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

Percentage Accurate: 97.6% → 97.9%

Time: 10.1s

Alternatives: 9

Speedup: 0.9×

• 25.0% 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: 97.6% 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: 97.9% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -1000000000:\\ \;\;\;\;\mathsf{fma}\left(\frac{z - t}{y}, x, t\right)\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(\frac{x}{y}, z - t, t\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= x -1000000000.0) (fma (/ (- z t) y) x t) (fma (/ x y) (- z t) t)))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (x <= -1000000000.0) {
		tmp = fma(((z - t) / y), x, t);
	} else {
		tmp = fma((x / y), (z - t), t);
	}
	return tmp;
}

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (x <= -1000000000.0)
		tmp = fma(Float64(Float64(z - t) / y), x, t);
	else
		tmp = fma(Float64(x / y), Float64(z - t), t);
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[x, -1000000000.0], N[(N[(N[(z - t), $MachinePrecision] / y), $MachinePrecision] * x + t), $MachinePrecision], N[(N[(x / y), $MachinePrecision] * N[(z - t), $MachinePrecision] + t), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < -1e9

   1. Initial program 90.4%

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

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

   if -1e9 < x

   1. Initial program 98.6%

      \[\frac{x}{y} \cdot \left(z - t\right) + t \]
   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 98.6

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

   4. Applied rewrites 98.6%

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

Alternative 2: 94.2% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;\frac{x}{y} \leq -4000000:\\ \;\;\;\;\frac{x}{y} \cdot \left(z - t\right)\\ \mathbf{elif}\;\frac{x}{y} \leq 0.5:\\ \;\;\;\;\frac{z \cdot x}{y} + t\\ \mathbf{else}:\\ \;\;\;\;\frac{\left(z - t\right) \cdot x}{y}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= (/ x y) -4000000.0)
   (* (/ x y) (- z t))
   (if (<= (/ x y) 0.5) (+ (/ (* z x) y) t) (/ (* (- z t) x) y))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((x / y) <= -4000000.0) {
		tmp = (x / y) * (z - t);
	} else if ((x / y) <= 0.5) {
		tmp = ((z * x) / y) + t;
	} else {
		tmp = ((z - t) * x) / 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 ((x / y) <= (-4000000.0d0)) then
        tmp = (x / y) * (z - t)
    else if ((x / y) <= 0.5d0) then
        tmp = ((z * x) / y) + t
    else
        tmp = ((z - t) * x) / y
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if ((x / y) <= -4000000.0) {
		tmp = (x / y) * (z - t);
	} else if ((x / y) <= 0.5) {
		tmp = ((z * x) / y) + t;
	} else {
		tmp = ((z - t) * x) / y;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (x / y) <= -4000000.0:
		tmp = (x / y) * (z - t)
	elif (x / y) <= 0.5:
		tmp = ((z * x) / y) + t
	else:
		tmp = ((z - t) * x) / y
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (Float64(x / y) <= -4000000.0)
		tmp = Float64(Float64(x / y) * Float64(z - t));
	elseif (Float64(x / y) <= 0.5)
		tmp = Float64(Float64(Float64(z * x) / y) + t);
	else
		tmp = Float64(Float64(Float64(z - t) * x) / y);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((x / y) <= -4000000.0)
		tmp = (x / y) * (z - t);
	elseif ((x / y) <= 0.5)
		tmp = ((z * x) / y) + t;
	else
		tmp = ((z - t) * x) / y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[N[(x / y), $MachinePrecision], -4000000.0], N[(N[(x / y), $MachinePrecision] * N[(z - t), $MachinePrecision]), $MachinePrecision], If[LessEqual[N[(x / y), $MachinePrecision], 0.5], N[(N[(N[(z * x), $MachinePrecision] / y), $MachinePrecision] + t), $MachinePrecision], N[(N[(N[(z - t), $MachinePrecision] * x), $MachinePrecision] / y), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if (/.f64 x y) < -4e6

