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

Percentage Accurate: 97.5% → 97.8%

Time: 6.2s

Alternatives: 10

Speedup: 1.1×

• 24.7% 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: 97.5% 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

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq 3.6 \cdot 10^{-43}:\\ \;\;\;\;\frac{x}{y} \cdot \left(z - t\right) + t\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(\frac{z - t}{y}, x, t\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= x 3.6e-43) (+ (* (/ x y) (- z t)) t) (fma (/ (- z t) y) x t)))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (x <= 3.6e-43) {
		tmp = ((x / y) * (z - t)) + t;
	} else {
		tmp = fma(((z - t) / y), x, t);
	}
	return tmp;
}

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (x <= 3.6e-43)
		tmp = Float64(Float64(Float64(x / y) * Float64(z - t)) + t);
	else
		tmp = fma(Float64(Float64(z - t) / y), x, t);
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[x, 3.6e-43], N[(N[(N[(x / y), $MachinePrecision] * N[(z - t), $MachinePrecision]), $MachinePrecision] + t), $MachinePrecision], N[(N[(N[(z - t), $MachinePrecision] / y), $MachinePrecision] * x + t), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < 3.5999999999999999e-43

   1. Initial program 98.8%

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

   if 3.5999999999999999e-43 < x

   1. Initial program 91.8%

      \[\frac{x}{y} \cdot \left(z - t\right) + t \]
   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 98.2

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

   4. Applied rewrites 98.2%

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

Alternative 2: 82.8% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;\frac{x}{y} \leq -1 \cdot 10^{-45} \lor \neg \left(\frac{x}{y} \leq 2 \cdot 10^{-19}\right):\\ \;\;\;\;\frac{z - t}{y} \cdot x\\ \mathbf{else}:\\ \;\;\;\;\left(1 - \frac{x}{y}\right) \cdot t\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= (/ x y) -1e-45) (not (<= (/ x y) 2e-19)))
   (* (/ (- z t) y) x)
   (* (- 1.0 (/ x y)) t)))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (((x / y) <= -1e-45) || !((x / y) <= 2e-19)) {
		tmp = ((z - t) / y) * x;
	} else {
		tmp = (1.0 - (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 (((x / y) <= (-1d-45)) .or. (.not. ((x / y) <= 2d-19))) then
        tmp = ((z - t) / y) * x
    else
        tmp = (1.0d0 - (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 (((x / y) <= -1e-45) || !((x / y) <= 2e-19)) {
		tmp = ((z - t) / y) * x;
	} else {
		tmp = (1.0 - (x / y)) * t;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if ((x / y) <= -1e-45) or not ((x / y) <= 2e-19):
		tmp = ((z - t) / y) * x
	else:
		tmp = (1.0 - (x / y)) * t
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((Float64(x / y) <= -1e-45) || !(Float64(x / y) <= 2e-19))
		tmp = Float64(Float64(Float64(z - t) / y) * x);
	else
		tmp = Float64(Float64(1.0 - Float64(x / y)) * t);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (((x / y) <= -1e-45) || ~(((x / y) <= 2e-19)))
		tmp = ((z - t) / y) * x;
	else
		tmp = (1.0 - (x / y)) * t;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[N[(x / y), $MachinePrecision], -1e-45], N[Not[LessEqual[N[(x / y), $MachinePrecision], 2e-19]], $MachinePrecision]], N[(N[(N[(z - t), $MachinePrecision] / y), $MachinePrecision] * x), $MachinePrecision], N[(N[(1.0 - N[(x / y), $MachinePrecision]), $MachinePrecision] * t), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if (/.f64 x y) < -9.99999999999999984e-46 or 2e-19 < (/.f64 x y)

