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

Percentage Accurate: 97.9% → 97.9%

Time: 5.3s

Alternatives: 7

Speedup: 1.1×

• 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: 97.9% 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, 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 98.2%

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

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

4. Applied rewrites 98.2%

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

Alternative 2: 93.3% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;\frac{x}{y} \leq -20000000000 \lor \neg \left(\frac{x}{y} \leq 2 \cdot 10^{-7}\right):\\ \;\;\;\;\frac{z - t}{y} \cdot x\\ \mathbf{else}:\\ \;\;\;\;\frac{z \cdot x}{y} + t\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= (/ x y) -20000000000.0) (not (<= (/ x y) 2e-7)))
   (* (/ (- z t) y) x)
   (+ (/ (* z x) y) t)))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (((x / y) <= -20000000000.0) || !((x / y) <= 2e-7)) {
		tmp = ((z - t) / y) * x;
	} else {
		tmp = ((z * 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) <= (-20000000000.0d0)) .or. (.not. ((x / y) <= 2d-7))) then
        tmp = ((z - t) / y) * x
    else
        tmp = ((z * 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) <= -20000000000.0) || !((x / y) <= 2e-7)) {
		tmp = ((z - t) / y) * x;
	} else {
		tmp = ((z * x) / y) + t;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if ((x / y) <= -20000000000.0) or not ((x / y) <= 2e-7):
		tmp = ((z - t) / y) * x
	else:
		tmp = ((z * x) / y) + t
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((Float64(x / y) <= -20000000000.0) || !(Float64(x / y) <= 2e-7))
		tmp = Float64(Float64(Float64(z - t) / y) * x);
	else
		tmp = Float64(Float64(Float64(z * x) / y) + t);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (((x / y) <= -20000000000.0) || ~(((x / y) <= 2e-7)))
		tmp = ((z - t) / y) * x;
	else
		tmp = ((z * x) / y) + t;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[N[(x / y), $MachinePrecision], -20000000000.0], N[Not[LessEqual[N[(x / y), $MachinePrecision], 2e-7]], $MachinePrecision]], N[(N[(N[(z - t), $MachinePrecision] / y), $MachinePrecision] * x), $MachinePrecision], N[(N[(N[(z * x), $MachinePrecision] / y), $MachinePrecision] + t), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if (/.f64 x y) < -2e10 or 1.9999999999999999e-7 < (/.f64 x y)

   1. Initial program 97.8%

      \[\frac{x}{y} \cdot \left(z - t\right) + t \]
   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 95.2

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

   5. Applied rewrites 95.2%

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

   if -2e10 < (/.f64 x y) < 1.9999999999999999e-7

   1. Initial program 98.7%

      \[\frac{x}{y} \cdot \left(z - t\right) + t \]
   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. associate-*l/ N/A

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

      4. lower-/.f64 N/A

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

      5. *-commutative N/A

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

      6. lower-*.f64 92.6

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

   4. Applied rewrites 92.6%

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

   5. Taylor expanded in z around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 94.4

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

   7. Applied rewrites 94.4%

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

4. Final simplification 94.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{x}{y} \leq -20000000000 \lor \neg \left(\frac{x}{y} \leq 2 \cdot 10^{-7}\right):\\ \;\;\;\;\frac{z - t}{y} \cdot x\\ \mathbf{else}:\\ \;\;\;\;\frac{z \cdot x}{y} + t\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 83.2% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;\frac{x}{y} \leq -2 \cdot 10^{-66} \lor \neg \left(\frac{x}{y} \leq 2 \cdot 10^{-7}\right):\\ \;\;\;\;\frac{z - t}{y} \cdot x\\ \mathbf{else}:\\ \;\;\;\;\left(1 - \frac{x}{y}\right) \cdot t\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= (/ x y) -2e-66) (not (<= (/ x y) 2e-7)))
   (* (/ (- 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) <= -2e-66) || !((x / y) <= 2e-7)) {
		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) <= (-2d-66)) .or. (.not. ((x / y) <= 2d-7))) 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) <= -2e-66) || !((x / y) <= 2e-7)) {
		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) <= -2e-66) or not ((x / y) <= 2e-7):
		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) <= -2e-66) || !(Float64(x / y) <= 2e-7))
		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) <= -2e-66) || ~(((x / y) <= 2e-7)))
		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], -2e-66], N[Not[LessEqual[N[(x / y), $MachinePrecision], 2e-7]], $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) < -2e-66 or 1.9999999999999999e-7 < (/.f64 x y)

   1. Initial program 98.0%

      \[\frac{x}{y} \cdot \left(z - t\right) + t \]
   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 93.2