   1. Initial program 94.5%

      \[\frac{x}{y} \cdot \left(z - t\right) + t \]
   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 89.9

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

   5. Applied rewrites 89.9%

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

   7. Applied rewrites 93.3%

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

   if -4e6 < (/.f64 x y) < 0.5

   1. Initial program 98.8%

      \[\frac{x}{y} \cdot \left(z - t\right) + t \]
   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 94.7

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

   5. Applied rewrites 94.7%

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

   if 0.5 < (/.f64 x y)

   1. Initial program 92.9%

      \[\frac{x}{y} \cdot \left(z - t\right) + t \]
   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 91.5

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

   5. Applied rewrites 91.5%

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

Alternative 3: 85.1% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;\frac{x}{y} \leq -4 \cdot 10^{-7}:\\ \;\;\;\;\frac{x}{y} \cdot \left(z - t\right)\\ \mathbf{elif}\;\frac{x}{y} \leq 100:\\ \;\;\;\;\left(1 - \frac{x}{y}\right) \cdot t\\ \mathbf{else}:\\ \;\;\;\;\frac{\left(z - t\right) \cdot x}{y}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= (/ x y) -4e-7)
   (* (/ x y) (- z t))
   (if (<= (/ x y) 100.0) (* (- 1.0 (/ x y)) t) (/ (* (- z t) x) y))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((x / y) <= -4e-7) {
		tmp = (x / y) * (z - t);
	} else if ((x / y) <= 100.0) {
		tmp = (1.0 - (x / y)) * t;
	} else {
		tmp = ((z - t) * x) / 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 ((x / y) <= (-4d-7)) then
        tmp = (x / y) * (z - t)
    else if ((x / y) <= 100.0d0) then
        tmp = (1.0d0 - (x / y)) * t
    else
        tmp = ((z - t) * x) / y
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if ((x / y) <= -4e-7) {
		tmp = (x / y) * (z - t);
	} else if ((x / y) <= 100.0) {
		tmp = (1.0 - (x / y)) * t;
	} else {
		tmp = ((z - t) * x) / y;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (x / y) <= -4e-7:
		tmp = (x / y) * (z - t)
	elif (x / y) <= 100.0:
		tmp = (1.0 - (x / y)) * t
	else:
		tmp = ((z - t) * x) / y
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (Float64(x / y) <= -4e-7)
		tmp = Float64(Float64(x / y) * Float64(z - t));
	elseif (Float64(x / y) <= 100.0)
		tmp = Float64(Float64(1.0 - Float64(x / y)) * t);
	else
		tmp = Float64(Float64(Float64(z - t) * x) / y);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((x / y) <= -4e-7)
		tmp = (x / y) * (z - t);
	elseif ((x / y) <= 100.0)
		tmp = (1.0 - (x / y)) * t;
	else
		tmp = ((z - t) * x) / y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[N[(x / y), $MachinePrecision], -4e-7], N[(N[(x / y), $MachinePrecision] * N[(z - t), $MachinePrecision]), $MachinePrecision], If[LessEqual[N[(x / y), $MachinePrecision], 100.0], N[(N[(1.0 - N[(x / y), $MachinePrecision]), $MachinePrecision] * t), $MachinePrecision], N[(N[(N[(z - t), $MachinePrecision] * x), $MachinePrecision] / y), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if (/.f64 x y) < -3.9999999999999998e-7

   1. Initial program 94.8%

      \[\frac{x}{y} \cdot \left(z - t\right) + t \]
   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 89.1

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

   5. Applied rewrites 89.1%

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

   7. Applied rewrites 92.5%

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

   if -3.9999999999999998e-7 < (/.f64 x y) < 100

   1. Initial program 98.8%

      \[\frac{x}{y} \cdot \left(z - t\right) + t \]
   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 82.0

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

   5. Applied rewrites 82.0%

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

   if 100 < (/.f64 x y)