   1. Initial program 95.3%

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

   3. Taylor expanded in x around inf

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

      1. div-sub N/A

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

      2. *-commutative N/A

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

      3. lower-*.f64 N/A

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

      4. lower-/.f64 N/A

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

      5. lower--.f64 86.5

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

   5. Applied rewrites 86.5%

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

   if -9.99999999999999984e-46 < (/.f64 x y) < 2e-19

   1. Initial program 99.1%

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

   3. Taylor expanded in z around 0

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

      1. mul-1-neg N/A

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

      2. associate-/l* N/A

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

      3. distribute-rgt-neg-in N/A

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

      4. mul-1-neg N/A

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

      5. *-rgt-identity N/A

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

      6. distribute-lft-in N/A

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

      7. *-commutative N/A

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

      8. lower-*.f64 N/A

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

      9. fp-cancel-sign-sub-inv N/A

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

      10. metadata-eval N/A

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

      11. *-lft-identity N/A

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

      12. lower--.f64 N/A

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

      13. lower-/.f64 76.6

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

   5. Applied rewrites 76.6%

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

4. Final simplification 82.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{x}{y} \leq -1 \cdot 10^{-45} \lor \neg \left(\frac{x}{y} \leq 2 \cdot 10^{-19}\right):\\ \;\;\;\;\frac{z - t}{y} \cdot x\\ \mathbf{else}:\\ \;\;\;\;\left(1 - \frac{x}{y}\right) \cdot t\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 82.6% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;\frac{x}{y} \leq -1 \cdot 10^{-45}:\\ \;\;\;\;\frac{\left(z - t\right) \cdot x}{y}\\ \mathbf{elif}\;\frac{x}{y} \leq 2 \cdot 10^{-19}:\\ \;\;\;\;\left(1 - \frac{x}{y}\right) \cdot t\\ \mathbf{else}:\\ \;\;\;\;\frac{z - t}{y} \cdot x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= (/ x y) -1e-45)
   (/ (* (- z t) x) y)
   (if (<= (/ x y) 2e-19) (* (- 1.0 (/ x y)) t) (* (/ (- z t) y) x))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((x / y) <= -1e-45) {
		tmp = ((z - t) * x) / y;
	} else if ((x / y) <= 2e-19) {
		tmp = (1.0 - (x / y)) * t;
	} else {
		tmp = ((z - t) / y) * x;
	}
	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) <= (-1d-45)) then
        tmp = ((z - t) * x) / y
    else if ((x / y) <= 2d-19) then
        tmp = (1.0d0 - (x / y)) * t
    else
        tmp = ((z - t) / y) * x
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if ((x / y) <= -1e-45) {
		tmp = ((z - t) * x) / y;
	} else if ((x / y) <= 2e-19) {
		tmp = (1.0 - (x / y)) * t;
	} else {
		tmp = ((z - t) / y) * x;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (x / y) <= -1e-45:
		tmp = ((z - t) * x) / y
	elif (x / y) <= 2e-19:
		tmp = (1.0 - (x / y)) * t
	else:
		tmp = ((z - t) / y) * x
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (Float64(x / y) <= -1e-45)
		tmp = Float64(Float64(Float64(z - t) * x) / y);
	elseif (Float64(x / y) <= 2e-19)
		tmp = Float64(Float64(1.0 - Float64(x / y)) * t);
	else
		tmp = Float64(Float64(Float64(z - t) / y) * x);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((x / y) <= -1e-45)
		tmp = ((z - t) * x) / y;
	elseif ((x / y) <= 2e-19)
		tmp = (1.0 - (x / y)) * t;
	else
		tmp = ((z - t) / y) * x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[N[(x / y), $MachinePrecision], -1e-45], N[(N[(N[(z - t), $MachinePrecision] * x), $MachinePrecision] / y), $MachinePrecision], If[LessEqual[N[(x / y), $MachinePrecision], 2e-19], N[(N[(1.0 - N[(x / y), $MachinePrecision]), $MachinePrecision] * t), $MachinePrecision], N[(N[(N[(z - t), $MachinePrecision] / y), $MachinePrecision] * x), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if (/.f64 x y) < -9.99999999999999984e-46

