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

Percentage Accurate: 97.8% → 97.8%

Time: 6.5s

Alternatives: 6

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: 97.8% 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: 97.8% 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 98.4%

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

3. Final simplification 98.4%

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

Alternative 2: 83.9% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -40000000000 \lor \neg \left(t \leq 5.5 \cdot 10^{+80}\right):\\ \;\;\;\;t \cdot \left(1 - \frac{x}{y}\right)\\ \mathbf{else}:\\ \;\;\;\;t + x \cdot \frac{z}{y}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= t -40000000000.0) (not (<= t 5.5e+80)))
   (* t (- 1.0 (/ x y)))
   (+ t (* x (/ z y)))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((t <= -40000000000.0) || !(t <= 5.5e+80)) {
		tmp = t * (1.0 - (x / y));
	} else {
		tmp = t + (x * (z / y));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if ((t <= (-40000000000.0d0)) .or. (.not. (t <= 5.5d+80))) then
        tmp = t * (1.0d0 - (x / y))
    else
        tmp = t + (x * (z / y))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if ((t <= -40000000000.0) || !(t <= 5.5e+80)) {
		tmp = t * (1.0 - (x / y));
	} else {
		tmp = t + (x * (z / y));
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (t <= -40000000000.0) or not (t <= 5.5e+80):
		tmp = t * (1.0 - (x / y))
	else:
		tmp = t + (x * (z / y))
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((t <= -40000000000.0) || !(t <= 5.5e+80))
		tmp = Float64(t * Float64(1.0 - Float64(x / y)));
	else
		tmp = Float64(t + Float64(x * Float64(z / y)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((t <= -40000000000.0) || ~((t <= 5.5e+80)))
		tmp = t * (1.0 - (x / y));
	else
		tmp = t + (x * (z / y));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[t, -40000000000.0], N[Not[LessEqual[t, 5.5e+80]], $MachinePrecision]], N[(t * N[(1.0 - N[(x / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(t + N[(x * N[(z / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if t < -4e10 or 5.49999999999999967e80 < t

   1. Initial program 99.9%

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

      1. associate-*l/ 89.9%

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

      2. associate-/l* 88.2%

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

      3. fma-define 88.2%

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

   3. Simplified 88.2%

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

   5. Taylor expanded in z around 0 82.0%

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

      1. mul-1-neg 82.0%

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

      2. *-rgt-identity 82.0%

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

      3. associate-/l* 90.4%

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

      4. distribute-rgt-neg-in 90.4%

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

      5. mul-1-neg 90.4%

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

      6. distribute-lft-in 90.4%

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

      7. mul-1-neg 90.4%

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

      8. unsub-neg 90.4%

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

   7. Simplified 90.4%

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

   if -4e10 < t < 5.49999999999999967e80

   1. Initial program 97.1%

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

   3. Taylor expanded in z around inf 82.4%

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

      1. associate-/l* 83.5%

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

   5. Simplified 83.5%

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

4. Final simplification 86.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -40000000000 \lor \neg \left(t \leq 5.5 \cdot 10^{+80}\right):\\ \;\;\;\;t \cdot \left(1 - \frac{x}{y}\right)\\ \mathbf{else}:\\ \;\;\;\;t + x \cdot \frac{z}{y}\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 85.7% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -530000000 \lor \neg \left(t \leq 8 \cdot 10^{+80}\right):\\ \;\;\;\;t \cdot \left(1 - \frac{x}{y}\right)\\ \mathbf{else}:\\ \;\;\;\;t + \frac{x}{y} \cdot z\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= t -530000000.0) (not (<= t 8e+80)))
   (* t (- 1.0 (/ x y)))
   (+ t (* (/ x y) z))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((t <= -530000000.0) || !(t <= 8e+80)) {
		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 <= (-530000000.0d0)) .or. (.not. (t <= 8d+80))) 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 <= -530000000.0) || !(t <= 8e+80)) {
		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 <= -530000000.0) or not (t <= 8e+80):
		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 <= -530000000.0) || !(t <= 8e+80))
		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 <= -530000000.0) || ~((t <= 8e+80)))
		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, -530000000.0], N[Not[LessEqual[t, 8e+80]], $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 < -5.3e8 or 8e80 < t

