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

Percentage Accurate: 97.7% → 97.7%

Time: 5.6s

Alternatives: 8

Speedup: 1.0×

• 25.6% 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: 97.7% 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 98.1%

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

2. Final simplification 98.1%

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

Alternative 2: 76.0% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;\frac{x}{y} \leq -1 \cdot 10^{+28} \lor \neg \left(\frac{x}{y} \leq 2 \cdot 10^{+113}\right) \land \frac{x}{y} \leq 5 \cdot 10^{+220}:\\ \;\;\;\;\frac{x}{y} \cdot \left(-t\right)\\ \mathbf{else}:\\ \;\;\;\;t + \frac{x}{y} \cdot z\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= (/ x y) -1e+28)
         (and (not (<= (/ x y) 2e+113)) (<= (/ x y) 5e+220)))
   (* (/ x y) (- t))
   (+ t (* (/ x y) z))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (((x / y) <= -1e+28) || (!((x / y) <= 2e+113) && ((x / y) <= 5e+220))) {
		tmp = (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 (((x / y) <= (-1d+28)) .or. (.not. ((x / y) <= 2d+113)) .and. ((x / y) <= 5d+220)) then
        tmp = (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 (((x / y) <= -1e+28) || (!((x / y) <= 2e+113) && ((x / y) <= 5e+220))) {
		tmp = (x / y) * -t;
	} else {
		tmp = t + ((x / y) * z);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if ((x / y) <= -1e+28) or (not ((x / y) <= 2e+113) and ((x / y) <= 5e+220)):
		tmp = (x / y) * -t
	else:
		tmp = t + ((x / y) * z)
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((Float64(x / y) <= -1e+28) || (!(Float64(x / y) <= 2e+113) && (Float64(x / y) <= 5e+220)))
		tmp = Float64(Float64(x / y) * Float64(-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 (((x / y) <= -1e+28) || (~(((x / y) <= 2e+113)) && ((x / y) <= 5e+220)))
		tmp = (x / y) * -t;
	else
		tmp = t + ((x / y) * z);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[N[(x / y), $MachinePrecision], -1e+28], And[N[Not[LessEqual[N[(x / y), $MachinePrecision], 2e+113]], $MachinePrecision], LessEqual[N[(x / y), $MachinePrecision], 5e+220]]], N[(N[(x / y), $MachinePrecision] * (-t)), $MachinePrecision], N[(t + N[(N[(x / y), $MachinePrecision] * z), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if (/.f64 x y) < -9.99999999999999958e27 or 2e113 < (/.f64 x y) < 5.0000000000000002e220

   1. Initial program 96.9%

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

   2. Taylor expanded in x around 0 95.8%

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

      1. *-commutative 95.8%

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

      2. associate-*r/ 92.7%

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

   4. Simplified 92.7%

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

      1. clear-num 92.7%

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

      2. associate-/r/ 92.8%

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

   6. Applied egg-rr 92.8%

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

   7. Taylor expanded in t around -inf 62.4%

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

      1. associate-*r* 62.4%

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

      2. neg-mul-1 62.4%

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

      3. sub-neg 62.4%

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

      4. metadata-eval 62.4%

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

   9. Simplified 62.4%

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

   10. Taylor expanded in x around inf 62.4%

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

   if -9.99999999999999958e27 < (/.f64 x y) < 2e113 or 5.0000000000000002e220 < (/.f64 x y)

   1. Initial program 98.7%

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

   2. Taylor expanded in z around inf 79.7%

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

      1. associate-*r/ 86.4%

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

   4. Simplified 86.4%

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

4. Final simplification 77.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{x}{y} \leq -1 \cdot 10^{+28} \lor \neg \left(\frac{x}{y} \leq 2 \cdot 10^{+113}\right) \land \frac{x}{y} \leq 5 \cdot 10^{+220}:\\ \;\;\;\;\frac{x}{y} \cdot \left(-t\right)\\ \mathbf{else}:\\ \;\;\;\;t + \frac{x}{y} \cdot z\\ \end{array} \]

