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

Percentage Accurate: 97.4% → 97.4%

Time: 7.6s

Alternatives: 12

Speedup: 1.0×

• 25.1% of points produce a very large (infinite) output. You may want to add a precondition.

Specification

Math

\[\begin{array}{l} \\ \frac{x}{y} \cdot \left(z - t\right) + t \end{array} \]

FPCore

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

C

double code(double x, double y, double z, double t) {
	return ((x / y) * (z - t)) + 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 - t)) + t
end function

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Initial Program: 97.4% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \frac{x}{y} \cdot \left(z - t\right) + t \end{array} \]

FPCore

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

C

double code(double x, double y, double z, double t) {
	return ((x / y) * (z - t)) + 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 - t)) + t
end function

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Alternative 1: 97.4% accurate, 0.1× speedup

Math

\[\begin{array}{l} \\ \mathsf{fma}\left(\frac{x}{y}, z - t, t\right) \end{array} \]

FPCore

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

C

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

Julia

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

Wolfram

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

Derivation

1. Initial program 97.9%

   \[\frac{x}{y} \cdot \left(z - t\right) + t \]
2. Step-by-step derivation

   1. fma-def 97.9%

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

3. Simplified 97.9%

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

4. Final simplification 97.9%

   \[\leadsto \mathsf{fma}\left(\frac{x}{y}, z - t, t\right) \]

Alternative 2: 94.9% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;\frac{x}{y} \leq -500:\\ \;\;\;\;\frac{x \cdot \left(z - t\right)}{y}\\ \mathbf{elif}\;\frac{x}{y} \leq 4 \cdot 10^{-26}:\\ \;\;\;\;t + \frac{x}{y} \cdot z\\ \mathbf{else}:\\ \;\;\;\;t + x \cdot \frac{z - t}{y}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= (/ x y) -500.0)
   (/ (* x (- z t)) y)
   (if (<= (/ x y) 4e-26) (+ t (* (/ x y) z)) (+ t (* x (/ (- z t) y))))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((x / y) <= -500.0) {
		tmp = (x * (z - t)) / y;
	} else if ((x / y) <= 4e-26) {
		tmp = t + ((x / y) * z);
	} else {
		tmp = t + (x * ((z - t) / 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) <= (-500.0d0)) then
        tmp = (x * (z - t)) / y
    else if ((x / y) <= 4d-26) then
        tmp = t + ((x / y) * z)
    else
        tmp = t + (x * ((z - t) / 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) <= -500.0) {
		tmp = (x * (z - t)) / y;
	} else if ((x / y) <= 4e-26) {
		tmp = t + ((x / y) * z);
	} else {
		tmp = t + (x * ((z - t) / y));
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (x / y) <= -500.0:
		tmp = (x * (z - t)) / y
	elif (x / y) <= 4e-26:
		tmp = t + ((x / y) * z)
	else:
		tmp = t + (x * ((z - t) / y))
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (Float64(x / y) <= -500.0)
		tmp = Float64(Float64(x * Float64(z - t)) / y);
	elseif (Float64(x / y) <= 4e-26)
		tmp = Float64(t + Float64(Float64(x / y) * z));
	else
		tmp = Float64(t + Float64(x * Float64(Float64(z - t) / y)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((x / y) <= -500.0)
		tmp = (x * (z - t)) / y;
	elseif ((x / y) <= 4e-26)
		tmp = t + ((x / y) * z);
	else
		tmp = t + (x * ((z - t) / y));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[N[(x / y), $MachinePrecision], -500.0], N[(N[(x * N[(z - t), $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision], If[LessEqual[N[(x / y), $MachinePrecision], 4e-26], N[(t + N[(N[(x / y), $MachinePrecision] * z), $MachinePrecision]), $MachinePrecision], N[(t + N[(x * N[(N[(z - t), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if (/.f64 x y) < -500

   1. Initial program 94.0%

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

   2. Taylor expanded in x around 0 97.9%

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

   3. Taylor expanded in x around -inf 94.8%

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

   if -500 < (/.f64 x y) < 4.0000000000000002e-26

   1. Initial program 99.0%

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

   2. Taylor expanded in z around inf 95.1%

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

      1. associate-*r/ 99.0%

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

   4. Simplified 99.0%

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

   if 4.0000000000000002e-26 < (/.f64 x y)

   1. Initial program 98.4%

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

   2. Taylor expanded in x around 0 89.9%

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

      1. associate-*l/ 93.6%

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

      2. *-commutative 93.6%

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

   4. Simplified 93.6%

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

4. Final simplification 96.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{x}{y} \leq -500:\\ \;\;\;\;\frac{x \cdot \left(z - t\right)}{y}\\ \mathbf{elif}\;\frac{x}{y} \leq 4 \cdot 10^{-26}:\\ \;\;\;\;t + \frac{x}{y} \cdot z\\ \mathbf{else}:\\ \;\;\;\;t + x \cdot \frac{z - t}{y}\\ \end{array} \]