   1. Initial program 99.9%

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

      1. associate-*l/ 89.9%

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

      2. associate-/l* 88.2%

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

      3. fma-define 88.2%

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

   3. Simplified 88.2%

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

   5. Taylor expanded in z around 0 82.0%

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

      1. mul-1-neg 82.0%

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

      2. *-rgt-identity 82.0%

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

      3. associate-/l* 90.4%

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

      4. distribute-rgt-neg-in 90.4%

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

      5. mul-1-neg 90.4%

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

      6. distribute-lft-in 90.4%

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

      7. mul-1-neg 90.4%

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

      8. unsub-neg 90.4%

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

   7. Simplified 90.4%

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

   if -5.3e8 < t < 8e80

   1. Initial program 97.1%

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

   3. Taylor expanded in x around 0 95.3%

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

   4. Taylor expanded in z around inf 82.4%

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

      1. associate-*l/ 86.2%

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

      2. *-commutative 86.2%

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

   6. Simplified 86.2%

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

4. Final simplification 88.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -530000000 \lor \neg \left(t \leq 8 \cdot 10^{+80}\right):\\ \;\;\;\;t \cdot \left(1 - \frac{x}{y}\right)\\ \mathbf{else}:\\ \;\;\;\;t + \frac{x}{y} \cdot z\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 85.8% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -12000000000 \lor \neg \left(t \leq 6 \cdot 10^{+80}\right):\\ \;\;\;\;t - \frac{x}{y} \cdot t\\ \mathbf{else}:\\ \;\;\;\;t + \frac{x}{y} \cdot z\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= t -12000000000.0) (not (<= t 6e+80)))
   (- t (* (/ x y) t))
   (+ t (* (/ x y) z))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((t <= -12000000000.0) || !(t <= 6e+80)) {
		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 <= (-12000000000.0d0)) .or. (.not. (t <= 6d+80))) 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 <= -12000000000.0) || !(t <= 6e+80)) {
		tmp = t - ((x / y) * t);
	} else {
		tmp = t + ((x / y) * z);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (t <= -12000000000.0) or not (t <= 6e+80):
		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 <= -12000000000.0) || !(t <= 6e+80))
		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 <= -12000000000.0) || ~((t <= 6e+80)))
		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, -12000000000.0], N[Not[LessEqual[t, 6e+80]], $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 < -1.2e10 or 5.99999999999999974e80 < t

   1. Initial program 99.9%

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

   3. Taylor expanded in z around 0 82.0%

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

      1. associate-*r/ 82.0%

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

      2. mul-1-neg 82.0%

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

      3. *-commutative 82.0%

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

      4. distribute-rgt-neg-out 82.0%

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

      5. associate-/l* 78.7%

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

      6. distribute-neg-frac 78.7%

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

      7. distribute-neg-frac2 78.7%

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

   5. Simplified 78.7%

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

   6. Taylor expanded in x around 0 82.0%

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

      1. associate-/l* 90.4%

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

      2. associate-*r* 90.4%

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

      3. neg-mul-1 90.4%

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

      4. cancel-sign-sub-inv 90.4%

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

   8. Simplified 90.4%

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

   if -1.2e10 < t < 5.99999999999999974e80

   1. Initial program 97.1%

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

   3. Taylor expanded in x around 0 95.3%

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

   4. Taylor expanded in z around inf 82.4%

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

      1. associate-*l/ 86.2%

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

      2. *-commutative 86.2%

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

   6. Simplified 86.2%

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

4. Final simplification 88.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -12000000000 \lor \neg \left(t \leq 6 \cdot 10^{+80}\right):\\ \;\;\;\;t - \frac{x}{y} \cdot t\\ \mathbf{else}:\\ \;\;\;\;t + \frac{x}{y} \cdot z\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 66.1% accurate, 1.3× speedup

Math

\[\begin{array}{l} \\ t \cdot \left(1 - \frac{x}{y}\right) \end{array} \]

FPCore

(FPCore (x y z t) :precision binary64 (* t (- 1.0 (/ x y))))

C

double code(double x, double y, double z, double t) {
	return t * (1.0 - (x / y));
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    code = t * (1.0d0 - (x / y))
end function

Java

public static double code(double x, double y, double z, double t) {
	return t * (1.0 - (x / y));
}

Python

def code(x, y, z, t):
	return t * (1.0 - (x / y))

Julia

function code(x, y, z, t)
	return Float64(t * Float64(1.0 - Float64(x / y)))
end

MATLAB

function tmp = code(x, y, z, t)
	tmp = t * (1.0 - (x / y));
end

Wolfram

code[x_, y_, z_, t_] := N[(t * N[(1.0 - N[(x / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]

Derivation

1. Initial program 98.4%

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

   1. associate-*l/ 92.9%

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

   2. associate-/l* 92.5%

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

   3. fma-define 92.5%

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

3. Simplified 92.5%

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

5. Taylor expanded in z around 0 59.2%

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

   1. mul-1-neg 59.2%

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

   2. *-rgt-identity 59.2%

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

   3. associate-/l* 63.3%

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

   4. distribute-rgt-neg-in 63.3%

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

   5. mul-1-neg 63.3%

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

   6. distribute-lft-in 63.3%

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

   7. mul-1-neg 63.3%

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

   8. unsub-neg 63.3%

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

7. Simplified 63.3%

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

8. Final simplification 63.3%

   \[\leadsto t \cdot \left(1 - \frac{x}{y}\right) \]
9. Add Preprocessing

Alternative 6: 39.3% 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 98.4%

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

   1. associate-*l/ 92.9%

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

   2. associate-/l* 92.5%

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

   3. fma-define 92.5%

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

3. Simplified 92.5%

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

5. Taylor expanded in x around 0 32.4%

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

6. Final simplification 32.4%

   \[\leadsto t \]
7. Add Preprocessing

Developer target: 97.6% 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 2024115 
(FPCore (x y z t)
  :name "Numeric.Signal.Multichannel:$cget from hsignal-0.2.7.1"
  :precision binary64

  :alt
  (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))