Alternative 3: 84.5% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -145 \lor \neg \left(z \leq 2.25 \cdot 10^{-153}\right) \land \left(z \leq 7.4 \cdot 10^{+24} \lor \neg \left(z \leq 1.42 \cdot 10^{+57}\right)\right):\\ \;\;\;\;t + \frac{x}{y} \cdot z\\ \mathbf{else}:\\ \;\;\;\;t - \frac{x}{y} \cdot t\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= z -145.0)
         (and (not (<= z 2.25e-153))
              (or (<= z 7.4e+24) (not (<= z 1.42e+57)))))
   (+ t (* (/ x y) z))
   (- t (* (/ x y) t))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((z <= -145.0) || (!(z <= 2.25e-153) && ((z <= 7.4e+24) || !(z <= 1.42e+57)))) {
		tmp = t + ((x / y) * z);
	} else {
		tmp = t - ((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 ((z <= (-145.0d0)) .or. (.not. (z <= 2.25d-153)) .and. (z <= 7.4d+24) .or. (.not. (z <= 1.42d+57))) then
        tmp = t + ((x / y) * z)
    else
        tmp = t - ((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 ((z <= -145.0) || (!(z <= 2.25e-153) && ((z <= 7.4e+24) || !(z <= 1.42e+57)))) {
		tmp = t + ((x / y) * z);
	} else {
		tmp = t - ((x / y) * t);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (z <= -145.0) or (not (z <= 2.25e-153) and ((z <= 7.4e+24) or not (z <= 1.42e+57))):
		tmp = t + ((x / y) * z)
	else:
		tmp = t - ((x / y) * t)
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((z <= -145.0) || (!(z <= 2.25e-153) && ((z <= 7.4e+24) || !(z <= 1.42e+57))))
		tmp = Float64(t + Float64(Float64(x / y) * z));
	else
		tmp = Float64(t - Float64(Float64(x / y) * t));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((z <= -145.0) || (~((z <= 2.25e-153)) && ((z <= 7.4e+24) || ~((z <= 1.42e+57)))))
		tmp = t + ((x / y) * z);
	else
		tmp = t - ((x / y) * t);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[z, -145.0], And[N[Not[LessEqual[z, 2.25e-153]], $MachinePrecision], Or[LessEqual[z, 7.4e+24], N[Not[LessEqual[z, 1.42e+57]], $MachinePrecision]]]], N[(t + N[(N[(x / y), $MachinePrecision] * z), $MachinePrecision]), $MachinePrecision], N[(t - N[(N[(x / y), $MachinePrecision] * t), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -145 or 2.25e-153 < z < 7.39999999999999998e24 or 1.42e57 < z

   1. Initial program 98.7%

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

   2. Taylor expanded in z around inf 80.5%

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

      1. associate-*r/ 86.8%

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

   4. Simplified 86.8%

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

   if -145 < z < 2.25e-153 or 7.39999999999999998e24 < z < 1.42e57

   1. Initial program 97.0%

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

   2. Taylor expanded in z around 0 83.6%

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

      1. mul-1-neg 83.6%

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

      2. unsub-neg 83.6%

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

      3. associate-*r/ 86.5%

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

   4. Simplified 86.5%

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

4. Final simplification 86.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -145 \lor \neg \left(z \leq 2.25 \cdot 10^{-153}\right) \land \left(z \leq 7.4 \cdot 10^{+24} \lor \neg \left(z \leq 1.42 \cdot 10^{+57}\right)\right):\\ \;\;\;\;t + \frac{x}{y} \cdot z\\ \mathbf{else}:\\ \;\;\;\;t - \frac{x}{y} \cdot t\\ \end{array} \]

Alternative 4: 84.6% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := t + \frac{x}{y} \cdot z\\ \mathbf{if}\;z \leq -130:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq 2.25 \cdot 10^{-153}:\\ \;\;\;\;t - \frac{t}{\frac{y}{x}}\\ \mathbf{elif}\;z \leq 6.5 \cdot 10^{+24} \lor \neg \left(z \leq 6 \cdot 10^{+57}\right):\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t - \frac{x}{y} \cdot t\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (+ t (* (/ x y) z))))
   (if (<= z -130.0)
     t_1
     (if (<= z 2.25e-153)
       (- t (/ t (/ y x)))
       (if (or (<= z 6.5e+24) (not (<= z 6e+57))) t_1 (- t (* (/ x y) t)))))))

