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

Percentage Accurate: 98.0% → 98.1%

Time: 6.6s

Alternatives: 8

Speedup: 1.1×

• 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: 98.0% 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: 98.1% accurate, 0.8× speedup

Math

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

FPCore

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

C

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 97.9%

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

   1. lift-*.f64 N/A

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

   2. *-commutative N/A

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

   3. lift-/.f64 N/A

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

   4. clear-num N/A

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

   5. un-div-inv N/A

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

   6. lower-/.f64 N/A

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

   7. lower-/.f64 98.0

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

4. Applied rewrites 98.0%

   \[\leadsto \color{blue}{\frac{z - t}{\frac{y}{x}}} + t \]
5. Add Preprocessing

Alternative 2: 84.1% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;\frac{x}{y} \leq -4000000000000 \lor \neg \left(\frac{x}{y} \leq 10^{-8}\right):\\ \;\;\;\;\frac{z - t}{y} \cdot x\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(\frac{x}{y}, -t, t\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= (/ x y) -4000000000000.0) (not (<= (/ x y) 1e-8)))
   (* (/ (- z t) y) x)
   (fma (/ x y) (- t) t)))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (((x / y) <= -4000000000000.0) || !((x / y) <= 1e-8)) {
		tmp = ((z - t) / y) * x;
	} else {
		tmp = fma((x / y), -t, t);
	}
	return tmp;
}

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((Float64(x / y) <= -4000000000000.0) || !(Float64(x / y) <= 1e-8))
		tmp = Float64(Float64(Float64(z - t) / y) * x);
	else
		tmp = fma(Float64(x / y), Float64(-t), t);
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[N[(x / y), $MachinePrecision], -4000000000000.0], N[Not[LessEqual[N[(x / y), $MachinePrecision], 1e-8]], $MachinePrecision]], N[(N[(N[(z - t), $MachinePrecision] / y), $MachinePrecision] * x), $MachinePrecision], N[(N[(x / y), $MachinePrecision] * (-t) + t), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if (/.f64 x y) < -4e12 or 1e-8 < (/.f64 x y)

   1. Initial program 97.1%

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

   3. Taylor expanded in x around inf

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

      1. div-sub N/A

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

      2. associate-/l* N/A

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

      3. lower-/.f64 N/A

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

      4. *-commutative N/A

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

      5. lower-*.f64 N/A

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

      6. lower--.f64 90.7

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

   5. Applied rewrites 90.7%

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

   7. Applied rewrites 94.2%

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

   if -4e12 < (/.f64 x y) < 1e-8

   1. Initial program 98.8%

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

      1. lift-+.f64 N/A

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

      2. lift-*.f64 N/A

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

      3. lower-fma.f64 98.8

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

   4. Applied rewrites 98.8%

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

   5. Taylor expanded in z around 0

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

      1. mul-1-neg N/A

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

      2. lower-neg.f64 80.6

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

   7. Applied rewrites 80.6%

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

4. Final simplification 87.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{x}{y} \leq -4000000000000 \lor \neg \left(\frac{x}{y} \leq 10^{-8}\right):\\ \;\;\;\;\frac{z - t}{y} \cdot x\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(\frac{x}{y}, -t, t\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 84.1% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;\frac{x}{y} \leq -4000000000000 \lor \neg \left(\frac{x}{y} \leq 10^{-8}\right):\\ \;\;\;\;\frac{z - t}{y} \cdot x\\ \mathbf{else}:\\ \;\;\;\;t - \frac{x}{y} \cdot t\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= (/ x y) -4000000000000.0) (not (<= (/ x y) 1e-8)))
   (* (/ (- z t) y) x)
   (- t (* (/ x y) t))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (((x / y) <= -4000000000000.0) || !((x / y) <= 1e-8)) {
		tmp = ((z - t) / y) * x;
	} 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 (((x / y) <= (-4000000000000.0d0)) .or. (.not. ((x / y) <= 1d-8))) then
        tmp = ((z - t) / y) * x
    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 (((x / y) <= -4000000000000.0) || !((x / y) <= 1e-8)) {
		tmp = ((z - t) / y) * x;
	} else {
		tmp = t - ((x / y) * t);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if ((x / y) <= -4000000000000.0) or not ((x / y) <= 1e-8):
		tmp = ((z - t) / y) * x
	else:
		tmp = t - ((x / y) * t)
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((Float64(x / y) <= -4000000000000.0) || !(Float64(x / y) <= 1e-8))
		tmp = Float64(Float64(Float64(z - t) / y) * x);
	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 (((x / y) <= -4000000000000.0) || ~(((x / y) <= 1e-8)))
		tmp = ((z - t) / y) * x;
	else
		tmp = t - ((x / y) * t);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[N[(x / y), $MachinePrecision], -4000000000000.0], N[Not[LessEqual[N[(x / y), $MachinePrecision], 1e-8]], $MachinePrecision]], N[(N[(N[(z - t), $MachinePrecision] / y), $MachinePrecision] * x), $MachinePrecision], N[(t - N[(N[(x / y), $MachinePrecision] * t), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if (/.f64 x y) < -4e12 or 1e-8 < (/.f64 x y)

