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

Percentage Accurate: 97.8% → 97.8%

Time: 7.6s

Alternatives: 9

Speedup: 1.1×

• 25.4% 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, 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 97.6%

   \[\frac{x}{y} \cdot \left(z - t\right) + t \]
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 97.7

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

4. Applied rewrites 97.7%

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

Alternative 2: 94.8% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{x}{y} \cdot \left(z - t\right)\\ \mathbf{if}\;\frac{x}{y} \leq -1 \cdot 10^{-15}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;\frac{x}{y} \leq 2 \cdot 10^{-16}:\\ \;\;\;\;\frac{x \cdot z}{y} + t\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (* (/ x y) (- z t))))
   (if (<= (/ x y) -1e-15)
     t_1
     (if (<= (/ x y) 2e-16) (+ (/ (* x z) y) t) t_1))))

C

double code(double x, double y, double z, double t) {
	double t_1 = (x / y) * (z - t);
	double tmp;
	if ((x / y) <= -1e-15) {
		tmp = t_1;
	} else if ((x / y) <= 2e-16) {
		tmp = ((x * z) / 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)
    if ((x / y) <= (-1d-15)) then
        tmp = t_1
    else if ((x / y) <= 2d-16) then
        tmp = ((x * z) / 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);
	double tmp;
	if ((x / y) <= -1e-15) {
		tmp = t_1;
	} else if ((x / y) <= 2e-16) {
		tmp = ((x * z) / y) + t;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = (x / y) * (z - t)
	tmp = 0
	if (x / y) <= -1e-15:
		tmp = t_1
	elif (x / y) <= 2e-16:
		tmp = ((x * z) / y) + t
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(Float64(x / y) * Float64(z - t))
	tmp = 0.0
	if (Float64(x / y) <= -1e-15)
		tmp = t_1;
	elseif (Float64(x / y) <= 2e-16)
		tmp = Float64(Float64(Float64(x * z) / 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);
	tmp = 0.0;
	if ((x / y) <= -1e-15)
		tmp = t_1;
	elseif ((x / y) <= 2e-16)
		tmp = ((x * z) / y) + t;
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(N[(x / y), $MachinePrecision] * N[(z - t), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[N[(x / y), $MachinePrecision], -1e-15], t$95$1, If[LessEqual[N[(x / y), $MachinePrecision], 2e-16], N[(N[(N[(x * z), $MachinePrecision] / y), $MachinePrecision] + t), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if (/.f64 x y) < -1.0000000000000001e-15 or 2e-16 < (/.f64 x y)

   1. Initial program 97.1%

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

   3. Taylor expanded in y around 0

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

      1. lower-/.f64 N/A

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

      2. *-commutative N/A

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

      3. lower-*.f64 N/A

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

      4. lower--.f64 89.0

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

   5. Applied rewrites 89.0%

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

   7. Applied rewrites 96.7%

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

   if -1.0000000000000001e-15 < (/.f64 x y) < 2e-16

   1. Initial program 98.3%

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

   3. Taylor expanded in t around 0

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

      1. lower-/.f64 N/A

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

      2. *-commutative N/A

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

      3. lower-*.f64 96.6

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

   5. Applied rewrites 96.6%

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

4. Final simplification 96.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{x}{y} \leq -1 \cdot 10^{-15}:\\ \;\;\;\;\frac{x}{y} \cdot \left(z - t\right)\\ \mathbf{elif}\;\frac{x}{y} \leq 2 \cdot 10^{-16}:\\ \;\;\;\;\frac{x \cdot z}{y} + t\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{y} \cdot \left(z - t\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 85.4% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{x}{y} \cdot \left(z - t\right)\\ \mathbf{if}\;\frac{x}{y} \leq -1 \cdot 10^{-15}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;\frac{x}{y} \leq 9 \cdot 10^{-72}:\\ \;\;\;\;\left(1 - \frac{x}{y}\right) \cdot t\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (* (/ x y) (- z t))))
   (if (<= (/ x y) -1e-15)
     t_1
     (if (<= (/ x y) 9e-72) (* (- 1.0 (/ x y)) t) t_1))))