Alternative 3: 51.4% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{t}{\frac{y}{-x}}\\ \mathbf{if}\;y \leq -9.5 \cdot 10^{-44}:\\ \;\;\;\;t\\ \mathbf{elif}\;y \leq -5.4 \cdot 10^{-238}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq 2.25 \cdot 10^{-307}:\\ \;\;\;\;x \cdot \frac{z}{y}\\ \mathbf{elif}\;y \leq 8.8 \cdot 10^{-277}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq 2.1 \cdot 10^{-76}:\\ \;\;\;\;\frac{x \cdot z}{y}\\ \mathbf{else}:\\ \;\;\;\;t\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (/ t (/ y (- x)))))
   (if (<= y -9.5e-44)
     t
     (if (<= y -5.4e-238)
       t_1
       (if (<= y 2.25e-307)
         (* x (/ z y))
         (if (<= y 8.8e-277) t_1 (if (<= y 2.1e-76) (/ (* x z) y) t)))))))

C

double code(double x, double y, double z, double t) {
	double t_1 = t / (y / -x);
	double tmp;
	if (y <= -9.5e-44) {
		tmp = t;
	} else if (y <= -5.4e-238) {
		tmp = t_1;
	} else if (y <= 2.25e-307) {
		tmp = x * (z / y);
	} else if (y <= 8.8e-277) {
		tmp = t_1;
	} else if (y <= 2.1e-76) {
		tmp = (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) :: t_1
    real(8) :: tmp
    t_1 = t / (y / -x)
    if (y <= (-9.5d-44)) then
        tmp = t
    else if (y <= (-5.4d-238)) then
        tmp = t_1
    else if (y <= 2.25d-307) then
        tmp = x * (z / y)
    else if (y <= 8.8d-277) then
        tmp = t_1
    else if (y <= 2.1d-76) then
        tmp = (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 t_1 = t / (y / -x);
	double tmp;
	if (y <= -9.5e-44) {
		tmp = t;
	} else if (y <= -5.4e-238) {
		tmp = t_1;
	} else if (y <= 2.25e-307) {
		tmp = x * (z / y);
	} else if (y <= 8.8e-277) {
		tmp = t_1;
	} else if (y <= 2.1e-76) {
		tmp = (x * z) / y;
	} else {
		tmp = t;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = t / (y / -x)
	tmp = 0
	if y <= -9.5e-44:
		tmp = t
	elif y <= -5.4e-238:
		tmp = t_1
	elif y <= 2.25e-307:
		tmp = x * (z / y)
	elif y <= 8.8e-277:
		tmp = t_1
	elif y <= 2.1e-76:
		tmp = (x * z) / y
	else:
		tmp = t
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(t / Float64(y / Float64(-x)))
	tmp = 0.0
	if (y <= -9.5e-44)
		tmp = t;
	elseif (y <= -5.4e-238)
		tmp = t_1;
	elseif (y <= 2.25e-307)
		tmp = Float64(x * Float64(z / y));
	elseif (y <= 8.8e-277)
		tmp = t_1;
	elseif (y <= 2.1e-76)
		tmp = Float64(Float64(x * z) / y);
	else
		tmp = t;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = t / (y / -x);
	tmp = 0.0;
	if (y <= -9.5e-44)
		tmp = t;
	elseif (y <= -5.4e-238)
		tmp = t_1;
	elseif (y <= 2.25e-307)
		tmp = x * (z / y);
	elseif (y <= 8.8e-277)
		tmp = t_1;
	elseif (y <= 2.1e-76)
		tmp = (x * z) / y;
	else
		tmp = t;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(t / N[(y / (-x)), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -9.5e-44], t, If[LessEqual[y, -5.4e-238], t$95$1, If[LessEqual[y, 2.25e-307], N[(x * N[(z / y), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 8.8e-277], t$95$1, If[LessEqual[y, 2.1e-76], N[(N[(x * z), $MachinePrecision] / y), $MachinePrecision], t]]]]]]

Derivation

1. Split input into 4 regimes

2. if y < -9.49999999999999924e-44 or 2.09999999999999992e-76 < y

   1. Initial program 99.2%

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

   2. Taylor expanded in x around 0 63.8%

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

   if -9.49999999999999924e-44 < y < -5.39999999999999981e-238 or 2.24999999999999994e-307 < y < 8.79999999999999983e-277