   1. Initial program 92.7%

      \[\frac{x}{y} \cdot \left(z - t\right) + t \]
   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 94.5

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

   5. Applied rewrites 94.5%

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

Alternative 4: 84.9% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{x}{y} \cdot \left(z - t\right)\\ \mathbf{if}\;\frac{x}{y} \leq -4 \cdot 10^{-7}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;\frac{x}{y} \leq 2 \cdot 10^{-93}:\\ \;\;\;\;\left(1 - \frac{x}{y}\right) \cdot t\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (* (/ x y) (- z t))))
   (if (<= (/ x y) -4e-7)
     t_1
     (if (<= (/ x y) 2e-93) (* (- 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) <= -4e-7) {
		tmp = t_1;
	} else if ((x / y) <= 2e-93) {
		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) <= (-4d-7)) then
        tmp = t_1
    else if ((x / y) <= 2d-93) 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) <= -4e-7) {
		tmp = t_1;
	} else if ((x / y) <= 2e-93) {
		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) <= -4e-7:
		tmp = t_1
	elif (x / y) <= 2e-93:
		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) <= -4e-7)
		tmp = t_1;
	elseif (Float64(x / y) <= 2e-93)
		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) <= -4e-7)
		tmp = t_1;
	elseif ((x / y) <= 2e-93)
		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], -4e-7], t$95$1, If[LessEqual[N[(x / y), $MachinePrecision], 2e-93], 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) < -3.9999999999999998e-7 or 1.9999999999999998e-93 < (/.f64 x y)

   1. Initial program 94.8%

      \[\frac{x}{y} \cdot \left(z - t\right) + t \]
   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 83.9

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

   5. Applied rewrites 83.9%

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

   7. Applied rewrites 85.7%

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

   if -3.9999999999999998e-7 < (/.f64 x y) < 1.9999999999999998e-93

   1. Initial program 98.5%

      \[\frac{x}{y} \cdot \left(z - t\right) + t \]
   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 89.2

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

   5. Applied rewrites 89.2%

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

Alternative 5: 98.4% accurate, 0.5× speedup

Math

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

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= (+ (* (/ x y) (- z t)) t) (- INFINITY))
   (/ (* (- z t) x) y)
   (fma (/ x y) (- z t) t)))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((((x / y) * (z - t)) + t) <= -((double) INFINITY)) {
		tmp = ((z - t) * x) / y;
	} else {
		tmp = fma((x / y), (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) <= Float64(-Inf))
		tmp = Float64(Float64(Float64(z - t) * x) / y);
	else
		tmp = fma(Float64(x / y), Float64(z - t), t);
	end
	return tmp
end

Wolfram

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

Derivation

1. Split input into 2 regimes

2. if (+.f64 (*.f64 (/.f64 x y) (-.f64 z t)) t) < -inf.0

   1. Initial program 87.5%

      \[\frac{x}{y} \cdot \left(z - t\right) + t \]
   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 100.0

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

   5. Applied rewrites 100.0%

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

   if -inf.0 < (+.f64 (*.f64 (/.f64 x y) (-.f64 z t)) t)

   1. Initial program 97.9%

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

      1. lift-+.f64 N/A

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

      2. lift-*.f64 N/A

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

      3. lower-fma.f64 97.9

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

   4. Applied rewrites 97.9%

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

Alternative 6: 73.0% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(1 - \frac{x}{y}\right) \cdot t\\ \mathbf{if}\;t \leq -2.2 \cdot 10^{-49}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t \leq 10^{-167}:\\ \;\;\;\;\frac{z \cdot x}{y}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (* (- 1.0 (/ x y)) t)))
   (if (<= t -2.2e-49) t_1 (if (<= t 1e-167) (/ (* z x) y) t_1))))

