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

Percentage Accurate: 97.9% → 97.9%

Time: 5.3s

Alternatives: 8

Speedup: 1.0×

• 25.0% 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: 97.9% 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: 97.9% 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 97.5%

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

2. Final simplification 97.5%

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

Alternative 2: 64.6% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;\frac{x}{y} \leq -100000 \lor \neg \left(\frac{x}{y} \leq 5 \cdot 10^{-20}\right):\\ \;\;\;\;\frac{x}{y} \cdot \left(-t\right)\\ \mathbf{else}:\\ \;\;\;\;t\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= (/ x y) -100000.0) (not (<= (/ x y) 5e-20))) (* (/ x y) (- t)) t))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (((x / y) <= -100000.0) || !((x / y) <= 5e-20)) {
		tmp = (x / y) * -t;
	} 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 (((x / y) <= (-100000.0d0)) .or. (.not. ((x / y) <= 5d-20))) then
        tmp = (x / y) * -t
    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 (((x / y) <= -100000.0) || !((x / y) <= 5e-20)) {
		tmp = (x / y) * -t;
	} else {
		tmp = t;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if ((x / y) <= -100000.0) or not ((x / y) <= 5e-20):
		tmp = (x / y) * -t
	else:
		tmp = t
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((Float64(x / y) <= -100000.0) || !(Float64(x / y) <= 5e-20))
		tmp = Float64(Float64(x / y) * Float64(-t));
	else
		tmp = t;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (((x / y) <= -100000.0) || ~(((x / y) <= 5e-20)))
		tmp = (x / y) * -t;
	else
		tmp = t;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[N[(x / y), $MachinePrecision], -100000.0], N[Not[LessEqual[N[(x / y), $MachinePrecision], 5e-20]], $MachinePrecision]], N[(N[(x / y), $MachinePrecision] * (-t)), $MachinePrecision], t]

Derivation

1. Split input into 2 regimes

2. if (/.f64 x y) < -1e5 or 4.9999999999999999e-20 < (/.f64 x y)

   1. Initial program 97.5%

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

   2. Taylor expanded in z around 0 40.3%

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

      1. mul-1-neg 40.3%

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

      2. unsub-neg 40.3%

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

      3. associate-/l* 45.6%

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

      4. associate-/r/ 41.8%

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

   4. Simplified 41.8%

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

      1. associate-*l/ 40.3%

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

      2. associate-/l* 45.6%

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

   6. Applied egg-rr 45.6%

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

   7. Taylor expanded in y around 0 38.4%

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

      1. mul-1-neg 38.4%

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

      2. associate-*r/ 43.6%

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

      3. distribute-lft-neg-out 43.6%

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

      4. *-commutative 43.6%

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

   9. Simplified 43.6%

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

   if -1e5 < (/.f64 x y) < 4.9999999999999999e-20

   1. Initial program 97.4%

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

   2. Taylor expanded in x around 0 67.4%

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

4. Final simplification 56.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{x}{y} \leq -100000 \lor \neg \left(\frac{x}{y} \leq 5 \cdot 10^{-20}\right):\\ \;\;\;\;\frac{x}{y} \cdot \left(-t\right)\\ \mathbf{else}:\\ \;\;\;\;t\\ \end{array} \]

Alternative 3: 95.2% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -5.4 \cdot 10^{-94} \lor \neg \left(x \leq 2.9 \cdot 10^{-137}\right):\\ \;\;\;\;t + x \cdot \frac{z - t}{y}\\ \mathbf{else}:\\ \;\;\;\;t + \frac{x \cdot z}{y}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= x -5.4e-94) (not (<= x 2.9e-137)))
   (+ t (* x (/ (- z t) y)))
   (+ t (/ (* x z) y))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((x <= -5.4e-94) || !(x <= 2.9e-137)) {
		tmp = t + (x * ((z - t) / 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 ((x <= (-5.4d-94)) .or. (.not. (x <= 2.9d-137))) then
        tmp = t + (x * ((z - t) / 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 ((x <= -5.4e-94) || !(x <= 2.9e-137)) {
		tmp = t + (x * ((z - t) / y));
	} else {
		tmp = t + ((x * z) / y);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (x <= -5.4e-94) or not (x <= 2.9e-137):
		tmp = t + (x * ((z - t) / y))
	else:
		tmp = t + ((x * z) / y)
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((x <= -5.4e-94) || !(x <= 2.9e-137))
		tmp = Float64(t + Float64(x * Float64(Float64(z - t) / y)));
	else
		tmp = Float64(t + Float64(Float64(x * z) / y));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((x <= -5.4e-94) || ~((x <= 2.9e-137)))
		tmp = t + (x * ((z - t) / y));
	else
		tmp = t + ((x * z) / y);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[x, -5.4e-94], N[Not[LessEqual[x, 2.9e-137]], $MachinePrecision]], N[(t + N[(x * N[(N[(z - t), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(t + N[(N[(x * z), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < -5.4000000000000002e-94 or 2.89999999999999985e-137 < x

