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

Percentage Accurate: 97.9% → 98.2%

Time: 7.3s

Alternatives: 8

Speedup: 1.1×

• 24.9% 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: 98.2% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq 2 \cdot 10^{-65}:\\ \;\;\;\;\mathsf{fma}\left(\frac{x}{y}, z - t, t\right)\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(\frac{z - t}{y}, x, t\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= x 2e-65) (fma (/ x y) (- z t) t) (fma (/ (- z t) y) x t)))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (x <= 2e-65) {
		tmp = fma((x / y), (z - t), t);
	} else {
		tmp = fma(((z - t) / y), x, t);
	}
	return tmp;
}

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (x <= 2e-65)
		tmp = fma(Float64(x / y), Float64(z - t), t);
	else
		tmp = fma(Float64(Float64(z - t) / y), x, t);
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[x, 2e-65], N[(N[(x / y), $MachinePrecision] * N[(z - t), $MachinePrecision] + t), $MachinePrecision], N[(N[(N[(z - t), $MachinePrecision] / y), $MachinePrecision] * x + t), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < 1.99999999999999985e-65

   1. Initial program 98.7%

      \[\frac{x}{y} \cdot \left(z - t\right) + t \]
   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 98.7

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

   4. Applied rewrites 98.7%

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

   if 1.99999999999999985e-65 < x

   1. Initial program 93.7%

      \[\frac{x}{y} \cdot \left(z - t\right) + t \]
   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. lift-/.f64 N/A

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

      4. associate-*l/ N/A

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

      5. associate-/l* N/A

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

      6. *-commutative N/A

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

      7. lower-fma.f64 N/A

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

      8. lower-/.f64 99.8

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

   4. Applied rewrites 99.8%

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

Alternative 2: 92.5% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x \cdot \frac{z - t}{y}\\ \mathbf{if}\;\frac{x}{y} \leq -1 \cdot 10^{+16}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;\frac{x}{y} \leq 0.0001:\\ \;\;\;\;t + \frac{x \cdot z}{y}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (* x (/ (- z t) y))))
   (if (<= (/ x y) -1e+16)
     t_1
     (if (<= (/ x y) 0.0001) (+ t (/ (* x z) y)) t_1))))

C

double code(double x, double y, double z, double t) {
	double t_1 = x * ((z - t) / y);
	double tmp;
	if ((x / y) <= -1e+16) {
		tmp = t_1;
	} else if ((x / y) <= 0.0001) {
		tmp = t + ((x * z) / y);
	} 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 * ((z - t) / y)
    if ((x / y) <= (-1d+16)) then
        tmp = t_1
    else if ((x / y) <= 0.0001d0) then
        tmp = t + ((x * z) / y)
    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 * ((z - t) / y);
	double tmp;
	if ((x / y) <= -1e+16) {
		tmp = t_1;
	} else if ((x / y) <= 0.0001) {
		tmp = t + ((x * z) / y);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = x * ((z - t) / y)
	tmp = 0
	if (x / y) <= -1e+16:
		tmp = t_1
	elif (x / y) <= 0.0001:
		tmp = t + ((x * z) / y)
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(x * Float64(Float64(z - t) / y))
	tmp = 0.0
	if (Float64(x / y) <= -1e+16)
		tmp = t_1;
	elseif (Float64(x / y) <= 0.0001)
		tmp = Float64(t + Float64(Float64(x * z) / y));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = x * ((z - t) / y);
	tmp = 0.0;
	if ((x / y) <= -1e+16)
		tmp = t_1;
	elseif ((x / y) <= 0.0001)
		tmp = t + ((x * z) / y);
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(x * N[(N[(z - t), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[N[(x / y), $MachinePrecision], -1e+16], t$95$1, If[LessEqual[N[(x / y), $MachinePrecision], 0.0001], N[(t + N[(N[(x * z), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if (/.f64 x y) < -1e16 or 1.00000000000000005e-4 < (/.f64 x y)

   1. Initial program 95.2%

      \[\frac{x}{y} \cdot \left(z - t\right) + t \]
   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. lower-*.f64 N/A

