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

Percentage Accurate: 97.6% → 97.6%

Time: 1.2s

Alternatives: 8

Speedup: 1.0×

• 24.8% of points produce a very large (infinite) output. You may want to add a precondition.

Specification

\[\mathsf{TRUE}\left(\right)\]

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: 97.6% 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: 97.6% 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]

Derivation

1. Initial program 96.3%

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

Alternative 2: 82.4% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{x}{y} \cdot \left(z - t\right)\\ \mathbf{if}\;\frac{x}{y} \leq -8.2 \cdot 10^{-40}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;\frac{x}{y} \leq 4.1 \cdot 10^{-14}:\\ \;\;\;\;\frac{x}{y} + t\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (* (/ x y) (- z t))))
   (if (<= (/ x y) -8.2e-40) t_1 (if (<= (/ x y) 4.1e-14) (+ (/ 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) <= -8.2e-40) {
		tmp = t_1;
	} else if ((x / y) <= 4.1e-14) {
		tmp = (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) <= (-8.2d-40)) then
        tmp = t_1
    else if ((x / y) <= 4.1d-14) then
        tmp = (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) <= -8.2e-40) {
		tmp = t_1;
	} else if ((x / y) <= 4.1e-14) {
		tmp = (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) <= -8.2e-40:
		tmp = t_1
	elif (x / y) <= 4.1e-14:
		tmp = (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) <= -8.2e-40)
		tmp = t_1;
	elseif (Float64(x / y) <= 4.1e-14)
		tmp = Float64(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) <= -8.2e-40)
		tmp = t_1;
	elseif ((x / y) <= 4.1e-14)
		tmp = (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], -8.2e-40], t$95$1, If[LessEqual[N[(x / y), $MachinePrecision], 4.1e-14], N[(N[(x / y), $MachinePrecision] + t), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if (/.f64 x y) < -8.19999999999999926e-40 or 4.1000000000000002e-14 < (/.f64 x y)

   1. Initial program 93.0%

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

   3. Taylor expanded in x around 0

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

   5. Applied rewrites 88.7%

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

   if -8.19999999999999926e-40 < (/.f64 x y) < 4.1000000000000002e-14

   1. Initial program 99.9%

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

   3. Taylor expanded in x around 0

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

   5. Applied rewrites 73.8%

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

Alternative 3: 46.1% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;\frac{x}{y} \cdot \left(z - t\right) + t \leq 10^{+307}:\\ \;\;\;\;\frac{x}{y} + t\\ \mathbf{else}:\\ \;\;\;\;\left(z - t\right) \cdot \left(z - t\right) + t\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= (+ (* (/ x y) (- z t)) t) 1e+307)
   (+ (/ x y) t)
   (+ (* (- z t) (- z t)) t)))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((((x / y) * (z - t)) + t) <= 1e+307) {
		tmp = (x / y) + t;
	} else {
		tmp = ((z - t) * (z - t)) + 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) * (z - t)) + t) <= 1d+307) then
        tmp = (x / y) + t
    else
        tmp = ((z - t) * (z - t)) + 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) * (z - t)) + t) <= 1e+307) {
		tmp = (x / y) + t;
	} else {
		tmp = ((z - t) * (z - t)) + t;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (((x / y) * (z - t)) + t) <= 1e+307:
		tmp = (x / y) + t
	else:
		tmp = ((z - t) * (z - t)) + t
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (Float64(Float64(Float64(x / y) * Float64(z - t)) + t) <= 1e+307)
		tmp = Float64(Float64(x / y) + t);
	else
		tmp = Float64(Float64(Float64(z - t) * Float64(z - t)) + t);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((((x / y) * (z - t)) + t) <= 1e+307)
		tmp = (x / y) + t;
	else
		tmp = ((z - t) * (z - t)) + t;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[N[(N[(N[(x / y), $MachinePrecision] * N[(z - t), $MachinePrecision]), $MachinePrecision] + t), $MachinePrecision], 1e+307], N[(N[(x / y), $MachinePrecision] + t), $MachinePrecision], N[(N[(N[(z - t), $MachinePrecision] * N[(z - t), $MachinePrecision]), $MachinePrecision] + t), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if (+.f64 (*.f64 (/.f64 x y) (-.f64 z t)) t) < 9.99999999999999986e306

   1. Initial program 97.0%

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

   3. Taylor expanded in x around 0

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

   5. Applied rewrites 45.8%

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

   if 9.99999999999999986e306 < (+.f64 (*.f64 (/.f64 x y) (-.f64 z t)) t)