C

double code(double x, double y, double z, double t) {
	double t_1 = t + ((x / y) * z);
	double tmp;
	if (z <= -130.0) {
		tmp = t_1;
	} else if (z <= 2.25e-153) {
		tmp = t - (t / (y / x));
	} else if ((z <= 6.5e+24) || !(z <= 6e+57)) {
		tmp = t_1;
	} else {
		tmp = t - ((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) :: t_1
    real(8) :: tmp
    t_1 = t + ((x / y) * z)
    if (z <= (-130.0d0)) then
        tmp = t_1
    else if (z <= 2.25d-153) then
        tmp = t - (t / (y / x))
    else if ((z <= 6.5d+24) .or. (.not. (z <= 6d+57))) then
        tmp = t_1
    else
        tmp = t - ((x / y) * t)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double t_1 = t + ((x / y) * z);
	double tmp;
	if (z <= -130.0) {
		tmp = t_1;
	} else if (z <= 2.25e-153) {
		tmp = t - (t / (y / x));
	} else if ((z <= 6.5e+24) || !(z <= 6e+57)) {
		tmp = t_1;
	} else {
		tmp = t - ((x / y) * t);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = t + ((x / y) * z)
	tmp = 0
	if z <= -130.0:
		tmp = t_1
	elif z <= 2.25e-153:
		tmp = t - (t / (y / x))
	elif (z <= 6.5e+24) or not (z <= 6e+57):
		tmp = t_1
	else:
		tmp = t - ((x / y) * t)
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(t + Float64(Float64(x / y) * z))
	tmp = 0.0
	if (z <= -130.0)
		tmp = t_1;
	elseif (z <= 2.25e-153)
		tmp = Float64(t - Float64(t / Float64(y / x)));
	elseif ((z <= 6.5e+24) || !(z <= 6e+57))
		tmp = t_1;
	else
		tmp = Float64(t - Float64(Float64(x / y) * t));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = t + ((x / y) * z);
	tmp = 0.0;
	if (z <= -130.0)
		tmp = t_1;
	elseif (z <= 2.25e-153)
		tmp = t - (t / (y / x));
	elseif ((z <= 6.5e+24) || ~((z <= 6e+57)))
		tmp = t_1;
	else
		tmp = t - ((x / y) * t);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(t + N[(N[(x / y), $MachinePrecision] * z), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -130.0], t$95$1, If[LessEqual[z, 2.25e-153], N[(t - N[(t / N[(y / x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[Or[LessEqual[z, 6.5e+24], N[Not[LessEqual[z, 6e+57]], $MachinePrecision]], t$95$1, N[(t - N[(N[(x / y), $MachinePrecision] * t), $MachinePrecision]), $MachinePrecision]]]]]

Derivation

1. Split input into 3 regimes

2. if z < -130 or 2.25e-153 < z < 6.4999999999999996e24 or 5.9999999999999999e57 < z

   1. Initial program 98.7%

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

   2. Taylor expanded in z around inf 80.5%

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

      1. associate-*r/ 86.8%

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

   4. Simplified 86.8%

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

   if -130 < z < 2.25e-153

   1. Initial program 96.8%

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

   2. Taylor expanded in z around 0 82.4%

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

      1. mul-1-neg 82.4%

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

      2. unsub-neg 82.4%

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

      3. associate-/l* 85.5%

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

      4. associate-/r/ 85.4%

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

   4. Simplified 85.4%

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

      1. associate-/r/ 85.5%

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

   6. Applied egg-rr 85.5%

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

   if 6.4999999999999996e24 < z < 5.9999999999999999e57

   1. Initial program 99.8%

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

   2. Taylor expanded in z around 0 98.8%

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

      1. mul-1-neg 98.8%

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

      2. unsub-neg 98.8%

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

      3. associate-*r/ 98.7%

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

   4. Simplified 98.7%

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

4. Final simplification 86.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -130:\\ \;\;\;\;t + \frac{x}{y} \cdot z\\ \mathbf{elif}\;z \leq 2.25 \cdot 10^{-153}:\\ \;\;\;\;t - \frac{t}{\frac{y}{x}}\\ \mathbf{elif}\;z \leq 6.5 \cdot 10^{+24} \lor \neg \left(z \leq 6 \cdot 10^{+57}\right):\\ \;\;\;\;t + \frac{x}{y} \cdot z\\ \mathbf{else}:\\ \;\;\;\;t - \frac{x}{y} \cdot t\\ \end{array} \]