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

      5. lower--.f64 89.8

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

   5. Applied rewrites 89.8%

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

   7. Applied rewrites 91.7%

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

   if -1e16 < (/.f64 x y) < 1.00000000000000005e-4

   1. Initial program 99.0%

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

   3. Taylor expanded in z around inf

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

      1. lower-/.f64 N/A

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

      2. lower-*.f64 95.6

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

   5. Applied rewrites 95.6%

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

4. Final simplification 93.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{x}{y} \leq -1 \cdot 10^{+16}:\\ \;\;\;\;x \cdot \frac{z - t}{y}\\ \mathbf{elif}\;\frac{x}{y} \leq 0.0001:\\ \;\;\;\;t + \frac{x \cdot z}{y}\\ \mathbf{else}:\\ \;\;\;\;x \cdot \frac{z - t}{y}\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 81.7% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x \cdot \frac{z - t}{y}\\ \mathbf{if}\;\frac{x}{y} \leq -2 \cdot 10^{-29}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;\frac{x}{y} \leq 0.0001:\\ \;\;\;\;t - \frac{x \cdot t}{y}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (* x (/ (- z t) y))))
   (if (<= (/ x y) -2e-29)
     t_1
     (if (<= (/ x y) 0.0001) (- t (/ (* x t) y)) t_1))))

C

double code(double x, double y, double z, double t) {
	double t_1 = x * ((z - t) / y);
	double tmp;
	if ((x / y) <= -2e-29) {
		tmp = t_1;
	} else if ((x / y) <= 0.0001) {
		tmp = t - ((x * t) / y);
	} 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 * ((z - t) / y)
    if ((x / y) <= (-2d-29)) then
        tmp = t_1
    else if ((x / y) <= 0.0001d0) then
        tmp = t - ((x * t) / y)
    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 * ((z - t) / y);
	double tmp;
	if ((x / y) <= -2e-29) {
		tmp = t_1;
	} else if ((x / y) <= 0.0001) {
		tmp = t - ((x * t) / y);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = x * ((z - t) / y)
	tmp = 0
	if (x / y) <= -2e-29:
		tmp = t_1
	elif (x / y) <= 0.0001:
		tmp = t - ((x * t) / y)
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(x * Float64(Float64(z - t) / y))
	tmp = 0.0
	if (Float64(x / y) <= -2e-29)
		tmp = t_1;
	elseif (Float64(x / y) <= 0.0001)
		tmp = Float64(t - Float64(Float64(x * t) / y));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = x * ((z - t) / y);
	tmp = 0.0;
	if ((x / y) <= -2e-29)
		tmp = t_1;
	elseif ((x / y) <= 0.0001)
		tmp = t - ((x * t) / y);
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(x * N[(N[(z - t), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[N[(x / y), $MachinePrecision], -2e-29], t$95$1, If[LessEqual[N[(x / y), $MachinePrecision], 0.0001], N[(t - N[(N[(x * t), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if (/.f64 x y) < -1.99999999999999989e-29 or 1.00000000000000005e-4 < (/.f64 x y)

   1. Initial program 95.5%

      \[\frac{x}{y} \cdot \left(z - t\right) + t \]
   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. lower-*.f64 N/A

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

      5. lower--.f64 88.4

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

   5. Applied rewrites 88.4%

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

   7. Applied rewrites 89.5%

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

   if -1.99999999999999989e-29 < (/.f64 x y) < 1.00000000000000005e-4

   1. Initial program 99.0%

      \[\frac{x}{y} \cdot \left(z - t\right) + t \]
   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. lower-/.f64 N/A