   1. Initial program 97.3%

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

   2. Taylor expanded in x around 0 99.9%

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

   3. Taylor expanded in x around -inf 90.6%

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

   4. Taylor expanded in z around 0 71.3%

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

      1. mul-1-neg 71.3%

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

      2. distribute-frac-neg 71.3%

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

      3. distribute-rgt-neg-in 71.3%

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

      4. associate-/l* 70.3%

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

   6. Simplified 70.3%

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

   if -5.39999999999999981e-238 < y < 2.24999999999999994e-307

   1. Initial program 87.5%

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

   2. Taylor expanded in x around 0 87.1%

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

   3. Taylor expanded in x around -inf 86.7%

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

   4. Taylor expanded in z around inf 68.6%

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

      1. *-commutative 68.6%

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

      2. associate-*r/ 81.6%

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

   6. Simplified 81.6%

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

   if 8.79999999999999983e-277 < y < 2.09999999999999992e-76

   1. Initial program 97.1%

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

   2. Taylor expanded in x around 0 99.4%

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

   3. Taylor expanded in x around -inf 92.5%

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

   4. Taylor expanded in z around inf 66.0%

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

4. Final simplification 66.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -9.5 \cdot 10^{-44}:\\ \;\;\;\;t\\ \mathbf{elif}\;y \leq -5.4 \cdot 10^{-238}:\\ \;\;\;\;\frac{t}{\frac{y}{-x}}\\ \mathbf{elif}\;y \leq 2.25 \cdot 10^{-307}:\\ \;\;\;\;x \cdot \frac{z}{y}\\ \mathbf{elif}\;y \leq 8.8 \cdot 10^{-277}:\\ \;\;\;\;\frac{t}{\frac{y}{-x}}\\ \mathbf{elif}\;y \leq 2.1 \cdot 10^{-76}:\\ \;\;\;\;\frac{x \cdot z}{y}\\ \mathbf{else}:\\ \;\;\;\;t\\ \end{array} \]

Alternative 4: 51.2% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -1.96 \cdot 10^{-44}:\\ \;\;\;\;t\\ \mathbf{elif}\;y \leq -2.25 \cdot 10^{-238}:\\ \;\;\;\;\frac{x \cdot \left(-t\right)}{y}\\ \mathbf{elif}\;y \leq 2.2 \cdot 10^{-307}:\\ \;\;\;\;x \cdot \frac{z}{y}\\ \mathbf{elif}\;y \leq 3.4 \cdot 10^{-277}:\\ \;\;\;\;\frac{t}{\frac{y}{-x}}\\ \mathbf{elif}\;y \leq 7.6 \cdot 10^{-78}:\\ \;\;\;\;\frac{x \cdot z}{y}\\ \mathbf{else}:\\ \;\;\;\;t\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= y -1.96e-44)
   t
   (if (<= y -2.25e-238)
     (/ (* x (- t)) y)
     (if (<= y 2.2e-307)
       (* x (/ z y))
       (if (<= y 3.4e-277)
         (/ t (/ y (- x)))
         (if (<= y 7.6e-78) (/ (* x z) y) t))))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (y <= -1.96e-44) {
		tmp = t;
	} else if (y <= -2.25e-238) {
		tmp = (x * -t) / y;
	} else if (y <= 2.2e-307) {
		tmp = x * (z / y);
	} else if (y <= 3.4e-277) {
		tmp = t / (y / -x);
	} else if (y <= 7.6e-78) {
		tmp = (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 <= (-1.96d-44)) then
        tmp = t
    else if (y <= (-2.25d-238)) then
        tmp = (x * -t) / y
    else if (y <= 2.2d-307) then
        tmp = x * (z / y)
    else if (y <= 3.4d-277) then
        tmp = t / (y / -x)
    else if (y <= 7.6d-78) then
        tmp = (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 <= -1.96e-44) {
		tmp = t;
	} else if (y <= -2.25e-238) {
		tmp = (x * -t) / y;
	} else if (y <= 2.2e-307) {
		tmp = x * (z / y);
	} else if (y <= 3.4e-277) {
		tmp = t / (y / -x);
	} else if (y <= 7.6e-78) {
		tmp = (x * z) / y;
	} else {
		tmp = t;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if y <= -1.96e-44:
		tmp = t
	elif y <= -2.25e-238:
		tmp = (x * -t) / y
	elif y <= 2.2e-307:
		tmp = x * (z / y)
	elif y <= 3.4e-277:
		tmp = t / (y / -x)
	elif y <= 7.6e-78:
		tmp = (x * z) / y
	else:
		tmp = t
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (y <= -1.96e-44)
		tmp = t;
	elseif (y <= -2.25e-238)
		tmp = Float64(Float64(x * Float64(-t)) / y);
	elseif (y <= 2.2e-307)
		tmp = Float64(x * Float64(z / y));
	elseif (y <= 3.4e-277)
		tmp = Float64(t / Float64(y / Float64(-x)));
	elseif (y <= 7.6e-78)
		tmp = Float64(Float64(x * z) / y);
	else
		tmp = t;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (y <= -1.96e-44)
		tmp = t;
	elseif (y <= -2.25e-238)
		tmp = (x * -t) / y;
	elseif (y <= 2.2e-307)
		tmp = x * (z / y);
	elseif (y <= 3.4e-277)
		tmp = t / (y / -x);
	elseif (y <= 7.6e-78)
		tmp = (x * z) / y;
	else
		tmp = t;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[y, -1.96e-44], t, If[LessEqual[y, -2.25e-238], N[(N[(x * (-t)), $MachinePrecision] / y), $MachinePrecision], If[LessEqual[y, 2.2e-307], N[(x * N[(z / y), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 3.4e-277], N[(t / N[(y / (-x)), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 7.6e-78], N[(N[(x * z), $MachinePrecision] / y), $MachinePrecision], t]]]]]