   1. Initial program 94.7%

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

   3. Taylor expanded in x around inf

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

      1. div-sub N/A

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

      2. *-commutative N/A

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

      3. lower-*.f64 N/A

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

      4. lower-/.f64 N/A

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

      5. lower--.f64 84.8

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

   5. Applied rewrites 84.8%

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

   7. Applied rewrites 86.5%

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

   if -9.99999999999999984e-46 < (/.f64 x y) < 2e-19

   1. Initial program 99.1%

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

   3. Taylor expanded in z around 0

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

      1. mul-1-neg N/A

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

      2. associate-/l* N/A

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

      3. distribute-rgt-neg-in N/A

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

      4. mul-1-neg N/A

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

      5. *-rgt-identity N/A

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

      6. distribute-lft-in N/A

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

      7. *-commutative N/A

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

      8. lower-*.f64 N/A

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

      9. fp-cancel-sign-sub-inv N/A

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

      10. metadata-eval N/A

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

      11. *-lft-identity N/A

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

      12. lower--.f64 N/A

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

      13. lower-/.f64 76.6

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

   5. Applied rewrites 76.6%

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

   if 2e-19 < (/.f64 x y)

   1. Initial program 95.8%

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

   3. Taylor expanded in x around inf

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

      1. div-sub N/A

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

      2. *-commutative N/A

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

      3. lower-*.f64 N/A

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

      4. lower-/.f64 N/A

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

      5. lower--.f64 88.3

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

   5. Applied rewrites 88.3%

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

Alternative 4: 74.6% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -5.9 \cdot 10^{+149} \lor \neg \left(z \leq 1.15 \cdot 10^{+107}\right):\\ \;\;\;\;\frac{x}{y} \cdot z\\ \mathbf{else}:\\ \;\;\;\;\left(1 - \frac{x}{y}\right) \cdot t\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= z -5.9e+149) (not (<= z 1.15e+107)))
   (* (/ x y) z)
   (* (- 1.0 (/ x y)) t)))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((z <= -5.9e+149) || !(z <= 1.15e+107)) {
		tmp = (x / y) * z;
	} else {
		tmp = (1.0 - (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 <= (-5.9d+149)) .or. (.not. (z <= 1.15d+107))) then
        tmp = (x / y) * z
    else
        tmp = (1.0d0 - (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 <= -5.9e+149) || !(z <= 1.15e+107)) {
		tmp = (x / y) * z;
	} else {
		tmp = (1.0 - (x / y)) * t;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (z <= -5.9e+149) or not (z <= 1.15e+107):
		tmp = (x / y) * z
	else:
		tmp = (1.0 - (x / y)) * t
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((z <= -5.9e+149) || !(z <= 1.15e+107))
		tmp = Float64(Float64(x / y) * z);
	else
		tmp = Float64(Float64(1.0 - Float64(x / y)) * t);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((z <= -5.9e+149) || ~((z <= 1.15e+107)))
		tmp = (x / y) * z;
	else
		tmp = (1.0 - (x / y)) * t;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[z, -5.9e+149], N[Not[LessEqual[z, 1.15e+107]], $MachinePrecision]], N[(N[(x / y), $MachinePrecision] * z), $MachinePrecision], N[(N[(1.0 - N[(x / y), $MachinePrecision]), $MachinePrecision] * t), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -5.9000000000000002e149 or 1.15e107 < z