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

      5. lower-*.f64 77.0

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

   5. Applied rewrites 77.0%

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

4. Final simplification 83.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{x}{y} \leq -2 \cdot 10^{-29}:\\ \;\;\;\;x \cdot \frac{z - t}{y}\\ \mathbf{elif}\;\frac{x}{y} \leq 0.0001:\\ \;\;\;\;t - \frac{x \cdot t}{y}\\ \mathbf{else}:\\ \;\;\;\;x \cdot \frac{z - t}{y}\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 49.4% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -1.38 \cdot 10^{+146}:\\ \;\;\;\;\frac{x \cdot \left(-t\right)}{y}\\ \mathbf{elif}\;t \leq 1.2 \cdot 10^{+74}:\\ \;\;\;\;\frac{x}{y} \cdot z\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{y} \cdot \left(-t\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= t -1.38e+146)
   (/ (* x (- t)) y)
   (if (<= t 1.2e+74) (* (/ x y) z) (* (/ x y) (- t)))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (t <= -1.38e+146) {
		tmp = (x * -t) / y;
	} else if (t <= 1.2e+74) {
		tmp = (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 (t <= (-1.38d+146)) then
        tmp = (x * -t) / y
    else if (t <= 1.2d+74) then
        tmp = (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 (t <= -1.38e+146) {
		tmp = (x * -t) / y;
	} else if (t <= 1.2e+74) {
		tmp = (x / y) * z;
	} else {
		tmp = (x / y) * -t;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if t <= -1.38e+146:
		tmp = (x * -t) / y
	elif t <= 1.2e+74:
		tmp = (x / y) * z
	else:
		tmp = (x / y) * -t
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (t <= -1.38e+146)
		tmp = Float64(Float64(x * Float64(-t)) / y);
	elseif (t <= 1.2e+74)
		tmp = 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 (t <= -1.38e+146)
		tmp = (x * -t) / y;
	elseif (t <= 1.2e+74)
		tmp = (x / y) * z;
	else
		tmp = (x / y) * -t;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[t, -1.38e+146], N[(N[(x * (-t)), $MachinePrecision] / y), $MachinePrecision], If[LessEqual[t, 1.2e+74], N[(N[(x / y), $MachinePrecision] * z), $MachinePrecision], N[(N[(x / y), $MachinePrecision] * (-t)), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if t < -1.38e146

   1. Initial program 100.0%

      \[\frac{x}{y} \cdot \left(z - t\right) + t \]
   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. lower-*.f64 N/A

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

      5. lower--.f64 54.1

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

   5. Applied rewrites 54.1%

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

   6. Taylor expanded in z around 0

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

   8. Applied rewrites 54.0%

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

   if -1.38e146 < t < 1.20000000000000004e74

   1. Initial program 95.8%

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

   3. Taylor expanded in z around inf

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

      1. lower-/.f64 N/A

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

      2. lower-*.f64 44.9

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

   5. Applied rewrites 44.9%

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

   7. Applied rewrites 49.2%

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

   if 1.20000000000000004e74 < t

   1. Initial program 99.9%

      \[\frac{x}{y} \cdot \left(z - t\right) + t \]
   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. lower-*.f64 N/A

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

      5. lower--.f64 50.9

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

   5. Applied rewrites 50.9%

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

   6. Taylor expanded in z around 0

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

   8. Applied rewrites 48.5%

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

   10. Applied rewrites 55.9%

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

Alternative 5: 49.7% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{x}{y} \cdot \left(-t\right)\\ \mathbf{if}\;t \leq -1.38 \cdot 10^{+146}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t \leq 1.2 \cdot 10^{+74}:\\ \;\;\;\;\frac{x}{y} \cdot z\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (* (/ x y) (- t))))
   (if (<= t -1.38e+146) t_1 (if (<= t 1.2e+74) (* (/ x y) z) t_1))))