   1. Initial program 97.7%

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

   2. Taylor expanded in x around 0 86.1%

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

      1. *-commutative 86.1%

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

      2. associate-*r/ 98.7%

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

   4. Simplified 98.7%

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

   if -5.4000000000000002e-94 < x < 2.89999999999999985e-137

   1. Initial program 96.9%

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

   2. Taylor expanded in z around inf 94.1%

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

4. Final simplification 97.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -5.4 \cdot 10^{-94} \lor \neg \left(x \leq 2.9 \cdot 10^{-137}\right):\\ \;\;\;\;t + x \cdot \frac{z - t}{y}\\ \mathbf{else}:\\ \;\;\;\;t + \frac{x \cdot z}{y}\\ \end{array} \]

Alternative 4: 86.2% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -2.15 \cdot 10^{+137} \lor \neg \left(t \leq 1.1 \cdot 10^{+89}\right):\\ \;\;\;\;t - \frac{x}{y} \cdot t\\ \mathbf{else}:\\ \;\;\;\;t + \frac{x}{y} \cdot z\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= t -2.15e+137) (not (<= t 1.1e+89)))
   (- t (* (/ x y) t))
   (+ t (* (/ x y) z))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((t <= -2.15e+137) || !(t <= 1.1e+89)) {
		tmp = t - ((x / y) * t);
	} 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 <= (-2.15d+137)) .or. (.not. (t <= 1.1d+89))) then
        tmp = t - ((x / y) * t)
    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 <= -2.15e+137) || !(t <= 1.1e+89)) {
		tmp = t - ((x / y) * t);
	} else {
		tmp = t + ((x / y) * z);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (t <= -2.15e+137) or not (t <= 1.1e+89):
		tmp = t - ((x / y) * t)
	else:
		tmp = t + ((x / y) * z)
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((t <= -2.15e+137) || !(t <= 1.1e+89))
		tmp = Float64(t - Float64(Float64(x / y) * t));
	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 <= -2.15e+137) || ~((t <= 1.1e+89)))
		tmp = t - ((x / y) * t);
	else
		tmp = t + ((x / y) * z);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[t, -2.15e+137], N[Not[LessEqual[t, 1.1e+89]], $MachinePrecision]], N[(t - N[(N[(x / y), $MachinePrecision] * t), $MachinePrecision]), $MachinePrecision], N[(t + N[(N[(x / y), $MachinePrecision] * z), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if t < -2.14999999999999982e137 or 1.1e89 < t

   1. Initial program 99.9%

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

   2. Taylor expanded in z around 0 79.8%

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

      1. mul-1-neg 79.8%

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

      2. unsub-neg 79.8%

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

      3. associate-*r/ 90.1%

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

   4. Simplified 90.1%

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

   if -2.14999999999999982e137 < t < 1.1e89

   1. Initial program 96.4%

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

   2. Taylor expanded in z around inf 82.8%

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

      1. associate-*r/ 87.3%

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

   4. Simplified 87.3%

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

4. Final simplification 88.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -2.15 \cdot 10^{+137} \lor \neg \left(t \leq 1.1 \cdot 10^{+89}\right):\\ \;\;\;\;t - \frac{x}{y} \cdot t\\ \mathbf{else}:\\ \;\;\;\;t + \frac{x}{y} \cdot z\\ \end{array} \]