Derivation

1. Split input into 5 regimes

2. if y < -1.9599999999999999e-44 or 7.5999999999999998e-78 < y

   1. Initial program 99.2%

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

   2. Taylor expanded in x around 0 63.8%

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

   if -1.9599999999999999e-44 < y < -2.24999999999999998e-238

   1. Initial program 96.7%

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

   2. Taylor expanded in x around 0 99.8%

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

   3. Taylor expanded in x around -inf 90.7%

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

   4. Taylor expanded in z around 0 70.5%

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

      1. neg-mul-1 70.5%

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

      2. distribute-lft-neg-in 70.5%

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

      3. *-commutative 70.5%

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

   6. Simplified 70.5%

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

   if -2.24999999999999998e-238 < y < 2.2e-307

   1. Initial program 87.5%

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

   2. Taylor expanded in x around 0 87.1%

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

   3. Taylor expanded in x around -inf 86.7%

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

   4. Taylor expanded in z around inf 68.6%

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

      1. *-commutative 68.6%

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

      2. associate-*r/ 81.6%

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

   6. Simplified 81.6%

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

   if 2.2e-307 < y < 3.39999999999999982e-277

   1. Initial program 99.8%

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

   2. Taylor expanded in x around 0 100.0%

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

   3. Taylor expanded in x around -inf 90.4%

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

   4. Taylor expanded in z around 0 74.8%

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

      1. mul-1-neg 74.8%

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

      2. distribute-frac-neg 74.8%

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

      3. distribute-rgt-neg-in 74.8%

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

      4. associate-/l* 74.8%

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

   6. Simplified 74.8%

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

   if 3.39999999999999982e-277 < y < 7.5999999999999998e-78

   1. Initial program 97.1%

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

   2. Taylor expanded in x around 0 99.4%

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

   3. Taylor expanded in x around -inf 92.5%

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

   4. Taylor expanded in z around inf 66.0%

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

4. Final simplification 66.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.96 \cdot 10^{-44}:\\ \;\;\;\;t\\ \mathbf{elif}\;y \leq -2.25 \cdot 10^{-238}:\\ \;\;\;\;\frac{x \cdot \left(-t\right)}{y}\\ \mathbf{elif}\;y \leq 2.2 \cdot 10^{-307}:\\ \;\;\;\;x \cdot \frac{z}{y}\\ \mathbf{elif}\;y \leq 3.4 \cdot 10^{-277}:\\ \;\;\;\;\frac{t}{\frac{y}{-x}}\\ \mathbf{elif}\;y \leq 7.6 \cdot 10^{-78}:\\ \;\;\;\;\frac{x \cdot z}{y}\\ \mathbf{else}:\\ \;\;\;\;t\\ \end{array} \]

Alternative 5: 73.1% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{x \cdot z}{y}\\ t_2 := t \cdot \left(1 - \frac{x}{y}\right)\\ \mathbf{if}\;t \leq -1.75 \cdot 10^{-116}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;t \leq -5 \cdot 10^{-149}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t \leq -6.5 \cdot 10^{-179}:\\ \;\;\;\;t\\ \mathbf{elif}\;t \leq 5 \cdot 10^{-148}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (/ (* x z) y)) (t_2 (* t (- 1.0 (/ x y)))))
   (if (<= t -1.75e-116)
     t_2
     (if (<= t -5e-149)
       t_1
       (if (<= t -6.5e-179) t (if (<= t 5e-148) t_1 t_2))))))

C

double code(double x, double y, double z, double t) {
	double t_1 = (x * z) / y;
	double t_2 = t * (1.0 - (x / y));
	double tmp;
	if (t <= -1.75e-116) {
		tmp = t_2;
	} else if (t <= -5e-149) {
		tmp = t_1;
	} else if (t <= -6.5e-179) {
		tmp = t;
	} else if (t <= 5e-148) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = (x * z) / y
    t_2 = t * (1.0d0 - (x / y))
    if (t <= (-1.75d-116)) then
        tmp = t_2
    else if (t <= (-5d-149)) then
        tmp = t_1
    else if (t <= (-6.5d-179)) then
        tmp = t
    else if (t <= 5d-148) then
        tmp = t_1
    else
        tmp = t_2
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double t_1 = (x * z) / y;
	double t_2 = t * (1.0 - (x / y));
	double tmp;
	if (t <= -1.75e-116) {
		tmp = t_2;
	} else if (t <= -5e-149) {
		tmp = t_1;
	} else if (t <= -6.5e-179) {
		tmp = t;
	} else if (t <= 5e-148) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = (x * z) / y
	t_2 = t * (1.0 - (x / y))
	tmp = 0
	if t <= -1.75e-116:
		tmp = t_2
	elif t <= -5e-149:
		tmp = t_1
	elif t <= -6.5e-179:
		tmp = t
	elif t <= 5e-148:
		tmp = t_1
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(Float64(x * z) / y)
	t_2 = Float64(t * Float64(1.0 - Float64(x / y)))
	tmp = 0.0
	if (t <= -1.75e-116)
		tmp = t_2;
	elseif (t <= -5e-149)
		tmp = t_1;
	elseif (t <= -6.5e-179)
		tmp = t;
	elseif (t <= 5e-148)
		tmp = t_1;
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = (x * z) / y;
	t_2 = t * (1.0 - (x / y));
	tmp = 0.0;
	if (t <= -1.75e-116)
		tmp = t_2;
	elseif (t <= -5e-149)
		tmp = t_1;
	elseif (t <= -6.5e-179)
		tmp = t;
	elseif (t <= 5e-148)
		tmp = t_1;
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(N[(x * z), $MachinePrecision] / y), $MachinePrecision]}, Block[{t$95$2 = N[(t * N[(1.0 - N[(x / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t, -1.75e-116], t$95$2, If[LessEqual[t, -5e-149], t$95$1, If[LessEqual[t, -6.5e-179], t, If[LessEqual[t, 5e-148], t$95$1, t$95$2]]]]]]

