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

Percentage Accurate: 97.7% → 96.6%

Time: 4.9s

Alternatives: 6

Speedup: N/A×

• 25.3% 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: 97.7% 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: 96.6% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq 1.6 \cdot 10^{-199}:\\ \;\;\;\;t + \frac{x}{y} \cdot \left(z - t\right)\\ \mathbf{else}:\\ \;\;\;\;t + x \cdot \frac{z - t}{y}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= y 1.6e-199) (+ t (* (/ x y) (- z t))) (+ t (* x (/ (- z t) y)))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (y <= 1.6e-199) {
		tmp = t + ((x / y) * (z - t));
	} 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 (y <= 1.6d-199) then
        tmp = t + ((x / y) * (z - t))
    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 (y <= 1.6e-199) {
		tmp = t + ((x / y) * (z - t));
	} else {
		tmp = t + (x * ((z - t) / y));
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if y <= 1.6e-199:
		tmp = t + ((x / y) * (z - t))
	else:
		tmp = t + (x * ((z - t) / y))
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (y <= 1.6e-199)
		tmp = Float64(t + Float64(Float64(x / y) * Float64(z - t)));
	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 (y <= 1.6e-199)
		tmp = t + ((x / y) * (z - t));
	else
		tmp = t + (x * ((z - t) / y));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[y, 1.6e-199], N[(t + N[(N[(x / y), $MachinePrecision] * N[(z - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(t + N[(x * N[(N[(z - t), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < 1.6e-199

   1. Initial program 99.2%

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

   if 1.6e-199 < y

   1. Initial program 93.7%

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

   3. Taylor expanded in x around 0 91.1%

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

      1. associate-*r/ 98.9%

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

   5. Simplified 98.9%

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

4. Final simplification 99.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq 1.6 \cdot 10^{-199}:\\ \;\;\;\;t + \frac{x}{y} \cdot \left(z - t\right)\\ \mathbf{else}:\\ \;\;\;\;t + x \cdot \frac{z - t}{y}\\ \end{array} \]
5. Add Preprocessing

Alternative 2: 83.0% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -2.7 \cdot 10^{-52}:\\ \;\;\;\;t + \frac{x}{\frac{y}{z}}\\ \mathbf{elif}\;z \leq 1.5 \cdot 10^{-135}:\\ \;\;\;\;t - \frac{x \cdot t}{y}\\ \mathbf{else}:\\ \;\;\;\;t + \frac{x}{y} \cdot z\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= z -2.7e-52)
   (+ t (/ x (/ y z)))
   (if (<= z 1.5e-135) (- t (/ (* x t) y)) (+ t (* (/ x y) z)))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (z <= -2.7e-52) {
		tmp = t + (x / (y / z));
	} else if (z <= 1.5e-135) {
		tmp = t - ((x * 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 (z <= (-2.7d-52)) then
        tmp = t + (x / (y / z))
    else if (z <= 1.5d-135) then
        tmp = t - ((x * 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 (z <= -2.7e-52) {
		tmp = t + (x / (y / z));
	} else if (z <= 1.5e-135) {
		tmp = t - ((x * t) / y);
	} else {
		tmp = t + ((x / y) * z);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if z <= -2.7e-52:
		tmp = t + (x / (y / z))
	elif z <= 1.5e-135:
		tmp = t - ((x * t) / y)
	else:
		tmp = t + ((x / y) * z)
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (z <= -2.7e-52)
		tmp = Float64(t + Float64(x / Float64(y / z)));
	elseif (z <= 1.5e-135)
		tmp = Float64(t - Float64(Float64(x * 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 (z <= -2.7e-52)
		tmp = t + (x / (y / z));
	elseif (z <= 1.5e-135)
		tmp = t - ((x * t) / y);
	else
		tmp = t + ((x / y) * z);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[z, -2.7e-52], N[(t + N[(x / N[(y / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 1.5e-135], N[(t - N[(N[(x * t), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision], N[(t + N[(N[(x / y), $MachinePrecision] * z), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if z < -2.70000000000000009e-52