C

double code(double x, double y, double z, double t) {
	double t_1 = (x / y) * -t;
	double tmp;
	if (t <= -1.38e+146) {
		tmp = t_1;
	} else if (t <= 1.2e+74) {
		tmp = (x / y) * z;
	} 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) * -t
    if (t <= (-1.38d+146)) then
        tmp = t_1
    else if (t <= 1.2d+74) then
        tmp = (x / y) * z
    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) * -t;
	double tmp;
	if (t <= -1.38e+146) {
		tmp = t_1;
	} else if (t <= 1.2e+74) {
		tmp = (x / y) * z;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = (x / y) * -t
	tmp = 0
	if t <= -1.38e+146:
		tmp = t_1
	elif t <= 1.2e+74:
		tmp = (x / y) * z
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(Float64(x / y) * Float64(-t))
	tmp = 0.0
	if (t <= -1.38e+146)
		tmp = t_1;
	elseif (t <= 1.2e+74)
		tmp = Float64(Float64(x / y) * z);
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = (x / y) * -t;
	tmp = 0.0;
	if (t <= -1.38e+146)
		tmp = t_1;
	elseif (t <= 1.2e+74)
		tmp = (x / y) * z;
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(N[(x / y), $MachinePrecision] * (-t)), $MachinePrecision]}, If[LessEqual[t, -1.38e+146], t$95$1, If[LessEqual[t, 1.2e+74], N[(N[(x / y), $MachinePrecision] * z), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if t < -1.38e146 or 1.20000000000000004e74 < t

   1. Initial program 99.9%

      \[\frac{x}{y} \cdot \left(z - t\right) + t \]
   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. lower-*.f64 N/A

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

      5. lower--.f64 51.9

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

   5. Applied rewrites 51.9%

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

   6. Taylor expanded in z around 0

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

   8. Applied rewrites 50.3%

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

   10. Applied rewrites 54.2%

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

   if -1.38e146 < t < 1.20000000000000004e74

   1. Initial program 95.8%

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

   3. Taylor expanded in z around inf

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

      1. lower-/.f64 N/A

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

      2. lower-*.f64 44.9

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

   5. Applied rewrites 44.9%

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

   7. Applied rewrites 49.2%

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

Alternative 6: 58.1% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq 1.8 \cdot 10^{+115}:\\ \;\;\;\;x \cdot \frac{z - t}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{y} \cdot \left(-t\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= t 1.8e+115) (* x (/ (- z t) y)) (* (/ x y) (- t))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (t <= 1.8e+115) {
		tmp = x * ((z - t) / y);
	} 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 (t <= 1.8d+115) then
        tmp = x * ((z - t) / y)
    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 (t <= 1.8e+115) {
		tmp = x * ((z - t) / y);
	} else {
		tmp = (x / y) * -t;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if t <= 1.8e+115:
		tmp = x * ((z - t) / y)
	else:
		tmp = (x / y) * -t
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (t <= 1.8e+115)
		tmp = Float64(x * Float64(Float64(z - t) / y));
	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 (t <= 1.8e+115)
		tmp = x * ((z - t) / y);
	else
		tmp = (x / y) * -t;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[t, 1.8e+115], N[(x * N[(N[(z - t), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision], N[(N[(x / y), $MachinePrecision] * (-t)), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if t < 1.8e115

   1. Initial program 96.5%

      \[\frac{x}{y} \cdot \left(z - t\right) + t \]
   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. lower-*.f64 N/A

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

      5. lower--.f64 54.8

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

   5. Applied rewrites 54.8%

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

   7. Applied rewrites 59.1%

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

   if 1.8e115 < t

   1. Initial program 100.0%

      \[\frac{x}{y} \cdot \left(z - t\right) + t \]
   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. lower-*.f64 N/A

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

      5. lower--.f64 53.3

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

   5. Applied rewrites 53.3%

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

   6. Taylor expanded in z around 0

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

   8. Applied rewrites 50.5%

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

   10. Applied rewrites 54.3%

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

4. Final simplification 58.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq 1.8 \cdot 10^{+115}:\\ \;\;\;\;x \cdot \frac{z - t}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{y} \cdot \left(-t\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 97.9% 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 97.2%

   \[\frac{x}{y} \cdot \left(z - t\right) + t \]
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 97.2

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

4. Applied rewrites 97.2%

   \[\leadsto \color{blue}{\mathsf{fma}\left(\frac{x}{y}, z - t, t\right)} \]
5. 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 97.2%

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

3. Taylor expanded in z around inf

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

   1. lower-/.f64 N/A

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

   2. lower-*.f64 34.6

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

5. Applied rewrites 34.6%

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

7. Applied rewrites 37.9%

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

Developer Target 1: 97.5% 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 2024233 
(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))