9. Step-by-step derivation

      1. expm1-def 24.8%

         \[\leadsto \color{blue}{\mathsf{expm1}\left(\mathsf{log1p}\left(\frac{t}{\frac{z}{y}}\right)\right)} \]

      2. expm1-log1p 25.0%

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

      3. associate-/l* 25.0%

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

      4. associate-*r/ 25.0%

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

   10. Simplified 25.0%

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

4. Final simplification 39.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -5.4 \cdot 10^{-118}:\\ \;\;\;\;t\\ \mathbf{elif}\;y \leq 6.5 \cdot 10^{-142}:\\ \;\;\;\;t \cdot \frac{y}{z}\\ \mathbf{else}:\\ \;\;\;\;t\\ \end{array} \]
5. Add Preprocessing

Alternative 10: 60.2% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -2 \cdot 10^{+47}:\\ \;\;\;\;t\\ \mathbf{elif}\;y \leq 2.55 \cdot 10^{+38}:\\ \;\;\;\;x \cdot \frac{t}{z}\\ \mathbf{else}:\\ \;\;\;\;t\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= y -2e+47) t (if (<= y 2.55e+38) (* x (/ t z)) t)))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (y <= -2e+47) {
		tmp = t;
	} else if (y <= 2.55e+38) {
		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 <= (-2d+47)) then
        tmp = t
    else if (y <= 2.55d+38) 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 <= -2e+47) {
		tmp = t;
	} else if (y <= 2.55e+38) {
		tmp = x * (t / z);
	} else {
		tmp = t;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if y <= -2e+47:
		tmp = t
	elif y <= 2.55e+38:
		tmp = x * (t / z)
	else:
		tmp = t
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (y <= -2e+47)
		tmp = t;
	elseif (y <= 2.55e+38)
		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 <= -2e+47)
		tmp = t;
	elseif (y <= 2.55e+38)
		tmp = x * (t / z);
	else
		tmp = t;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[y, -2e+47], t, If[LessEqual[y, 2.55e+38], N[(x * N[(t / z), $MachinePrecision]), $MachinePrecision], t]]

Derivation

1. Split input into 2 regimes

2. if y < -2.0000000000000001e47 or 2.5500000000000001e38 < y

   1. Initial program 99.8%

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

   3. Taylor expanded in y around inf 69.9%

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

   if -2.0000000000000001e47 < y < 2.5500000000000001e38

   1. Initial program 93.8%

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

   3. Taylor expanded in y around 0 66.7%

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

      1. associate-/l* 67.7%

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

      2. associate-/r/ 65.1%

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

   5. Simplified 65.1%

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

4. Final simplification 66.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -2 \cdot 10^{+47}:\\ \;\;\;\;t\\ \mathbf{elif}\;y \leq 2.55 \cdot 10^{+38}:\\ \;\;\;\;x \cdot \frac{t}{z}\\ \mathbf{else}:\\ \;\;\;\;t\\ \end{array} \]
5. Add Preprocessing

Alternative 11: 61.5% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -2.3 \cdot 10^{+48}:\\ \;\;\;\;t\\ \mathbf{elif}\;y \leq 1.95 \cdot 10^{+38}:\\ \;\;\;\;t \cdot \frac{x}{z}\\ \mathbf{else}:\\ \;\;\;\;t\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= y -2.3e+48) t (if (<= y 1.95e+38) (* t (/ x z)) t)))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (y <= -2.3e+48) {
		tmp = t;
	} else if (y <= 1.95e+38) {
		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 <= (-2.3d+48)) then
        tmp = t
    else if (y <= 1.95d+38) 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 <= -2.3e+48) {
		tmp = t;
	} else if (y <= 1.95e+38) {
		tmp = t * (x / z);
	} else {
		tmp = t;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if y <= -2.3e+48:
		tmp = t
	elif y <= 1.95e+38:
		tmp = t * (x / z)
	else:
		tmp = t
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (y <= -2.3e+48)
		tmp = t;
	elseif (y <= 1.95e+38)
		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 <= -2.3e+48)
		tmp = t;
	elseif (y <= 1.95e+38)
		tmp = t * (x / z);
	else
		tmp = t;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[y, -2.3e+48], t, If[LessEqual[y, 1.95e+38], N[(t * N[(x / z), $MachinePrecision]), $MachinePrecision], t]]

Derivation

1. Split input into 2 regimes

2. if y < -2.3e48 or 1.95000000000000012e38 < y

   1. Initial program 99.8%

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

   3. Taylor expanded in y around inf 69.9%

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

   if -2.3e48 < y < 1.95000000000000012e38

   1. Initial program 93.8%

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

   3. Taylor expanded in y around 0 68.2%

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

4. Final simplification 68.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -2.3 \cdot 10^{+48}:\\ \;\;\;\;t\\ \mathbf{elif}\;y \leq 1.95 \cdot 10^{+38}:\\ \;\;\;\;t \cdot \frac{x}{z}\\ \mathbf{else}:\\ \;\;\;\;t\\ \end{array} \]
5. Add Preprocessing

Alternative 12: 35.1% accurate, 9.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 96.0%

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

3. Taylor expanded in y around inf 31.9%

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

4. Final simplification 31.9%

   \[\leadsto t \]
5. Add Preprocessing

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 2024021 
(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))