C

double code(double x, double y, double z, double t) {
	double t_1 = (x / y) * (z - t);
	double tmp;
	if ((x / y) <= -1e-15) {
		tmp = t_1;
	} else if ((x / y) <= 9e-72) {
		tmp = (1.0 - (x / 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)
    if ((x / y) <= (-1d-15)) then
        tmp = t_1
    else if ((x / y) <= 9d-72) then
        tmp = (1.0d0 - (x / 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);
	double tmp;
	if ((x / y) <= -1e-15) {
		tmp = t_1;
	} else if ((x / y) <= 9e-72) {
		tmp = (1.0 - (x / y)) * t;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = (x / y) * (z - t)
	tmp = 0
	if (x / y) <= -1e-15:
		tmp = t_1
	elif (x / y) <= 9e-72:
		tmp = (1.0 - (x / y)) * t
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(Float64(x / y) * Float64(z - t))
	tmp = 0.0
	if (Float64(x / y) <= -1e-15)
		tmp = t_1;
	elseif (Float64(x / y) <= 9e-72)
		tmp = Float64(Float64(1.0 - Float64(x / 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);
	tmp = 0.0;
	if ((x / y) <= -1e-15)
		tmp = t_1;
	elseif ((x / y) <= 9e-72)
		tmp = (1.0 - (x / y)) * t;
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(N[(x / y), $MachinePrecision] * N[(z - t), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[N[(x / y), $MachinePrecision], -1e-15], t$95$1, If[LessEqual[N[(x / y), $MachinePrecision], 9e-72], N[(N[(1.0 - N[(x / y), $MachinePrecision]), $MachinePrecision] * t), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if (/.f64 x y) < -1.0000000000000001e-15 or 9e-72 < (/.f64 x y)

   1. Initial program 97.3%

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

   3. Taylor expanded in y around 0

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

      1. lower-/.f64 N/A

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

      2. *-commutative N/A

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

      3. lower-*.f64 N/A

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

      4. lower--.f64 87.0

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

   5. Applied rewrites 87.0%

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

   7. Applied rewrites 94.9%

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

   if -1.0000000000000001e-15 < (/.f64 x y) < 9e-72

   1. Initial program 98.1%

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

   3. Taylor expanded in t around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

      3. mul-1-neg N/A

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

      4. unsub-neg N/A

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

      5. lower--.f64 N/A

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

      6. lower-/.f64 84.5

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

   5. Applied rewrites 84.5%

      \[\leadsto \color{blue}{\left(1 - \frac{x}{y}\right) \cdot t} \]
3. Recombined 2 regimes into one program.
4. Add Preprocessing

Alternative 4: 73.7% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{x}{y} \cdot z\\ \mathbf{if}\;z \leq -4.2 \cdot 10^{+45}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq 4.6 \cdot 10^{+44}:\\ \;\;\;\;\left(1 - \frac{x}{y}\right) \cdot t\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (* (/ x y) z)))
   (if (<= z -4.2e+45) t_1 (if (<= z 4.6e+44) (* (- 1.0 (/ x y)) t) t_1))))

C

double code(double x, double y, double z, double t) {
	double t_1 = (x / y) * z;
	double tmp;
	if (z <= -4.2e+45) {
		tmp = t_1;
	} else if (z <= 4.6e+44) {
		tmp = (1.0 - (x / 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
    if (z <= (-4.2d+45)) then
        tmp = t_1
    else if (z <= 4.6d+44) then
        tmp = (1.0d0 - (x / 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;
	double tmp;
	if (z <= -4.2e+45) {
		tmp = t_1;
	} else if (z <= 4.6e+44) {
		tmp = (1.0 - (x / y)) * t;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = (x / y) * z
	tmp = 0
	if z <= -4.2e+45:
		tmp = t_1
	elif z <= 4.6e+44:
		tmp = (1.0 - (x / y)) * t
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(Float64(x / y) * z)
	tmp = 0.0
	if (z <= -4.2e+45)
		tmp = t_1;
	elseif (z <= 4.6e+44)
		tmp = Float64(Float64(1.0 - Float64(x / y)) * t);
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = (x / y) * z;
	tmp = 0.0;
	if (z <= -4.2e+45)
		tmp = t_1;
	elseif (z <= 4.6e+44)
		tmp = (1.0 - (x / y)) * t;
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(N[(x / y), $MachinePrecision] * z), $MachinePrecision]}, If[LessEqual[z, -4.2e+45], t$95$1, If[LessEqual[z, 4.6e+44], N[(N[(1.0 - N[(x / y), $MachinePrecision]), $MachinePrecision] * t), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if z < -4.1999999999999999e45 or 4.60000000000000009e44 < z

   1. Initial program 98.1%

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

   3. Taylor expanded in t around 0

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

      1. lower-/.f64 N/A

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

      2. *-commutative N/A

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

      3. lower-*.f64 64.3

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

   5. Applied rewrites 64.3%

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

   7. Applied rewrites 71.5%

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

   if -4.1999999999999999e45 < z < 4.60000000000000009e44

   1. Initial program 97.3%

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

   3. Taylor expanded in t around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

      3. mul-1-neg N/A

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

      4. unsub-neg N/A

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

      5. lower--.f64 N/A

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

      6. lower-/.f64 80.9

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

   5. Applied rewrites 80.9%

      \[\leadsto \color{blue}{\left(1 - \frac{x}{y}\right) \cdot t} \]
3. Recombined 2 regimes into one program.
4. Add Preprocessing