Derivation

1. Split input into 3 regimes

2. if t < -1.74999999999999992e-116 or 4.9999999999999999e-148 < t

   1. Initial program 99.9%

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

   2. Taylor expanded in z around 0 80.3%

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

      1. mul-1-neg 80.3%

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

      2. unsub-neg 80.3%

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

      3. associate-/l* 84.5%

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

      4. associate-/r/ 80.5%

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

   4. Simplified 80.5%

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

   5. Taylor expanded in t around 0 84.5%

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

   if -1.74999999999999992e-116 < t < -4.99999999999999968e-149 or -6.49999999999999996e-179 < t < 4.9999999999999999e-148

   1. Initial program 92.8%

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

   2. Taylor expanded in x around 0 94.1%

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

   3. Taylor expanded in x around -inf 72.7%

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

   4. Taylor expanded in z around inf 64.8%

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

   if -4.99999999999999968e-149 < t < -6.49999999999999996e-179

   1. Initial program 100.0%

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

   2. Taylor expanded in x around 0 86.9%

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

4. Final simplification 79.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -1.75 \cdot 10^{-116}:\\ \;\;\;\;t \cdot \left(1 - \frac{x}{y}\right)\\ \mathbf{elif}\;t \leq -5 \cdot 10^{-149}:\\ \;\;\;\;\frac{x \cdot z}{y}\\ \mathbf{elif}\;t \leq -6.5 \cdot 10^{-179}:\\ \;\;\;\;t\\ \mathbf{elif}\;t \leq 5 \cdot 10^{-148}:\\ \;\;\;\;\frac{x \cdot z}{y}\\ \mathbf{else}:\\ \;\;\;\;t \cdot \left(1 - \frac{x}{y}\right)\\ \end{array} \]

Alternative 6: 93.9% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;\frac{x}{y} \leq -500 \lor \neg \left(\frac{x}{y} \leq 4 \cdot 10^{-26}\right):\\ \;\;\;\;\frac{x \cdot \left(z - t\right)}{y}\\ \mathbf{else}:\\ \;\;\;\;t + \frac{x}{y} \cdot z\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= (/ x y) -500.0) (not (<= (/ x y) 4e-26)))
   (/ (* x (- z t)) y)
   (+ t (* (/ x y) z))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (((x / y) <= -500.0) || !((x / y) <= 4e-26)) {
		tmp = (x * (z - t)) / y;
	} else {
		tmp = t + ((x / y) * z);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if (((x / y) <= (-500.0d0)) .or. (.not. ((x / y) <= 4d-26))) then
        tmp = (x * (z - t)) / y
    else
        tmp = t + ((x / y) * z)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if (((x / y) <= -500.0) || !((x / y) <= 4e-26)) {
		tmp = (x * (z - t)) / y;
	} else {
		tmp = t + ((x / y) * z);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if ((x / y) <= -500.0) or not ((x / y) <= 4e-26):
		tmp = (x * (z - t)) / y
	else:
		tmp = t + ((x / y) * z)
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((Float64(x / y) <= -500.0) || !(Float64(x / y) <= 4e-26))
		tmp = Float64(Float64(x * Float64(z - t)) / y);
	else
		tmp = Float64(t + Float64(Float64(x / y) * z));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (((x / y) <= -500.0) || ~(((x / y) <= 4e-26)))
		tmp = (x * (z - t)) / y;
	else
		tmp = t + ((x / y) * z);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[N[(x / y), $MachinePrecision], -500.0], N[Not[LessEqual[N[(x / y), $MachinePrecision], 4e-26]], $MachinePrecision]], N[(N[(x * N[(z - t), $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision], N[(t + N[(N[(x / y), $MachinePrecision] * z), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if (/.f64 x y) < -500 or 4.0000000000000002e-26 < (/.f64 x y)

   1. Initial program 96.5%

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

   2. Taylor expanded in x around 0 93.2%

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

   3. Taylor expanded in x around -inf 91.1%

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

   if -500 < (/.f64 x y) < 4.0000000000000002e-26

   1. Initial program 99.0%

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

   2. Taylor expanded in z around inf 95.1%

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

      1. associate-*r/ 99.0%

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

   4. Simplified 99.0%

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

4. Final simplification 95.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{x}{y} \leq -500 \lor \neg \left(\frac{x}{y} \leq 4 \cdot 10^{-26}\right):\\ \;\;\;\;\frac{x \cdot \left(z - t\right)}{y}\\ \mathbf{else}:\\ \;\;\;\;t + \frac{x}{y} \cdot z\\ \end{array} \]