   1. Initial program 98.6%

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

   3. Taylor expanded in z around inf

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

      1. associate-*l/ N/A

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

      2. lower-*.f64 N/A

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

      3. lower-/.f64 71.6

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

   5. Applied rewrites 71.6%

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

   if -5.9000000000000002e149 < z < 1.15e107

   1. Initial program 96.2%

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

   3. Taylor expanded in z around 0

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

      1. mul-1-neg N/A

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

      2. associate-/l* N/A

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

      3. distribute-rgt-neg-in N/A

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

      4. mul-1-neg N/A

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

      5. *-rgt-identity N/A

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

      6. distribute-lft-in N/A

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

      7. *-commutative N/A

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

      8. lower-*.f64 N/A

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

      9. fp-cancel-sign-sub-inv N/A

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

      10. metadata-eval N/A

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

      11. *-lft-identity N/A

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

      12. lower--.f64 N/A

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

      13. lower-/.f64 75.5

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

   5. Applied rewrites 75.5%

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

4. Final simplification 74.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -5.9 \cdot 10^{+149} \lor \neg \left(z \leq 1.15 \cdot 10^{+107}\right):\\ \;\;\;\;\frac{x}{y} \cdot z\\ \mathbf{else}:\\ \;\;\;\;\left(1 - \frac{x}{y}\right) \cdot t\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 49.5% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -8.5 \cdot 10^{+43} \lor \neg \left(t \leq 2.9 \cdot 10^{+97}\right):\\ \;\;\;\;\left(-t\right) \cdot \frac{x}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{y} \cdot z\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= t -8.5e+43) (not (<= t 2.9e+97)))
   (* (- t) (/ x y))
   (* (/ x y) z)))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((t <= -8.5e+43) || !(t <= 2.9e+97)) {
		tmp = -t * (x / y);
	} else {
		tmp = (x / y) * z;
	}
	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 <= (-8.5d+43)) .or. (.not. (t <= 2.9d+97))) then
        tmp = -t * (x / y)
    else
        tmp = (x / y) * z
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if ((t <= -8.5e+43) || !(t <= 2.9e+97)) {
		tmp = -t * (x / y);
	} else {
		tmp = (x / y) * z;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (t <= -8.5e+43) or not (t <= 2.9e+97):
		tmp = -t * (x / y)
	else:
		tmp = (x / y) * z
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((t <= -8.5e+43) || !(t <= 2.9e+97))
		tmp = Float64(Float64(-t) * Float64(x / y));
	else
		tmp = Float64(Float64(x / y) * z);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((t <= -8.5e+43) || ~((t <= 2.9e+97)))
		tmp = -t * (x / y);
	else
		tmp = (x / y) * z;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[t, -8.5e+43], N[Not[LessEqual[t, 2.9e+97]], $MachinePrecision]], N[((-t) * N[(x / y), $MachinePrecision]), $MachinePrecision], N[(N[(x / y), $MachinePrecision] * z), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if t < -8.5e43 or 2.89999999999999987e97 < t

   1. Initial program 100.0%

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

   3. Taylor expanded in x around inf

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

      1. div-sub N/A

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

      2. *-commutative N/A

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

      3. lower-*.f64 N/A

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

      4. lower-/.f64 N/A

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

      5. lower--.f64 44.5

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

   5. Applied rewrites 44.5%

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

   6. Taylor expanded in z around 0

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

   8. Applied rewrites 36.9%

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

   10. Applied rewrites 42.3%

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

   if -8.5e43 < t < 2.89999999999999987e97

   1. Initial program 94.9%

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

   3. Taylor expanded in z around inf

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

      1. associate-*l/ N/A

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

      2. lower-*.f64 N/A

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

      3. lower-/.f64 56.7

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

   5. Applied rewrites 56.7%

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

4. Final simplification 51.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -8.5 \cdot 10^{+43} \lor \neg \left(t \leq 2.9 \cdot 10^{+97}\right):\\ \;\;\;\;\left(-t\right) \cdot \frac{x}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{y} \cdot z\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 47.2% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -6 \cdot 10^{-152}:\\ \;\;\;\;\frac{z}{y} \cdot x\\ \mathbf{elif}\;z \leq 5.8 \cdot 10^{-172}:\\ \;\;\;\;\frac{-t}{y} \cdot x\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{y} \cdot z\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= z -6e-152)
   (* (/ z y) x)
   (if (<= z 5.8e-172) (* (/ (- t) y) x) (* (/ x y) z))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (z <= -6e-152) {
		tmp = (z / y) * x;
	} else if (z <= 5.8e-172) {
		tmp = (-t / y) * x;
	} else {
		tmp = (x / y) * z;
	}
	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 <= (-6d-152)) then
        tmp = (z / y) * x
    else if (z <= 5.8d-172) then
        tmp = (-t / y) * x
    else
        tmp = (x / y) * z
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if (z <= -6e-152) {
		tmp = (z / y) * x;
	} else if (z <= 5.8e-172) {
		tmp = (-t / y) * x;
	} else {
		tmp = (x / y) * z;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if z <= -6e-152:
		tmp = (z / y) * x
	elif z <= 5.8e-172:
		tmp = (-t / y) * x
	else:
		tmp = (x / y) * z
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (z <= -6e-152)
		tmp = Float64(Float64(z / y) * x);
	elseif (z <= 5.8e-172)
		tmp = Float64(Float64(Float64(-t) / y) * x);
	else
		tmp = Float64(Float64(x / y) * z);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (z <= -6e-152)
		tmp = (z / y) * x;
	elseif (z <= 5.8e-172)
		tmp = (-t / y) * x;
	else
		tmp = (x / y) * z;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[z, -6e-152], N[(N[(z / y), $MachinePrecision] * x), $MachinePrecision], If[LessEqual[z, 5.8e-172], N[(N[((-t) / y), $MachinePrecision] * x), $MachinePrecision], N[(N[(x / y), $MachinePrecision] * z), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if z < -6e-152

