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

Percentage Accurate: 96.8% → 96.8%

Time: 1.3s

Alternatives: 8

Speedup: 1.0×

Specification

Math

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

FPCore

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

C

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Initial Program: 96.8% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Alternative 1: 96.8% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 97.6%

   \[\frac{x - y}{z - y} \cdot t \]
2. Add Preprocessing
3. Add Preprocessing

Alternative 2: 14.8% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq 4.2 \cdot 10^{-132}:\\ \;\;\;\;\left(\left(\left(x - y\right) \cdot t\right) \cdot t\right) \cdot t\\ \mathbf{else}:\\ \;\;\;\;\frac{x - y}{z - y}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= t 4.2e-132) (* (* (* (- x y) t) t) t) (/ (- x y) (- z y))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (t <= 4.2e-132) {
		tmp = (((x - y) * t) * t) * t;
	} else {
		tmp = (x - y) / (z - y);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if (t <= 4.2d-132) then
        tmp = (((x - y) * t) * t) * t
    else
        tmp = (x - y) / (z - y)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if (t <= 4.2e-132) {
		tmp = (((x - y) * t) * t) * t;
	} else {
		tmp = (x - y) / (z - y);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if t <= 4.2e-132:
		tmp = (((x - y) * t) * t) * t
	else:
		tmp = (x - y) / (z - y)
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (t <= 4.2e-132)
		tmp = Float64(Float64(Float64(Float64(x - y) * t) * t) * t);
	else
		tmp = Float64(Float64(x - y) / Float64(z - y));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (t <= 4.2e-132)
		tmp = (((x - y) * t) * t) * t;
	else
		tmp = (x - y) / (z - y);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[t, 4.2e-132], N[(N[(N[(N[(x - y), $MachinePrecision] * t), $MachinePrecision] * t), $MachinePrecision] * t), $MachinePrecision], N[(N[(x - y), $MachinePrecision] / N[(z - y), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if t < 4.2000000000000002e-132

   1. Initial program 97.6%

      \[\frac{x - y}{z - y} \cdot t \]
   2. Add Preprocessing

   3. Taylor expanded in x around 0

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

   5. Applied rewrites 10.1%

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

   6. Taylor expanded in x around 0

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

   8. Applied rewrites 15.6%

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

   9. Taylor expanded in x around inf

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

   11. Applied rewrites 16.1%

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

   if 4.2000000000000002e-132 < t

   1. Initial program 97.6%

      \[\frac{x - y}{z - y} \cdot t \]
   2. Add Preprocessing

   3. Taylor expanded in x around 0

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

   5. Applied rewrites 13.5%

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

Alternative 3: 14.0% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq 1.32 \cdot 10^{-129}:\\ \;\;\;\;\left(\left(x - y\right) \cdot t\right) \cdot t\\ \mathbf{else}:\\ \;\;\;\;\frac{x - y}{z - y}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= t 1.32e-129) (* (* (- x y) t) t) (/ (- x y) (- z y))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (t <= 1.32e-129) {
		tmp = ((x - y) * t) * t;
	} else {
		tmp = (x - y) / (z - y);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if (t <= 1.32d-129) then
        tmp = ((x - y) * t) * t
    else
        tmp = (x - y) / (z - y)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if (t <= 1.32e-129) {
		tmp = ((x - y) * t) * t;
	} else {
		tmp = (x - y) / (z - y);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if t <= 1.32e-129:
		tmp = ((x - y) * t) * t
	else:
		tmp = (x - y) / (z - y)
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (t <= 1.32e-129)
		tmp = Float64(Float64(Float64(x - y) * t) * t);
	else
		tmp = Float64(Float64(x - y) / Float64(z - y));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (t <= 1.32e-129)
		tmp = ((x - y) * t) * t;
	else
		tmp = (x - y) / (z - y);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[t, 1.32e-129], N[(N[(N[(x - y), $MachinePrecision] * t), $MachinePrecision] * t), $MachinePrecision], N[(N[(x - y), $MachinePrecision] / N[(z - y), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if t < 1.31999999999999992e-129