   1. Initial program 97.1%

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

   3. Taylor expanded in x around inf

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

      1. div-sub N/A

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

      2. associate-/l* N/A

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

      3. lower-/.f64 N/A

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

      4. *-commutative N/A

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

      5. lower-*.f64 N/A

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

      6. lower--.f64 90.7

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

   5. Applied rewrites 90.7%

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

   7. Applied rewrites 94.2%

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

   if -4e12 < (/.f64 x y) < 1e-8

   1. Initial program 98.8%

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

   3. Taylor expanded in z around 0

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

      1. mul-1-neg N/A

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

      2. unsub-neg N/A

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

      3. lower--.f64 N/A

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

      4. *-commutative N/A

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

      5. associate-*l/ N/A

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

      6. lower-*.f64 N/A

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

      7. lower-/.f64 80.6

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

   5. Applied rewrites 80.6%

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

4. Final simplification 87.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{x}{y} \leq -4000000000000 \lor \neg \left(\frac{x}{y} \leq 10^{-8}\right):\\ \;\;\;\;\frac{z - t}{y} \cdot x\\ \mathbf{else}:\\ \;\;\;\;t - \frac{x}{y} \cdot t\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 47.8% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -4200000000:\\ \;\;\;\;\frac{z}{y} \cdot x\\ \mathbf{elif}\;z \leq 3.8 \cdot 10^{-21}:\\ \;\;\;\;\frac{-x}{y} \cdot t\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{y} \cdot z\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= z -4200000000.0)
   (* (/ z y) x)
   (if (<= z 3.8e-21) (* (/ (- x) y) t) (* (/ x y) z))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (z <= -4200000000.0) {
		tmp = (z / y) * x;
	} else if (z <= 3.8e-21) {
		tmp = (-x / y) * t;
	} else {
		tmp = (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 <= (-4200000000.0d0)) then
        tmp = (z / y) * x
    else if (z <= 3.8d-21) then
        tmp = (-x / y) * t
    else
        tmp = (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 <= -4200000000.0) {
		tmp = (z / y) * x;
	} else if (z <= 3.8e-21) {
		tmp = (-x / y) * t;
	} else {
		tmp = (x / y) * z;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if z <= -4200000000.0:
		tmp = (z / y) * x
	elif z <= 3.8e-21:
		tmp = (-x / y) * t
	else:
		tmp = (x / y) * z
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (z <= -4200000000.0)
		tmp = Float64(Float64(z / y) * x);
	elseif (z <= 3.8e-21)
		tmp = Float64(Float64(Float64(-x) / y) * t);
	else
		tmp = Float64(Float64(x / y) * z);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (z <= -4200000000.0)
		tmp = (z / y) * x;
	elseif (z <= 3.8e-21)
		tmp = (-x / y) * t;
	else
		tmp = (x / y) * z;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[z, -4200000000.0], N[(N[(z / y), $MachinePrecision] * x), $MachinePrecision], If[LessEqual[z, 3.8e-21], N[(N[((-x) / y), $MachinePrecision] * t), $MachinePrecision], N[(N[(x / y), $MachinePrecision] * z), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if z < -4.2e9