Alternative 5: 86.2% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -8 \cdot 10^{+138} \lor \neg \left(t \leq 1.9 \cdot 10^{+89}\right):\\ \;\;\;\;t - \frac{t}{\frac{y}{x}}\\ \mathbf{else}:\\ \;\;\;\;t + \frac{x}{y} \cdot z\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= t -8e+138) (not (<= t 1.9e+89)))
   (- t (/ t (/ y x)))
   (+ t (* (/ x y) z))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((t <= -8e+138) || !(t <= 1.9e+89)) {
		tmp = t - (t / (y / x));
	} else {
		tmp = t + ((x / y) * z);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if ((t <= (-8d+138)) .or. (.not. (t <= 1.9d+89))) then
        tmp = t - (t / (y / x))
    else
        tmp = t + ((x / y) * z)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if ((t <= -8e+138) || !(t <= 1.9e+89)) {
		tmp = t - (t / (y / x));
	} else {
		tmp = t + ((x / y) * z);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (t <= -8e+138) or not (t <= 1.9e+89):
		tmp = t - (t / (y / x))
	else:
		tmp = t + ((x / y) * z)
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((t <= -8e+138) || !(t <= 1.9e+89))
		tmp = Float64(t - Float64(t / Float64(y / x)));
	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 <= -8e+138) || ~((t <= 1.9e+89)))
		tmp = t - (t / (y / x));
	else
		tmp = t + ((x / y) * z);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[t, -8e+138], N[Not[LessEqual[t, 1.9e+89]], $MachinePrecision]], N[(t - N[(t / N[(y / x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(t + N[(N[(x / y), $MachinePrecision] * z), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if t < -8.0000000000000003e138 or 1.90000000000000012e89 < t

   1. Initial program 99.9%

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

   2. Taylor expanded in z around 0 79.8%

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

      1. mul-1-neg 79.8%

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

      2. unsub-neg 79.8%

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

      3. associate-/l* 90.2%

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

      4. associate-/r/ 84.2%

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

   4. Simplified 84.2%

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

      1. associate-*l/ 79.8%

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

      2. associate-/l* 90.2%

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

   6. Applied egg-rr 90.2%

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

   if -8.0000000000000003e138 < t < 1.90000000000000012e89

   1. Initial program 96.4%

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

   2. Taylor expanded in z around inf 82.8%

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

      1. associate-*r/ 87.3%

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

   4. Simplified 87.3%

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

4. Final simplification 88.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -8 \cdot 10^{+138} \lor \neg \left(t \leq 1.9 \cdot 10^{+89}\right):\\ \;\;\;\;t - \frac{t}{\frac{y}{x}}\\ \mathbf{else}:\\ \;\;\;\;t + \frac{x}{y} \cdot z\\ \end{array} \]

Alternative 6: 77.3% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;\frac{x}{y} \leq 10^{+280}:\\ \;\;\;\;t + \frac{x}{y} \cdot z\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{y} \cdot \left(-t\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= (/ x y) 1e+280) (+ t (* (/ x y) z)) (* (/ x y) (- t))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((x / y) <= 1e+280) {
		tmp = t + ((x / y) * z);
	} else {
		tmp = (x / y) * -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 ((x / y) <= 1d+280) then
        tmp = t + ((x / y) * z)
    else
        tmp = (x / y) * -t
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if ((x / y) <= 1e+280) {
		tmp = t + ((x / y) * z);
	} else {
		tmp = (x / y) * -t;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (x / y) <= 1e+280:
		tmp = t + ((x / y) * z)
	else:
		tmp = (x / y) * -t
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (Float64(x / y) <= 1e+280)
		tmp = Float64(t + Float64(Float64(x / y) * z));
	else
		tmp = Float64(Float64(x / y) * Float64(-t));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((x / y) <= 1e+280)
		tmp = t + ((x / y) * z);
	else
		tmp = (x / y) * -t;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[N[(x / y), $MachinePrecision], 1e+280], N[(t + N[(N[(x / y), $MachinePrecision] * z), $MachinePrecision]), $MachinePrecision], N[(N[(x / y), $MachinePrecision] * (-t)), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if (/.f64 x y) < 1e280