C

double code(double x, double y, double z, double t) {
	double t_1 = (1.0 - (x / y)) * t;
	double tmp;
	if (t <= -2.2e-49) {
		tmp = t_1;
	} else if (t <= 1e-167) {
		tmp = (z * 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 = (1.0d0 - (x / y)) * t
    if (t <= (-2.2d-49)) then
        tmp = t_1
    else if (t <= 1d-167) then
        tmp = (z * 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 = (1.0 - (x / y)) * t;
	double tmp;
	if (t <= -2.2e-49) {
		tmp = t_1;
	} else if (t <= 1e-167) {
		tmp = (z * x) / y;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = (1.0 - (x / y)) * t
	tmp = 0
	if t <= -2.2e-49:
		tmp = t_1
	elif t <= 1e-167:
		tmp = (z * x) / y
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(Float64(1.0 - Float64(x / y)) * t)
	tmp = 0.0
	if (t <= -2.2e-49)
		tmp = t_1;
	elseif (t <= 1e-167)
		tmp = Float64(Float64(z * x) / y);
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = (1.0 - (x / y)) * t;
	tmp = 0.0;
	if (t <= -2.2e-49)
		tmp = t_1;
	elseif (t <= 1e-167)
		tmp = (z * x) / y;
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(N[(1.0 - N[(x / y), $MachinePrecision]), $MachinePrecision] * t), $MachinePrecision]}, If[LessEqual[t, -2.2e-49], t$95$1, If[LessEqual[t, 1e-167], N[(N[(z * x), $MachinePrecision] / y), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if t < -2.1999999999999999e-49 or 1e-167 < t

   1. Initial program 99.4%

      \[\frac{x}{y} \cdot \left(z - t\right) + t \]
   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 84.9

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

   5. Applied rewrites 84.9%

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

   if -2.1999999999999999e-49 < t < 1e-167

   1. Initial program 89.4%

      \[\frac{x}{y} \cdot \left(z - t\right) + t \]
   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 69.0

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

   5. Applied rewrites 69.0%

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

Alternative 7: 48.0% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -3.1 \cdot 10^{+100}:\\ \;\;\;\;\frac{-t}{y} \cdot x\\ \mathbf{elif}\;t \leq 5.1 \cdot 10^{-44}:\\ \;\;\;\;\frac{x}{y} \cdot z\\ \mathbf{else}:\\ \;\;\;\;\left(-t\right) \cdot \frac{x}{y}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= t -3.1e+100)
   (* (/ (- t) y) x)
   (if (<= t 5.1e-44) (* (/ x y) z) (* (- t) (/ x y)))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (t <= -3.1e+100) {
		tmp = (-t / y) * x;
	} else if (t <= 5.1e-44) {
		tmp = (x / y) * z;
	} else {
		tmp = -t * (x / 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 <= (-3.1d+100)) then
        tmp = (-t / y) * x
    else if (t <= 5.1d-44) then
        tmp = (x / y) * z
    else
        tmp = -t * (x / y)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if (t <= -3.1e+100) {
		tmp = (-t / y) * x;
	} else if (t <= 5.1e-44) {
		tmp = (x / y) * z;
	} else {
		tmp = -t * (x / y);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if t <= -3.1e+100:
		tmp = (-t / y) * x
	elif t <= 5.1e-44:
		tmp = (x / y) * z
	else:
		tmp = -t * (x / y)
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (t <= -3.1e+100)
		tmp = Float64(Float64(Float64(-t) / y) * x);
	elseif (t <= 5.1e-44)
		tmp = Float64(Float64(x / y) * z);
	else
		tmp = Float64(Float64(-t) * Float64(x / y));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (t <= -3.1e+100)
		tmp = (-t / y) * x;
	elseif (t <= 5.1e-44)
		tmp = (x / y) * z;
	else
		tmp = -t * (x / y);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[t, -3.1e+100], N[(N[((-t) / y), $MachinePrecision] * x), $MachinePrecision], If[LessEqual[t, 5.1e-44], N[(N[(x / y), $MachinePrecision] * z), $MachinePrecision], N[((-t) * N[(x / y), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if t < -3.10000000000000007e100