   1. Initial program 97.6%

      \[\frac{x - y}{z - y} \cdot t \]
   2. Add Preprocessing

   3. Taylor expanded in x around 0

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

   5. Applied rewrites 10.1%

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

   6. Taylor expanded in x around 0

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

   8. Applied rewrites 15.6%

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

   if 1.31999999999999992e-129 < t

   1. Initial program 97.5%

      \[\frac{x - y}{z - y} \cdot t \]
   2. Add Preprocessing

   3. Taylor expanded in x around 0

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

   5. Applied rewrites 13.6%

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

Alternative 4: 84.4% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 97.6%

   \[\frac{x - y}{z - y} \cdot t \]
2. Add Preprocessing

3. Taylor expanded in x around 0

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

5. Applied rewrites 8.7%

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

6. Taylor expanded in x around 0

   \[\leadsto \frac{-1 \cdot y}{\color{blue}{z} - y} \]

8. Applied rewrites 82.2%

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

Alternative 5: 9.1% accurate, 1.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq 3.5 \cdot 10^{-69}:\\ \;\;\;\;\left(\left(z - y\right) \cdot t\right) \cdot t\\ \mathbf{else}:\\ \;\;\;\;\left(x - y\right) \cdot t\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= z 3.5e-69) (* (* (- z y) t) t) (* (- x y) t)))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (z <= 3.5e-69) {
		tmp = ((z - y) * t) * t;
	} 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 (z <= 3.5d-69) then
        tmp = ((z - y) * t) * t
    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 (z <= 3.5e-69) {
		tmp = ((z - y) * t) * t;
	} else {
		tmp = (x - y) * t;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if z <= 3.5e-69:
		tmp = ((z - y) * t) * t
	else:
		tmp = (x - y) * t
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (z <= 3.5e-69)
		tmp = Float64(Float64(Float64(z - y) * t) * t);
	else
		tmp = Float64(Float64(x - y) * t);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (z <= 3.5e-69)
		tmp = ((z - y) * t) * t;
	else
		tmp = (x - y) * t;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[z, 3.5e-69], N[(N[(N[(z - y), $MachinePrecision] * t), $MachinePrecision] * t), $MachinePrecision], N[(N[(x - y), $MachinePrecision] * t), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < 3.5000000000000001e-69

   1. Initial program 96.6%

      \[\frac{x - y}{z - y} \cdot t \]
   2. Add Preprocessing

   3. Taylor expanded in x around 0

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

   5. Applied rewrites 6.4%

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

   6. Taylor expanded in x around 0

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

   8. Applied rewrites 10.8%

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

   9. Taylor expanded in x around 0

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

   11. Applied rewrites 10.0%

       \[\leadsto \left(\left(z - y\right) \cdot t\right) \cdot t \]

   if 3.5000000000000001e-69 < z

   1. Initial program 99.7%

      \[\frac{x - y}{z - y} \cdot t \]
   2. Add Preprocessing

   3. Taylor expanded in x around 0

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

   5. Applied rewrites 13.8%

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

Alternative 6: 13.1% accurate, 1.6× speedup

Math

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

FPCore

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

C

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 97.6%

   \[\frac{x - y}{z - y} \cdot t \]
2. Add Preprocessing

3. Taylor expanded in x around 0

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

5. Applied rewrites 8.8%

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

6. Taylor expanded in x around 0

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

8. Applied rewrites 12.7%

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

Alternative 7: 8.8% accurate, 2.6× speedup

Math

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

FPCore

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

C

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 97.6%

   \[\frac{x - y}{z - y} \cdot t \]
2. Add Preprocessing

3. Taylor expanded in x around 0

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

5. Applied rewrites 8.8%

   \[\leadsto \color{blue}{\left(x - y\right)} \cdot t \]
6. Add Preprocessing

Alternative 8: 3.4% accurate, 5.8× speedup

Math

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

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 97.6%

   \[\frac{x - y}{z - y} \cdot t \]
2. Add Preprocessing

3. Taylor expanded in x around 0

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

5. Applied rewrites 8.7%

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

6. Taylor expanded in x around 0

   \[\leadsto -1 \cdot \color{blue}{\frac{y}{z - y}} \]

8. Applied rewrites 3.3%

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

Developer Target 1: 96.9% accurate, 0.8× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Reproduce

herbie shell --seed 2024313 
(FPCore (x y z t)
  :name "Numeric.Signal.Multichannel:$cput from hsignal-0.2.7.1"
  :precision binary64

  :alt
  (! :herbie-platform default (/ t (/ (- z y) (- x y))))

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