   1. Initial program 97.1%

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

      1. associate-*l/ 87.2%

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

      2. associate-/l* 95.8%

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

   4. Applied egg-rr 95.8%

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

   5. Taylor expanded in z around inf 87.8%

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

   if -2.70000000000000009e-52 < z < 1.50000000000000006e-135

   1. Initial program 94.9%

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

   3. Taylor expanded in z around 0 90.0%

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

      1. mul-1-neg 90.0%

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

      2. *-commutative 90.0%

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

   5. Simplified 90.0%

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

   if 1.50000000000000006e-135 < z

   1. Initial program 99.6%

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

   3. Taylor expanded in z around inf 85.4%

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

      1. associate-*l/ 91.3%

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

      2. *-commutative 91.3%

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

   5. Simplified 91.3%

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

4. Final simplification 89.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -2.7 \cdot 10^{-52}:\\ \;\;\;\;t + \frac{x}{\frac{y}{z}}\\ \mathbf{elif}\;z \leq 1.5 \cdot 10^{-135}:\\ \;\;\;\;t - \frac{x \cdot t}{y}\\ \mathbf{else}:\\ \;\;\;\;t + \frac{x}{y} \cdot z\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 83.8% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -3.4 \cdot 10^{-53}:\\ \;\;\;\;t + \frac{x}{\frac{y}{z}}\\ \mathbf{elif}\;z \leq 2.8 \cdot 10^{-94}:\\ \;\;\;\;t - x \cdot \frac{t}{y}\\ \mathbf{else}:\\ \;\;\;\;t + \frac{x}{y} \cdot z\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= z -3.4e-53)
   (+ t (/ x (/ y z)))
   (if (<= z 2.8e-94) (- t (* x (/ t y))) (+ t (* (/ x y) z)))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (z <= -3.4e-53) {
		tmp = t + (x / (y / z));
	} else if (z <= 2.8e-94) {
		tmp = t - (x * (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 (z <= (-3.4d-53)) then
        tmp = t + (x / (y / z))
    else if (z <= 2.8d-94) then
        tmp = t - (x * (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 (z <= -3.4e-53) {
		tmp = t + (x / (y / z));
	} else if (z <= 2.8e-94) {
		tmp = t - (x * (t / y));
	} else {
		tmp = t + ((x / y) * z);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if z <= -3.4e-53:
		tmp = t + (x / (y / z))
	elif z <= 2.8e-94:
		tmp = t - (x * (t / y))
	else:
		tmp = t + ((x / y) * z)
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (z <= -3.4e-53)
		tmp = Float64(t + Float64(x / Float64(y / z)));
	elseif (z <= 2.8e-94)
		tmp = Float64(t - Float64(x * Float64(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 (z <= -3.4e-53)
		tmp = t + (x / (y / z));
	elseif (z <= 2.8e-94)
		tmp = t - (x * (t / y));
	else
		tmp = t + ((x / y) * z);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[z, -3.4e-53], N[(t + N[(x / N[(y / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 2.8e-94], N[(t - N[(x * N[(t / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(t + N[(N[(x / y), $MachinePrecision] * z), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if z < -3.4e-53

   1. Initial program 97.1%

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

      1. associate-*l/ 87.2%

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

      2. associate-/l* 95.8%

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

   4. Applied egg-rr 95.8%

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

   5. Taylor expanded in z around inf 87.8%

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

   if -3.4e-53 < z < 2.7999999999999998e-94

   1. Initial program 95.2%

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

      1. associate-*l/ 94.4%

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

      2. associate-/l* 99.8%

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

   4. Applied egg-rr 99.8%

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

   5. Taylor expanded in z around 0 87.7%

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

      1. mul-1-neg 87.7%

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

      2. associate-*l/ 92.4%

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

      3. *-commutative 92.4%

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

      4. distribute-rgt-neg-in 92.4%

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

   7. Simplified 92.4%

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

   if 2.7999999999999998e-94 < z

   1. Initial program 99.5%

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

   3. Taylor expanded in z around inf 87.7%

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

      1. associate-*l/ 93.9%

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

      2. *-commutative 93.9%

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

   5. Simplified 93.9%

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

4. Final simplification 91.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -3.4 \cdot 10^{-53}:\\ \;\;\;\;t + \frac{x}{\frac{y}{z}}\\ \mathbf{elif}\;z \leq 2.8 \cdot 10^{-94}:\\ \;\;\;\;t - x \cdot \frac{t}{y}\\ \mathbf{else}:\\ \;\;\;\;t + \frac{x}{y} \cdot z\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 93.1% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 97.2%

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

3. Taylor expanded in x around 0 91.7%

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

   1. associate-*r/ 96.2%

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

5. Simplified 96.2%

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

6. Final simplification 96.2%

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

Alternative 5: 72.8% accurate, 1.3× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 97.2%

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

3. Taylor expanded in z around inf 72.5%

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

   1. *-commutative 72.5%

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

   2. associate-*l/ 74.8%

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

   3. *-commutative 74.8%

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

5. Simplified 74.8%

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

6. Final simplification 74.8%

   \[\leadsto t + x \cdot \frac{z}{y} \]
7. Add Preprocessing

Alternative 6: 76.1% accurate, 1.3× speedup

Math

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

FPCore

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

C

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

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)
end function

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 97.2%

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

3. Taylor expanded in z around inf 72.5%

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

   1. associate-*l/ 77.3%

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

   2. *-commutative 77.3%

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

5. Simplified 77.3%

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

6. Final simplification 77.3%

   \[\leadsto t + \frac{x}{y} \cdot z \]
7. Add Preprocessing

Developer target: 97.3% accurate, 0.5× 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 2024026 
(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))