   1. Initial program 91.5%

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

   3. Taylor expanded in x around 0

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

   5. Applied rewrites 68.3%

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

Alternative 4: 46.1% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;\frac{x}{y} \cdot \left(z - t\right) + t \leq 10^{+307}:\\ \;\;\;\;\frac{x}{y} + t\\ \mathbf{else}:\\ \;\;\;\;\left(z - t\right) \cdot \left(z - t\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= (+ (* (/ x y) (- z t)) t) 1e+307) (+ (/ x y) t) (* (- z t) (- z t))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((((x / y) * (z - t)) + t) <= 1e+307) {
		tmp = (x / y) + t;
	} else {
		tmp = (z - t) * (z - 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) * (z - t)) + t) <= 1d+307) then
        tmp = (x / y) + t
    else
        tmp = (z - t) * (z - 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) * (z - t)) + t) <= 1e+307) {
		tmp = (x / y) + t;
	} else {
		tmp = (z - t) * (z - t);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (((x / y) * (z - t)) + t) <= 1e+307:
		tmp = (x / y) + t
	else:
		tmp = (z - t) * (z - t)
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (Float64(Float64(Float64(x / y) * Float64(z - t)) + t) <= 1e+307)
		tmp = Float64(Float64(x / y) + t);
	else
		tmp = Float64(Float64(z - t) * Float64(z - t));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((((x / y) * (z - t)) + t) <= 1e+307)
		tmp = (x / y) + t;
	else
		tmp = (z - t) * (z - t);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[N[(N[(N[(x / y), $MachinePrecision] * N[(z - t), $MachinePrecision]), $MachinePrecision] + t), $MachinePrecision], 1e+307], N[(N[(x / y), $MachinePrecision] + t), $MachinePrecision], N[(N[(z - t), $MachinePrecision] * N[(z - t), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if (+.f64 (*.f64 (/.f64 x y) (-.f64 z t)) t) < 9.99999999999999986e306

   1. Initial program 97.0%

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

   3. Taylor expanded in x around 0

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

   5. Applied rewrites 45.8%

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

   if 9.99999999999999986e306 < (+.f64 (*.f64 (/.f64 x y) (-.f64 z t)) t)

   1. Initial program 91.5%

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

   3. Taylor expanded in x around 0

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

   5. Applied rewrites 91.5%

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

   6. Taylor expanded in x around 0

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

   8. Applied rewrites 68.3%

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

Alternative 5: 15.0% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;\frac{x}{y} \cdot \left(z - t\right) + t \leq -5 \cdot 10^{-221}:\\ \;\;\;\;\frac{x}{y}\\ \mathbf{else}:\\ \;\;\;\;\left(z - t\right) \cdot \left(z - t\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= (+ (* (/ x y) (- z t)) t) -5e-221) (/ x y) (* (- z t) (- z t))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((((x / y) * (z - t)) + t) <= -5e-221) {
		tmp = x / y;
	} else {
		tmp = (z - t) * (z - 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) * (z - t)) + t) <= (-5d-221)) then
        tmp = x / y
    else
        tmp = (z - t) * (z - 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) * (z - t)) + t) <= -5e-221) {
		tmp = x / y;
	} else {
		tmp = (z - t) * (z - t);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (((x / y) * (z - t)) + t) <= -5e-221:
		tmp = x / y
	else:
		tmp = (z - t) * (z - t)
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (Float64(Float64(Float64(x / y) * Float64(z - t)) + t) <= -5e-221)
		tmp = Float64(x / y);
	else
		tmp = Float64(Float64(z - t) * Float64(z - t));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((((x / y) * (z - t)) + t) <= -5e-221)
		tmp = x / y;
	else
		tmp = (z - t) * (z - t);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[N[(N[(N[(x / y), $MachinePrecision] * N[(z - t), $MachinePrecision]), $MachinePrecision] + t), $MachinePrecision], -5e-221], N[(x / y), $MachinePrecision], N[(N[(z - t), $MachinePrecision] * N[(z - t), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if (+.f64 (*.f64 (/.f64 x y) (-.f64 z t)) t) < -4.99999999999999996e-221

   1. Initial program 94.7%

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

   3. Taylor expanded in x around 0

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

   5. Applied rewrites 57.6%

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

   6. Taylor expanded in x around 0

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

   8. Applied rewrites 9.0%

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

   if -4.99999999999999996e-221 < (+.f64 (*.f64 (/.f64 x y) (-.f64 z t)) t)

   1. Initial program 97.8%

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

   3. Taylor expanded in x around 0

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

   5. Applied rewrites 57.3%

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

   6. Taylor expanded in x around 0

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

   8. Applied rewrites 21.7%

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

Alternative 6: 8.4% accurate, 1.9× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 96.3%

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

3. Taylor expanded in x around 0

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

5. Applied rewrites 57.5%

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

6. Taylor expanded in x around 0

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

8. Applied rewrites 8.2%

   \[\leadsto \frac{x}{\color{blue}{y}} \]
9. Add Preprocessing

Alternative 7: 3.1% accurate, 3.3× speedup

Math

\[\begin{array}{l} \\ \left(z - t\right) + t \end{array} \]

FPCore

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

C

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 96.3%

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

3. Taylor expanded in x around 0

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

5. Applied rewrites 42.5%

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

6. Taylor expanded in x around 0

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

8. Applied rewrites 2.8%

   \[\leadsto \left(z - \color{blue}{t}\right) + t \]
9. Add Preprocessing

Alternative 8: 3.0% accurate, 5.8× speedup

Math

\[\begin{array}{l} \\ z - t \end{array} \]

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 96.3%

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

3. Taylor expanded in x around 0

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

5. Applied rewrites 57.5%

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

6. Taylor expanded in y around inf

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

8. Applied rewrites 2.6%

   \[\leadsto \color{blue}{z - t} \]
9. Add Preprocessing

Developer Target 1: 97.3% 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 2024321 
(FPCore (x y z t)
  :name "Numeric.Signal.Multichannel:$cget from hsignal-0.2.7.1"
  :precision binary64
  :pre (TRUE)

  :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))