   1. Initial program 100.0%

      \[\frac{x}{y} \cdot \left(z - t\right) + t \]
   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 37.8

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

   5. Applied rewrites 37.8%

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

   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 39.5%

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

   if -3.10000000000000007e100 < t < 5.1000000000000005e-44

   1. Initial program 92.8%

      \[\frac{x}{y} \cdot \left(z - t\right) + t \]
   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 56.1

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

   5. Applied rewrites 56.1%

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

   7. Applied rewrites 59.1%

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

   if 5.1000000000000005e-44 < t

   1. Initial program 99.9%

      \[\frac{x}{y} \cdot \left(z - t\right) + t \]
   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 43.3

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

   5. Applied rewrites 43.3%

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

   7. Applied rewrites 46.9%

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

   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 42.7%

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

4. Final simplification 50.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -3.1 \cdot 10^{+100}:\\ \;\;\;\;\frac{-t}{y} \cdot x\\ \mathbf{elif}\;t \leq 5.1 \cdot 10^{-44}:\\ \;\;\;\;\frac{x}{y} \cdot z\\ \mathbf{else}:\\ \;\;\;\;\left(-t\right) \cdot \frac{x}{y}\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 47.5% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{-t}{y} \cdot x\\ \mathbf{if}\;t \leq -3.1 \cdot 10^{+100}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t \leq 5.1 \cdot 10^{-44}:\\ \;\;\;\;\frac{x}{y} \cdot z\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (* (/ (- t) y) x)))
   (if (<= t -3.1e+100) t_1 (if (<= t 5.1e-44) (* (/ x y) z) t_1))))

C

double code(double x, double y, double z, double t) {
	double t_1 = (-t / y) * x;
	double tmp;
	if (t <= -3.1e+100) {
		tmp = t_1;
	} else if (t <= 5.1e-44) {
		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 = (-t / y) * x
    if (t <= (-3.1d+100)) then
        tmp = t_1
    else if (t <= 5.1d-44) 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 = (-t / y) * x;
	double tmp;
	if (t <= -3.1e+100) {
		tmp = t_1;
	} else if (t <= 5.1e-44) {
		tmp = (x / y) * z;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = (-t / y) * x
	tmp = 0
	if t <= -3.1e+100:
		tmp = t_1
	elif t <= 5.1e-44:
		tmp = (x / y) * z
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(Float64(Float64(-t) / y) * x)
	tmp = 0.0
	if (t <= -3.1e+100)
		tmp = t_1;
	elseif (t <= 5.1e-44)
		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 = (-t / y) * x;
	tmp = 0.0;
	if (t <= -3.1e+100)
		tmp = t_1;
	elseif (t <= 5.1e-44)
		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[((-t) / y), $MachinePrecision] * x), $MachinePrecision]}, If[LessEqual[t, -3.1e+100], t$95$1, If[LessEqual[t, 5.1e-44], N[(N[(x / y), $MachinePrecision] * z), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if t < -3.10000000000000007e100 or 5.1000000000000005e-44 < t

   1. Initial program 100.0%

      \[\frac{x}{y} \cdot \left(z - t\right) + t \]
   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 41.2

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

   5. Applied rewrites 41.2%

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

   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 41.3%

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

   if -3.10000000000000007e100 < t < 5.1000000000000005e-44

   1. Initial program 92.8%

      \[\frac{x}{y} \cdot \left(z - t\right) + t \]
   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 56.1

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

   5. Applied rewrites 56.1%

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

   7. Applied rewrites 59.1%

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

Alternative 9: 40.3% 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 96.4%

   \[\frac{x}{y} \cdot \left(z - t\right) + t \]
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 32.8

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

5. Applied rewrites 32.8%

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

7. Applied rewrites 36.8%

   \[\leadsto \color{blue}{\frac{x}{y} \cdot z} \]
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 2024235 
(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))