   1. Initial program 95.6%

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

   3. Taylor expanded in x around inf

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

      1. div-sub N/A

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

      2. *-commutative N/A

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

      3. lower-*.f64 N/A

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

      4. lower-/.f64 N/A

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

      5. lower--.f64 61.8

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

   5. Applied rewrites 61.8%

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

   6. Taylor expanded in z around inf

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

   8. Applied rewrites 47.4%

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

   if -6e-152 < z < 5.79999999999999995e-172

   1. Initial program 95.2%

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

   3. Taylor expanded in x around inf

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

      1. div-sub N/A

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

      2. *-commutative N/A

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

      3. lower-*.f64 N/A

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

      4. lower-/.f64 N/A

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

      5. lower--.f64 54.4

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

   5. Applied rewrites 54.4%

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

   6. Taylor expanded in z around 0

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

   8. Applied rewrites 50.4%

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

   if 5.79999999999999995e-172 < z

   1. Initial program 99.0%

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

   3. Taylor expanded in z around inf

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

      1. associate-*l/ N/A

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

      2. lower-*.f64 N/A

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

      3. lower-/.f64 54.7

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

   5. Applied rewrites 54.7%

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

Alternative 7: 97.8% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq 3.6 \cdot 10^{-43}:\\ \;\;\;\;\mathsf{fma}\left(\frac{x}{y}, z - t, t\right)\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(\frac{z - t}{y}, x, t\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= x 3.6e-43) (fma (/ x y) (- z t) t) (fma (/ (- z t) y) x t)))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (x <= 3.6e-43) {
		tmp = fma((x / y), (z - t), t);
	} else {
		tmp = fma(((z - t) / y), x, t);
	}
	return tmp;
}

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (x <= 3.6e-43)
		tmp = fma(Float64(x / y), Float64(z - t), t);
	else
		tmp = fma(Float64(Float64(z - t) / y), x, t);
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[x, 3.6e-43], N[(N[(x / y), $MachinePrecision] * N[(z - t), $MachinePrecision] + t), $MachinePrecision], N[(N[(N[(z - t), $MachinePrecision] / y), $MachinePrecision] * x + t), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < 3.5999999999999999e-43

   1. Initial program 98.8%

      \[\frac{x}{y} \cdot \left(z - t\right) + t \]
   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 98.8

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

   4. Applied rewrites 98.8%

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

   if 3.5999999999999999e-43 < x

   1. Initial program 91.8%

      \[\frac{x}{y} \cdot \left(z - t\right) + t \]
   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 98.2

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

   4. Applied rewrites 98.2%

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

Alternative 8: 97.5% 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 96.9%

   \[\frac{x}{y} \cdot \left(z - t\right) + t \]
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 96.9

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

4. Applied rewrites 96.9%

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

Alternative 9: 40.6% 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 96.9%

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

3. Taylor expanded in z around inf

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

   1. associate-*l/ N/A

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

   2. lower-*.f64 N/A

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

   3. lower-/.f64 40.7

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

5. Applied rewrites 40.7%

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

Alternative 10: 37.2% accurate, 1.4× speedup

Math

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

FPCore

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

C

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

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 / y) * x
end function

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 96.9%

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

3. Taylor expanded in x around inf

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

   1. div-sub N/A

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

   2. *-commutative N/A

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

   3. lower-*.f64 N/A

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

   4. lower-/.f64 N/A

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

   5. lower--.f64 59.1

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

5. Applied rewrites 59.1%

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

6. Taylor expanded in z around inf

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

8. Applied rewrites 37.7%

   \[\leadsto \frac{z}{y} \cdot x \]
9. Add Preprocessing

Developer Target 1: 97.2% 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 2024320 
(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))