   1. Initial program 98.6%

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

   3. Taylor expanded in z around inf

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

      1. associate-*l/ N/A

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

      2. lower-*.f64 N/A

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

      3. lower-/.f64 65.1

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

   5. Applied rewrites 65.1%

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

   7. Applied rewrites 65.1%

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

   if -4.2e9 < z < 3.7999999999999998e-21

   1. Initial program 96.6%

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

   3. Taylor expanded in z around 0

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

      1. mul-1-neg N/A

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

      2. unsub-neg N/A

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

      3. lower--.f64 N/A

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

      4. *-commutative N/A

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

      5. associate-*l/ N/A

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

      6. lower-*.f64 N/A

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

      7. lower-/.f64 89.3

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

   5. Applied rewrites 89.3%

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

   6. Taylor expanded in x around inf

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

   8. Applied rewrites 38.7%

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

   10. Applied rewrites 41.3%

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

   if 3.7999999999999998e-21 < z

   1. Initial program 99.3%

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

   3. Taylor expanded in z around inf

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

      1. associate-*l/ N/A

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

      2. lower-*.f64 N/A

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

      3. lower-/.f64 66.0

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

   5. Applied rewrites 66.0%

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

Alternative 5: 47.0% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -4200000000:\\ \;\;\;\;\frac{z}{y} \cdot x\\ \mathbf{elif}\;z \leq 3.8 \cdot 10^{-21}:\\ \;\;\;\;\frac{-t}{y} \cdot x\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{y} \cdot z\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= z -4200000000.0)
   (* (/ z y) x)
   (if (<= z 3.8e-21) (* (/ (- t) y) x) (* (/ x y) z))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (z <= -4200000000.0) {
		tmp = (z / y) * x;
	} else if (z <= 3.8e-21) {
		tmp = (-t / y) * x;
	} else {
		tmp = (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 <= (-4200000000.0d0)) then
        tmp = (z / y) * x
    else if (z <= 3.8d-21) then
        tmp = (-t / y) * x
    else
        tmp = (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 <= -4200000000.0) {
		tmp = (z / y) * x;
	} else if (z <= 3.8e-21) {
		tmp = (-t / y) * x;
	} else {
		tmp = (x / y) * z;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if z <= -4200000000.0:
		tmp = (z / y) * x
	elif z <= 3.8e-21:
		tmp = (-t / y) * x
	else:
		tmp = (x / y) * z
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (z <= -4200000000.0)
		tmp = Float64(Float64(z / y) * x);
	elseif (z <= 3.8e-21)
		tmp = Float64(Float64(Float64(-t) / y) * x);
	else
		tmp = Float64(Float64(x / y) * z);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (z <= -4200000000.0)
		tmp = (z / y) * x;
	elseif (z <= 3.8e-21)
		tmp = (-t / y) * x;
	else
		tmp = (x / y) * z;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[z, -4200000000.0], N[(N[(z / y), $MachinePrecision] * x), $MachinePrecision], If[LessEqual[z, 3.8e-21], N[(N[((-t) / y), $MachinePrecision] * x), $MachinePrecision], N[(N[(x / y), $MachinePrecision] * z), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if z < -4.2e9

   1. Initial program 98.6%

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

   3. Taylor expanded in z around inf

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

      1. associate-*l/ N/A

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

      2. lower-*.f64 N/A

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

      3. lower-/.f64 65.1

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

   5. Applied rewrites 65.1%

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

   7. Applied rewrites 65.1%

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

   if -4.2e9 < z < 3.7999999999999998e-21

   1. Initial program 96.6%

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

   3. Taylor expanded in z around 0

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

      1. mul-1-neg N/A

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

      2. unsub-neg N/A

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

      3. lower--.f64 N/A

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

      4. *-commutative N/A

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

      5. associate-*l/ N/A

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

      6. lower-*.f64 N/A

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

      7. lower-/.f64 89.3

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

   5. Applied rewrites 89.3%

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

   6. Taylor expanded in x around inf

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

   8. Applied rewrites 38.7%

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

   if 3.7999999999999998e-21 < z

   1. Initial program 99.3%

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

   3. Taylor expanded in z around inf

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

      1. associate-*l/ N/A

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

      2. lower-*.f64 N/A

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

      3. lower-/.f64 66.0

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

   5. Applied rewrites 66.0%

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

Alternative 6: 98.0% accurate, 1.1× speedup

Math

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

FPCore

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

C

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

Julia

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

Wolfram

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

Derivation

1. Initial program 97.9%

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

   1. lift-+.f64 N/A

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

   2. lift-*.f64 N/A

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

   3. lower-fma.f64 97.9

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

4. Applied rewrites 97.9%

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

Alternative 7: 57.5% accurate, 1.2× speedup

Math

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

FPCore

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

C

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

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 = ((z - t) / y) * x
end function

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 97.9%

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

3. Taylor expanded in x around inf

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

   1. div-sub N/A

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

   2. associate-/l* N/A

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

   3. lower-/.f64 N/A

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

   4. *-commutative N/A

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

   5. lower-*.f64 N/A

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

   6. lower--.f64 55.7

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

5. Applied rewrites 55.7%

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

7. Applied rewrites 59.0%

   \[\leadsto \color{blue}{\frac{z - t}{y} \cdot x} \]
8. Add Preprocessing

Alternative 8: 40.4% accurate, 1.4× speedup

Math

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

FPCore

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

C

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 97.9%

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

3. Taylor expanded in z around inf

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

   1. associate-*l/ N/A

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

   2. lower-*.f64 N/A

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

   3. lower-/.f64 42.6

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

5. Applied rewrites 42.6%

   \[\leadsto \color{blue}{\frac{x}{y} \cdot z} \]
6. Add Preprocessing

Developer Target 1: 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 2024324 
(FPCore (x y z t)
  :name "Numeric.Signal.Multichannel:$cget from hsignal-0.2.7.1"
  :precision binary64

  :alt
  (! :herbie-platform default (if (< z 689864138640673/250000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000) (+ (* (/ x y) (- z t)) t) (if (< z 581748612718609/25000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000) (+ (* x (/ (- z t) y)) t) (+ (* (/ x y) (- z t)) t))))

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