Alternative 7: 51.6% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -1.95 \cdot 10^{-42}:\\ \;\;\;\;t\\ \mathbf{elif}\;y \leq -4.1 \cdot 10^{-227}:\\ \;\;\;\;\left(-x\right) \cdot \frac{t}{y}\\ \mathbf{elif}\;y \leq 1.85 \cdot 10^{-76}:\\ \;\;\;\;\frac{x \cdot z}{y}\\ \mathbf{else}:\\ \;\;\;\;t\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= y -1.95e-42)
   t
   (if (<= y -4.1e-227)
     (* (- x) (/ t y))
     (if (<= y 1.85e-76) (/ (* x z) y) t))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (y <= -1.95e-42) {
		tmp = t;
	} else if (y <= -4.1e-227) {
		tmp = -x * (t / y);
	} else if (y <= 1.85e-76) {
		tmp = (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 <= (-1.95d-42)) then
        tmp = t
    else if (y <= (-4.1d-227)) then
        tmp = -x * (t / y)
    else if (y <= 1.85d-76) then
        tmp = (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 <= -1.95e-42) {
		tmp = t;
	} else if (y <= -4.1e-227) {
		tmp = -x * (t / y);
	} else if (y <= 1.85e-76) {
		tmp = (x * z) / y;
	} else {
		tmp = t;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if y <= -1.95e-42:
		tmp = t
	elif y <= -4.1e-227:
		tmp = -x * (t / y)
	elif y <= 1.85e-76:
		tmp = (x * z) / y
	else:
		tmp = t
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (y <= -1.95e-42)
		tmp = t;
	elseif (y <= -4.1e-227)
		tmp = Float64(Float64(-x) * Float64(t / y));
	elseif (y <= 1.85e-76)
		tmp = Float64(Float64(x * z) / y);
	else
		tmp = t;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (y <= -1.95e-42)
		tmp = t;
	elseif (y <= -4.1e-227)
		tmp = -x * (t / y);
	elseif (y <= 1.85e-76)
		tmp = (x * z) / y;
	else
		tmp = t;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[y, -1.95e-42], t, If[LessEqual[y, -4.1e-227], N[((-x) * N[(t / y), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 1.85e-76], N[(N[(x * z), $MachinePrecision] / y), $MachinePrecision], t]]]

Derivation

1. Split input into 3 regimes

2. if y < -1.9500000000000001e-42 or 1.85000000000000006e-76 < y

   1. Initial program 99.2%

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

   2. Taylor expanded in x around 0 63.8%

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

   if -1.9500000000000001e-42 < y < -4.10000000000000009e-227

   1. Initial program 96.0%

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

   2. Taylor expanded in x around 0 99.9%

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

   3. Taylor expanded in x around -inf 88.9%

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

   4. Taylor expanded in z around 0 72.7%

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

      1. associate-/l* 71.1%

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

      2. neg-mul-1 71.1%

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

      3. distribute-neg-frac 71.1%

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

      4. associate-/r/ 70.3%

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

      5. *-commutative 70.3%

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

      6. distribute-frac-neg 70.3%

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

   6. Simplified 70.3%

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

   if -4.10000000000000009e-227 < y < 1.85000000000000006e-76

   1. Initial program 95.4%

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

   2. Taylor expanded in x around 0 96.6%

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

   3. Taylor expanded in x around -inf 91.4%

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

   4. Taylor expanded in z around inf 59.5%

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

4. Final simplification 63.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.95 \cdot 10^{-42}:\\ \;\;\;\;t\\ \mathbf{elif}\;y \leq -4.1 \cdot 10^{-227}:\\ \;\;\;\;\left(-x\right) \cdot \frac{t}{y}\\ \mathbf{elif}\;y \leq 1.85 \cdot 10^{-76}:\\ \;\;\;\;\frac{x \cdot z}{y}\\ \mathbf{else}:\\ \;\;\;\;t\\ \end{array} \]