   1. Initial program 97.7%

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

   2. Taylor expanded in z around inf 77.7%

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

      1. associate-*r/ 82.9%

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

   4. Simplified 82.9%

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

   if 1e280 < (/.f64 x y)

   1. Initial program 93.8%

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

   2. Taylor expanded in z around 0 73.9%

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

      1. mul-1-neg 73.9%

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

      2. unsub-neg 73.9%

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

      3. associate-/l* 74.1%

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

      4. associate-/r/ 73.9%

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

   4. Simplified 73.9%

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

      1. associate-*l/ 73.9%

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

      2. associate-/l* 74.1%

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

   6. Applied egg-rr 74.1%

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

   7. Taylor expanded in y around 0 73.9%

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

      1. mul-1-neg 73.9%

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

      2. associate-*r/ 74.1%

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

      3. distribute-lft-neg-out 74.1%

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

      4. *-commutative 74.1%

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

   9. Simplified 74.1%

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

4. Final simplification 82.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{x}{y} \leq 10^{+280}:\\ \;\;\;\;t + \frac{x}{y} \cdot z\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{y} \cdot \left(-t\right)\\ \end{array} \]

Alternative 7: 50.6% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -8.8 \cdot 10^{+142} \lor \neg \left(x \leq 2.05 \cdot 10^{-26}\right):\\ \;\;\;\;x \cdot \left(-\frac{t}{y}\right)\\ \mathbf{else}:\\ \;\;\;\;t\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= x -8.8e+142) (not (<= x 2.05e-26))) (* x (- (/ t y))) t))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((x <= -8.8e+142) || !(x <= 2.05e-26)) {
		tmp = x * -(t / 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 ((x <= (-8.8d+142)) .or. (.not. (x <= 2.05d-26))) then
        tmp = x * -(t / 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 ((x <= -8.8e+142) || !(x <= 2.05e-26)) {
		tmp = x * -(t / y);
	} else {
		tmp = t;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (x <= -8.8e+142) or not (x <= 2.05e-26):
		tmp = x * -(t / y)
	else:
		tmp = t
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((x <= -8.8e+142) || !(x <= 2.05e-26))
		tmp = Float64(x * Float64(-Float64(t / y)));
	else
		tmp = t;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((x <= -8.8e+142) || ~((x <= 2.05e-26)))
		tmp = x * -(t / y);
	else
		tmp = t;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[x, -8.8e+142], N[Not[LessEqual[x, 2.05e-26]], $MachinePrecision]], N[(x * (-N[(t / y), $MachinePrecision])), $MachinePrecision], t]

Derivation

1. Split input into 2 regimes

2. if x < -8.79999999999999947e142 or 2.0499999999999999e-26 < x

   1. Initial program 97.2%

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

   2. Taylor expanded in z around 0 39.2%

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

      1. mul-1-neg 39.2%

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

      2. unsub-neg 39.2%

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

      3. associate-/l* 48.6%

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

      4. associate-/r/ 46.8%

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

   4. Simplified 46.8%

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

      1. associate-*l/ 39.2%

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

      2. associate-/l* 48.6%

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

   6. Applied egg-rr 48.6%

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

   7. Taylor expanded in y around 0 31.5%

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

      1. mul-1-neg 31.5%

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

      2. associate-*l/ 35.7%

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

      3. *-commutative 35.7%

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

      4. distribute-rgt-neg-in 35.7%

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

      5. distribute-neg-frac 35.7%

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

   9. Simplified 35.7%

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

   if -8.79999999999999947e142 < x < 2.0499999999999999e-26

   1. Initial program 97.6%

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

   2. Taylor expanded in x around 0 54.2%

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

4. Final simplification 46.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -8.8 \cdot 10^{+142} \lor \neg \left(x \leq 2.05 \cdot 10^{-26}\right):\\ \;\;\;\;x \cdot \left(-\frac{t}{y}\right)\\ \mathbf{else}:\\ \;\;\;\;t\\ \end{array} \]

Alternative 8: 39.1% 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 97.5%

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

2. Taylor expanded in x around 0 36.4%

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

3. Final simplification 36.4%

   \[\leadsto t \]

Developer target: 97.6% 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 2023240 
(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))