Alternative 5: 84.4% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := t + \frac{x}{y} \cdot z\\ \mathbf{if}\;z \leq -95:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq 2.25 \cdot 10^{-153}:\\ \;\;\;\;t - \frac{t}{\frac{y}{x}}\\ \mathbf{elif}\;z \leq 8 \cdot 10^{+24} \lor \neg \left(z \leq 7.4 \cdot 10^{+56}\right):\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t - \frac{x \cdot t}{y}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (+ t (* (/ x y) z))))
   (if (<= z -95.0)
     t_1
     (if (<= z 2.25e-153)
       (- t (/ t (/ y x)))
       (if (or (<= z 8e+24) (not (<= z 7.4e+56))) t_1 (- t (/ (* x t) y)))))))

C

double code(double x, double y, double z, double t) {
	double t_1 = t + ((x / y) * z);
	double tmp;
	if (z <= -95.0) {
		tmp = t_1;
	} else if (z <= 2.25e-153) {
		tmp = t - (t / (y / x));
	} else if ((z <= 8e+24) || !(z <= 7.4e+56)) {
		tmp = t_1;
	} else {
		tmp = t - ((x * 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) :: t_1
    real(8) :: tmp
    t_1 = t + ((x / y) * z)
    if (z <= (-95.0d0)) then
        tmp = t_1
    else if (z <= 2.25d-153) then
        tmp = t - (t / (y / x))
    else if ((z <= 8d+24) .or. (.not. (z <= 7.4d+56))) then
        tmp = t_1
    else
        tmp = t - ((x * t) / y)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double t_1 = t + ((x / y) * z);
	double tmp;
	if (z <= -95.0) {
		tmp = t_1;
	} else if (z <= 2.25e-153) {
		tmp = t - (t / (y / x));
	} else if ((z <= 8e+24) || !(z <= 7.4e+56)) {
		tmp = t_1;
	} else {
		tmp = t - ((x * t) / y);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = t + ((x / y) * z)
	tmp = 0
	if z <= -95.0:
		tmp = t_1
	elif z <= 2.25e-153:
		tmp = t - (t / (y / x))
	elif (z <= 8e+24) or not (z <= 7.4e+56):
		tmp = t_1
	else:
		tmp = t - ((x * t) / y)
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(t + Float64(Float64(x / y) * z))
	tmp = 0.0
	if (z <= -95.0)
		tmp = t_1;
	elseif (z <= 2.25e-153)
		tmp = Float64(t - Float64(t / Float64(y / x)));
	elseif ((z <= 8e+24) || !(z <= 7.4e+56))
		tmp = t_1;
	else
		tmp = Float64(t - Float64(Float64(x * t) / y));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = t + ((x / y) * z);
	tmp = 0.0;
	if (z <= -95.0)
		tmp = t_1;
	elseif (z <= 2.25e-153)
		tmp = t - (t / (y / x));
	elseif ((z <= 8e+24) || ~((z <= 7.4e+56)))
		tmp = t_1;
	else
		tmp = t - ((x * t) / y);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(t + N[(N[(x / y), $MachinePrecision] * z), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -95.0], t$95$1, If[LessEqual[z, 2.25e-153], N[(t - N[(t / N[(y / x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[Or[LessEqual[z, 8e+24], N[Not[LessEqual[z, 7.4e+56]], $MachinePrecision]], t$95$1, N[(t - N[(N[(x * t), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision]]]]]

Derivation

1. Split input into 3 regimes

2. if z < -95 or 2.25e-153 < z < 7.9999999999999999e24 or 7.39999999999999994e56 < z