Alternative 8: 84.1% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -5.5 \cdot 10^{-45} \lor \neg \left(t \leq 2.45 \cdot 10^{-45}\right):\\ \;\;\;\;t \cdot \left(1 - \frac{x}{y}\right)\\ \mathbf{else}:\\ \;\;\;\;t + \frac{x}{y} \cdot z\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= t -5.5e-45) (not (<= t 2.45e-45)))
   (* t (- 1.0 (/ x y)))
   (+ t (* (/ x y) z))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((t <= -5.5e-45) || !(t <= 2.45e-45)) {
		tmp = t * (1.0 - (x / y));
	} else {
		tmp = t + ((x / y) * z);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if ((t <= (-5.5d-45)) .or. (.not. (t <= 2.45d-45))) then
        tmp = t * (1.0d0 - (x / y))
    else
        tmp = t + ((x / y) * z)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if ((t <= -5.5e-45) || !(t <= 2.45e-45)) {
		tmp = t * (1.0 - (x / y));
	} else {
		tmp = t + ((x / y) * z);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (t <= -5.5e-45) or not (t <= 2.45e-45):
		tmp = t * (1.0 - (x / y))
	else:
		tmp = t + ((x / y) * z)
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((t <= -5.5e-45) || !(t <= 2.45e-45))
		tmp = Float64(t * Float64(1.0 - Float64(x / y)));
	else
		tmp = Float64(t + Float64(Float64(x / y) * z));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((t <= -5.5e-45) || ~((t <= 2.45e-45)))
		tmp = t * (1.0 - (x / y));
	else
		tmp = t + ((x / y) * z);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[t, -5.5e-45], N[Not[LessEqual[t, 2.45e-45]], $MachinePrecision]], N[(t * N[(1.0 - N[(x / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(t + N[(N[(x / y), $MachinePrecision] * z), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if t < -5.5000000000000003e-45 or 2.4499999999999999e-45 < t

   1. Initial program 99.9%

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

   2. Taylor expanded in z around 0 87.4%

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

      1. mul-1-neg 87.4%

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

      2. unsub-neg 87.4%

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

      3. associate-/l* 92.5%

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

      4. associate-/r/ 87.5%

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

   4. Simplified 87.5%

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

   5. Taylor expanded in t around 0 92.6%

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

   if -5.5000000000000003e-45 < t < 2.4499999999999999e-45

   1. Initial program 95.4%

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

   2. Taylor expanded in z around inf 85.3%

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

      1. associate-*r/ 86.9%

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

   4. Simplified 86.9%

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

4. Final simplification 90.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -5.5 \cdot 10^{-45} \lor \neg \left(t \leq 2.45 \cdot 10^{-45}\right):\\ \;\;\;\;t \cdot \left(1 - \frac{x}{y}\right)\\ \mathbf{else}:\\ \;\;\;\;t + \frac{x}{y} \cdot z\\ \end{array} \]

Alternative 9: 51.3% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -5.5 \cdot 10^{-20}:\\ \;\;\;\;t\\ \mathbf{elif}\;y \leq 5.6 \cdot 10^{-78}:\\ \;\;\;\;x \cdot \frac{z}{y}\\ \mathbf{else}:\\ \;\;\;\;t\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= y -5.5e-20) t (if (<= y 5.6e-78) (* x (/ z y)) t)))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (y <= -5.5e-20) {
		tmp = t;
	} else if (y <= 5.6e-78) {
		tmp = 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 <= (-5.5d-20)) then
        tmp = t
    else if (y <= 5.6d-78) then
        tmp = 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 <= -5.5e-20) {
		tmp = t;
	} else if (y <= 5.6e-78) {
		tmp = x * (z / y);
	} else {
		tmp = t;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if y <= -5.5e-20:
		tmp = t
	elif y <= 5.6e-78:
		tmp = x * (z / y)
	else:
		tmp = t
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (y <= -5.5e-20)
		tmp = t;
	elseif (y <= 5.6e-78)
		tmp = 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 <= -5.5e-20)
		tmp = t;
	elseif (y <= 5.6e-78)
		tmp = x * (z / y);
	else
		tmp = t;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[y, -5.5e-20], t, If[LessEqual[y, 5.6e-78], N[(x * N[(z / y), $MachinePrecision]), $MachinePrecision], t]]

Derivation

1. Split input into 2 regimes

2. if y < -5.4999999999999996e-20 or 5.60000000000000047e-78 < y

   1. Initial program 99.1%

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

   2. Taylor expanded in x around 0 64.7%

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

   if -5.4999999999999996e-20 < y < 5.60000000000000047e-78

   1. Initial program 95.7%

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

   2. Taylor expanded in x around 0 97.6%

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

   3. Taylor expanded in x around -inf 90.0%

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

   4. Taylor expanded in z around inf 50.8%

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

      1. *-commutative 50.8%

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

      2. associate-*r/ 47.9%

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

   6. Simplified 47.9%

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

4. Final simplification 58.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -5.5 \cdot 10^{-20}:\\ \;\;\;\;t\\ \mathbf{elif}\;y \leq 5.6 \cdot 10^{-78}:\\ \;\;\;\;x \cdot \frac{z}{y}\\ \mathbf{else}:\\ \;\;\;\;t\\ \end{array} \]