Alternative 5: 50.0% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{x}{y} \cdot z\\ \mathbf{if}\;z \leq -4.6 \cdot 10^{-67}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq 5.8 \cdot 10^{-109}:\\ \;\;\;\;\frac{\left(-t\right) \cdot x}{y}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (* (/ x y) z)))
   (if (<= z -4.6e-67) t_1 (if (<= z 5.8e-109) (/ (* (- t) x) y) t_1))))

C

double code(double x, double y, double z, double t) {
	double t_1 = (x / y) * z;
	double tmp;
	if (z <= -4.6e-67) {
		tmp = t_1;
	} else if (z <= 5.8e-109) {
		tmp = (-t * x) / 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 / y) * z
    if (z <= (-4.6d-67)) then
        tmp = t_1
    else if (z <= 5.8d-109) then
        tmp = (-t * x) / 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 / y) * z;
	double tmp;
	if (z <= -4.6e-67) {
		tmp = t_1;
	} else if (z <= 5.8e-109) {
		tmp = (-t * x) / y;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = (x / y) * z
	tmp = 0
	if z <= -4.6e-67:
		tmp = t_1
	elif z <= 5.8e-109:
		tmp = (-t * x) / y
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(Float64(x / y) * z)
	tmp = 0.0
	if (z <= -4.6e-67)
		tmp = t_1;
	elseif (z <= 5.8e-109)
		tmp = Float64(Float64(Float64(-t) * x) / y);
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = (x / y) * z;
	tmp = 0.0;
	if (z <= -4.6e-67)
		tmp = t_1;
	elseif (z <= 5.8e-109)
		tmp = (-t * x) / y;
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(N[(x / y), $MachinePrecision] * z), $MachinePrecision]}, If[LessEqual[z, -4.6e-67], t$95$1, If[LessEqual[z, 5.8e-109], N[(N[((-t) * x), $MachinePrecision] / y), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if z < -4.6000000000000001e-67 or 5.8e-109 < z

   1. Initial program 98.6%

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

   3. Taylor expanded in t around 0

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

      1. lower-/.f64 N/A

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

      2. *-commutative N/A

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

      3. lower-*.f64 58.5

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

   5. Applied rewrites 58.5%

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

   7. Applied rewrites 64.4%

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

   if -4.6000000000000001e-67 < z < 5.8e-109

   1. Initial program 95.9%

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

   3. Taylor expanded in y around 0

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

      1. lower-/.f64 N/A

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

      2. *-commutative N/A

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

      3. lower-*.f64 N/A

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

      4. lower--.f64 44.2

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

   5. Applied rewrites 44.2%

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

   6. Taylor expanded in t around inf

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

   8. Applied rewrites 40.2%

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

Alternative 6: 50.1% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{x}{y} \cdot z\\ \mathbf{if}\;z \leq -4.6 \cdot 10^{-67}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq 1.15 \cdot 10^{-114}:\\ \;\;\;\;\left(-t\right) \cdot \frac{x}{y}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (* (/ x y) z)))
   (if (<= z -4.6e-67) t_1 (if (<= z 1.15e-114) (* (- t) (/ x y)) t_1))))

C

double code(double x, double y, double z, double t) {
	double t_1 = (x / y) * z;
	double tmp;
	if (z <= -4.6e-67) {
		tmp = t_1;
	} else if (z <= 1.15e-114) {
		tmp = -t * (x / 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 / y) * z
    if (z <= (-4.6d-67)) then
        tmp = t_1
    else if (z <= 1.15d-114) then
        tmp = -t * (x / 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 / y) * z;
	double tmp;
	if (z <= -4.6e-67) {
		tmp = t_1;
	} else if (z <= 1.15e-114) {
		tmp = -t * (x / y);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = (x / y) * z
	tmp = 0
	if z <= -4.6e-67:
		tmp = t_1
	elif z <= 1.15e-114:
		tmp = -t * (x / y)
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(Float64(x / y) * z)
	tmp = 0.0
	if (z <= -4.6e-67)
		tmp = t_1;
	elseif (z <= 1.15e-114)
		tmp = Float64(Float64(-t) * Float64(x / y));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = (x / y) * z;
	tmp = 0.0;
	if (z <= -4.6e-67)
		tmp = t_1;
	elseif (z <= 1.15e-114)
		tmp = -t * (x / y);
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(N[(x / y), $MachinePrecision] * z), $MachinePrecision]}, If[LessEqual[z, -4.6e-67], t$95$1, If[LessEqual[z, 1.15e-114], N[((-t) * N[(x / y), $MachinePrecision]), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if z < -4.6000000000000001e-67 or 1.15e-114 < z