   1. Initial program 98.7%

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

   2. Taylor expanded in z around inf 80.5%

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

      1. associate-*r/ 86.8%

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

   4. Simplified 86.8%

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

   if -95 < z < 2.25e-153

   1. Initial program 96.8%

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

   2. Taylor expanded in z around 0 82.4%

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

      1. mul-1-neg 82.4%

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

      2. unsub-neg 82.4%

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

      3. associate-/l* 85.5%

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

      4. associate-/r/ 85.4%

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

   4. Simplified 85.4%

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

      1. associate-/r/ 85.5%

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

   6. Applied egg-rr 85.5%

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

   if 7.9999999999999999e24 < z < 7.39999999999999994e56

   1. Initial program 99.8%

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

      1. *-commutative 99.8%

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

      2. clear-num 99.6%

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

      3. un-div-inv 99.8%

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

   3. Applied egg-rr 99.8%

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

   4. Taylor expanded in z around 0 98.8%

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

      1. mul-1-neg 98.8%

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

      2. associate-*r/ 98.7%

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

      3. unsub-neg 98.7%

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

      4. associate-*r/ 98.8%

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

   6. Simplified 98.8%

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

4. Final simplification 86.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -95:\\ \;\;\;\;t + \frac{x}{y} \cdot z\\ \mathbf{elif}\;z \leq 2.25 \cdot 10^{-153}:\\ \;\;\;\;t - \frac{t}{\frac{y}{x}}\\ \mathbf{elif}\;z \leq 8 \cdot 10^{+24} \lor \neg \left(z \leq 7.4 \cdot 10^{+56}\right):\\ \;\;\;\;t + \frac{x}{y} \cdot z\\ \mathbf{else}:\\ \;\;\;\;t - \frac{x \cdot t}{y}\\ \end{array} \]

Alternative 6: 64.0% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;\frac{x}{y} \leq -6.6 \cdot 10^{-12} \lor \neg \left(\frac{x}{y} \leq 5.2 \cdot 10^{-7}\right):\\ \;\;\;\;\frac{x}{y} \cdot \left(-t\right)\\ \mathbf{else}:\\ \;\;\;\;t\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= (/ x y) -6.6e-12) (not (<= (/ x y) 5.2e-7))) (* (/ x y) (- t)) t))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (((x / y) <= -6.6e-12) || !((x / y) <= 5.2e-7)) {
		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) <= (-6.6d-12)) .or. (.not. ((x / y) <= 5.2d-7))) 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) <= -6.6e-12) || !((x / y) <= 5.2e-7)) {
		tmp = (x / y) * -t;
	} else {
		tmp = t;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if ((x / y) <= -6.6e-12) or not ((x / y) <= 5.2e-7):
		tmp = (x / y) * -t
	else:
		tmp = t
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((Float64(x / y) <= -6.6e-12) || !(Float64(x / y) <= 5.2e-7))
		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) <= -6.6e-12) || ~(((x / y) <= 5.2e-7)))
		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], -6.6e-12], N[Not[LessEqual[N[(x / y), $MachinePrecision], 5.2e-7]], $MachinePrecision]], N[(N[(x / y), $MachinePrecision] * (-t)), $MachinePrecision], t]

Derivation

1. Split input into 2 regimes

2. if (/.f64 x y) < -6.6000000000000001e-12 or 5.19999999999999998e-7 < (/.f64 x y)

   1. Initial program 98.0%

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

   2. Taylor expanded in x around 0 91.3%

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

      1. *-commutative 91.3%

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

      2. associate-*r/ 91.9%

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

   4. Simplified 91.9%

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

      1. clear-num 91.8%

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

      2. associate-/r/ 91.8%

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

   6. Applied egg-rr 91.8%

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

   7. Taylor expanded in t around -inf 54.0%

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

      1. associate-*r* 54.0%

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

      2. neg-mul-1 54.0%

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

      3. sub-neg 54.0%

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

      4. metadata-eval 54.0%

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

   9. Simplified 54.0%

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

   10. Taylor expanded in x around inf 53.6%

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

   if -6.6000000000000001e-12 < (/.f64 x y) < 5.19999999999999998e-7

   1. Initial program 98.2%

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

   2. Taylor expanded in x around 0 74.8%

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

4. Final simplification 62.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{x}{y} \leq -6.6 \cdot 10^{-12} \lor \neg \left(\frac{x}{y} \leq 5.2 \cdot 10^{-7}\right):\\ \;\;\;\;\frac{x}{y} \cdot \left(-t\right)\\ \mathbf{else}:\\ \;\;\;\;t\\ \end{array} \]

Alternative 7: 93.0% 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 98.1%

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

2. Taylor expanded in x around 0 90.9%

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

   1. *-commutative 90.9%

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

   2. associate-*r/ 92.2%

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

4. Simplified 92.2%

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

5. Final simplification 92.2%

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

Alternative 8: 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 98.1%

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

2. Taylor expanded in x around 0 32.5%

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

3. Final simplification 32.5%

   \[\leadsto t \]

Developer target: 97.4% 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 2023199 
(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))