Alternative 10: 53.3% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -3.6 \cdot 10^{-25}:\\ \;\;\;\;t\\ \mathbf{elif}\;y \leq 6.4 \cdot 10^{-77}:\\ \;\;\;\;\frac{x \cdot z}{y}\\ \mathbf{else}:\\ \;\;\;\;t\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= y -3.6e-25) t (if (<= y 6.4e-77) (/ (* x z) y) t)))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (y <= -3.6e-25) {
		tmp = t;
	} else if (y <= 6.4e-77) {
		tmp = (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 <= (-3.6d-25)) then
        tmp = t
    else if (y <= 6.4d-77) then
        tmp = (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 <= -3.6e-25) {
		tmp = t;
	} else if (y <= 6.4e-77) {
		tmp = (x * z) / y;
	} else {
		tmp = t;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if y <= -3.6e-25:
		tmp = t
	elif y <= 6.4e-77:
		tmp = (x * z) / y
	else:
		tmp = t
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (y <= -3.6e-25)
		tmp = t;
	elseif (y <= 6.4e-77)
		tmp = Float64(Float64(x * z) / y);
	else
		tmp = t;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (y <= -3.6e-25)
		tmp = t;
	elseif (y <= 6.4e-77)
		tmp = (x * z) / y;
	else
		tmp = t;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[y, -3.6e-25], t, If[LessEqual[y, 6.4e-77], N[(N[(x * z), $MachinePrecision] / y), $MachinePrecision], t]]

Derivation

1. Split input into 2 regimes

2. if y < -3.5999999999999999e-25 or 6.39999999999999999e-77 < y

   1. Initial program 99.1%

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

   2. Taylor expanded in x around 0 64.7%

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

   if -3.5999999999999999e-25 < y < 6.39999999999999999e-77

   1. Initial program 95.7%

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

   2. Taylor expanded in x around 0 97.6%

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

   3. Taylor expanded in x around -inf 90.0%

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

   4. Taylor expanded in z around inf 50.8%

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

4. Final simplification 59.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -3.6 \cdot 10^{-25}:\\ \;\;\;\;t\\ \mathbf{elif}\;y \leq 6.4 \cdot 10^{-77}:\\ \;\;\;\;\frac{x \cdot z}{y}\\ \mathbf{else}:\\ \;\;\;\;t\\ \end{array} \]

Alternative 11: 97.4% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ t + \frac{x}{y} \cdot \left(z - t\right) \end{array} \]

FPCore

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

C

double code(double x, double y, double z, double t) {
	return t + ((x / y) * (z - 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 + ((x / y) * (z - t))
end function

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 97.9%

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

2. Final simplification 97.9%

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

Alternative 12: 38.3% accurate, 9.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 97.9%

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

2. Taylor expanded in x around 0 44.4%

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

3. Final simplification 44.4%

   \[\leadsto t \]

Developer target: 97.2% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{x}{y} \cdot \left(z - t\right) + t\\ \mathbf{if}\;z < 2.759456554562692 \cdot 10^{-282}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z < 2.326994450874436 \cdot 10^{-110}:\\ \;\;\;\;x \cdot \frac{z - t}{y} + t\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (+ (* (/ x y) (- z t)) t)))
   (if (< z 2.759456554562692e-282)
     t_1
     (if (< z 2.326994450874436e-110) (+ (* x (/ (- z t) y)) t) t_1))))

C

double code(double x, double y, double z, double t) {
	double t_1 = ((x / y) * (z - t)) + t;
	double tmp;
	if (z < 2.759456554562692e-282) {
		tmp = t_1;
	} else if (z < 2.326994450874436e-110) {
		tmp = (x * ((z - t) / y)) + t;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: t_1
    real(8) :: tmp
    t_1 = ((x / y) * (z - t)) + t
    if (z < 2.759456554562692d-282) then
        tmp = t_1
    else if (z < 2.326994450874436d-110) then
        tmp = (x * ((z - t) / y)) + t
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double t_1 = ((x / y) * (z - t)) + t;
	double tmp;
	if (z < 2.759456554562692e-282) {
		tmp = t_1;
	} else if (z < 2.326994450874436e-110) {
		tmp = (x * ((z - t) / y)) + t;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = ((x / y) * (z - t)) + t
	tmp = 0
	if z < 2.759456554562692e-282:
		tmp = t_1
	elif z < 2.326994450874436e-110:
		tmp = (x * ((z - t) / y)) + t
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(Float64(Float64(x / y) * Float64(z - t)) + t)
	tmp = 0.0
	if (z < 2.759456554562692e-282)
		tmp = t_1;
	elseif (z < 2.326994450874436e-110)
		tmp = Float64(Float64(x * Float64(Float64(z - t) / y)) + t);
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = ((x / y) * (z - t)) + t;
	tmp = 0.0;
	if (z < 2.759456554562692e-282)
		tmp = t_1;
	elseif (z < 2.326994450874436e-110)
		tmp = (x * ((z - t) / y)) + t;
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(N[(N[(x / y), $MachinePrecision] * N[(z - t), $MachinePrecision]), $MachinePrecision] + t), $MachinePrecision]}, If[Less[z, 2.759456554562692e-282], t$95$1, If[Less[z, 2.326994450874436e-110], N[(N[(x * N[(N[(z - t), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision] + t), $MachinePrecision], t$95$1]]]

Reproduce

herbie shell --seed 2023174 
(FPCore (x y z t)
  :name "Numeric.Signal.Multichannel:$cget from hsignal-0.2.7.1"
  :precision binary64

  :herbie-target
  (if (< z 2.759456554562692e-282) (+ (* (/ x y) (- z t)) t) (if (< z 2.326994450874436e-110) (+ (* x (/ (- z t) y)) t) (+ (* (/ x y) (- z t)) t)))

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