   1. Initial program 98.6%

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

   3. Taylor expanded in t around 0

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

      1. lower-/.f64 N/A

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

      2. *-commutative N/A

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

      3. lower-*.f64 58.1

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

   5. Applied rewrites 58.1%

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

   7. Applied rewrites 64.0%

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

   if -4.6000000000000001e-67 < z < 1.15e-114

   1. Initial program 95.9%

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

   3. Taylor expanded in y around 0

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

      1. lower-/.f64 N/A

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

      2. *-commutative N/A

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

      3. lower-*.f64 N/A

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

      4. lower--.f64 44.6

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

   5. Applied rewrites 44.6%

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

   7. Applied rewrites 43.0%

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

   8. Taylor expanded in t around inf

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

   10. Applied rewrites 39.7%

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

4. Final simplification 55.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -4.6 \cdot 10^{-67}:\\ \;\;\;\;\frac{x}{y} \cdot z\\ \mathbf{elif}\;z \leq 1.15 \cdot 10^{-114}:\\ \;\;\;\;\left(-t\right) \cdot \frac{x}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{y} \cdot z\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 49.8% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{x}{y} \cdot z\\ \mathbf{if}\;z \leq -4.6 \cdot 10^{-67}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq 1.15 \cdot 10^{-114}:\\ \;\;\;\;\frac{-t}{y} \cdot x\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (* (/ x y) z)))
   (if (<= z -4.6e-67) t_1 (if (<= z 1.15e-114) (* (/ (- t) y) x) t_1))))

C

double code(double x, double y, double z, double t) {
	double t_1 = (x / y) * z;
	double tmp;
	if (z <= -4.6e-67) {
		tmp = t_1;
	} else if (z <= 1.15e-114) {
		tmp = (-t / y) * x;
	} 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
    if (z <= (-4.6d-67)) then
        tmp = t_1
    else if (z <= 1.15d-114) then
        tmp = (-t / y) * x
    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;
	double tmp;
	if (z <= -4.6e-67) {
		tmp = t_1;
	} else if (z <= 1.15e-114) {
		tmp = (-t / y) * x;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = (x / y) * z
	tmp = 0
	if z <= -4.6e-67:
		tmp = t_1
	elif z <= 1.15e-114:
		tmp = (-t / y) * x
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(Float64(x / y) * z)
	tmp = 0.0
	if (z <= -4.6e-67)
		tmp = t_1;
	elseif (z <= 1.15e-114)
		tmp = Float64(Float64(Float64(-t) / y) * x);
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = (x / y) * z;
	tmp = 0.0;
	if (z <= -4.6e-67)
		tmp = t_1;
	elseif (z <= 1.15e-114)
		tmp = (-t / y) * x;
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(N[(x / y), $MachinePrecision] * z), $MachinePrecision]}, If[LessEqual[z, -4.6e-67], t$95$1, If[LessEqual[z, 1.15e-114], N[(N[((-t) / y), $MachinePrecision] * x), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if z < -4.6000000000000001e-67 or 1.15e-114 < z

   1. Initial program 98.6%

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

   3. Taylor expanded in t around 0

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

      1. lower-/.f64 N/A

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

      2. *-commutative N/A

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

      3. lower-*.f64 58.1

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

   5. Applied rewrites 58.1%

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

   7. Applied rewrites 64.0%

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

   if -4.6000000000000001e-67 < z < 1.15e-114

   1. Initial program 95.9%

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

   3. Taylor expanded in y around 0

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

      1. lower-/.f64 N/A

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

      2. *-commutative N/A

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

      3. lower-*.f64 N/A

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

      4. lower--.f64 44.6

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

   5. Applied rewrites 44.6%

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

   6. Taylor expanded in t around inf

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

   8. Applied rewrites 38.5%

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

Alternative 8: 97.8% 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 97.6%

   \[\frac{x}{y} \cdot \left(z - t\right) + t \]
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 97.6

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

4. Applied rewrites 97.6%

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

Alternative 9: 40.9% 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 97.6%

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

3. Taylor expanded in t around 0

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

   1. lower-/.f64 N/A

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

   2. *-commutative N/A

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

   3. lower-*.f64 38.9

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

5. Applied rewrites 38.9%

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

7. Applied rewrites 43.4%

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

Developer Target 1: 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 2024268 
(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))