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

   5. Applied rewrites 93.2%

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

   if -2e-66 < (/.f64 x y) < 1.9999999999999999e-7

   1. Initial program 98.5%

      \[\frac{x}{y} \cdot \left(z - t\right) + t \]
   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 75.3

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

   5. Applied rewrites 75.3%

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

4. Final simplification 86.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{x}{y} \leq -2 \cdot 10^{-66} \lor \neg \left(\frac{x}{y} \leq 2 \cdot 10^{-7}\right):\\ \;\;\;\;\frac{z - t}{y} \cdot x\\ \mathbf{else}:\\ \;\;\;\;\left(1 - \frac{x}{y}\right) \cdot t\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 73.7% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -4.6 \cdot 10^{-58} \lor \neg \left(t \leq 2.25 \cdot 10^{-39}\right):\\ \;\;\;\;\left(1 - \frac{x}{y}\right) \cdot t\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{y} \cdot z\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= t -4.6e-58) (not (<= t 2.25e-39)))
   (* (- 1.0 (/ x y)) t)
   (* (/ x y) z)))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((t <= -4.6e-58) || !(t <= 2.25e-39)) {
		tmp = (1.0 - (x / y)) * t;
	} 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 <= (-4.6d-58)) .or. (.not. (t <= 2.25d-39))) then
        tmp = (1.0d0 - (x / y)) * t
    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 <= -4.6e-58) || !(t <= 2.25e-39)) {
		tmp = (1.0 - (x / y)) * t;
	} else {
		tmp = (x / y) * z;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (t <= -4.6e-58) or not (t <= 2.25e-39):
		tmp = (1.0 - (x / y)) * t
	else:
		tmp = (x / y) * z
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((t <= -4.6e-58) || !(t <= 2.25e-39))
		tmp = Float64(Float64(1.0 - Float64(x / y)) * t);
	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 <= -4.6e-58) || ~((t <= 2.25e-39)))
		tmp = (1.0 - (x / y)) * t;
	else
		tmp = (x / y) * z;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[t, -4.6e-58], N[Not[LessEqual[t, 2.25e-39]], $MachinePrecision]], N[(N[(1.0 - N[(x / y), $MachinePrecision]), $MachinePrecision] * t), $MachinePrecision], N[(N[(x / y), $MachinePrecision] * z), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if t < -4.5999999999999998e-58 or 2.25e-39 < t

   1. Initial program 99.9%

      \[\frac{x}{y} \cdot \left(z - t\right) + t \]
   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 82.8

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

   5. Applied rewrites 82.8%

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

   if -4.5999999999999998e-58 < t < 2.25e-39

   1. Initial program 95.8%

      \[\frac{x}{y} \cdot \left(z - t\right) + t \]
   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 66.4

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

   5. Applied rewrites 66.4%

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

4. Final simplification 76.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -4.6 \cdot 10^{-58} \lor \neg \left(t \leq 2.25 \cdot 10^{-39}\right):\\ \;\;\;\;\left(1 - \frac{x}{y}\right) \cdot t\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{y} \cdot z\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 49.2% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -4 \cdot 10^{+111} \lor \neg \left(t \leq 8.4 \cdot 10^{+18}\right):\\ \;\;\;\;\frac{-x}{y} \cdot t\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{y} \cdot z\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= t -4e+111) (not (<= t 8.4e+18))) (* (/ (- x) y) t) (* (/ x y) z)))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((t <= -4e+111) || !(t <= 8.4e+18)) {
		tmp = (-x / y) * t;
	} 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 <= (-4d+111)) .or. (.not. (t <= 8.4d+18))) then
        tmp = (-x / y) * t
    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 <= -4e+111) || !(t <= 8.4e+18)) {
		tmp = (-x / y) * t;
	} else {
		tmp = (x / y) * z;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (t <= -4e+111) or not (t <= 8.4e+18):
		tmp = (-x / y) * t
	else:
		tmp = (x / y) * z
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((t <= -4e+111) || !(t <= 8.4e+18))
		tmp = Float64(Float64(Float64(-x) / y) * t);
	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 <= -4e+111) || ~((t <= 8.4e+18)))
		tmp = (-x / y) * t;
	else
		tmp = (x / y) * z;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[t, -4e+111], N[Not[LessEqual[t, 8.4e+18]], $MachinePrecision]], N[(N[((-x) / y), $MachinePrecision] * t), $MachinePrecision], N[(N[(x / y), $MachinePrecision] * z), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if t < -3.99999999999999983e111 or 8.4e18 < t

   1. Initial program 99.9%

      \[\frac{x}{y} \cdot \left(z - t\right) + t \]
   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 56.6

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

   5. Applied rewrites 56.6%

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

   6. Taylor expanded in z around 0

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

   8. Applied rewrites 54.8%

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

   if -3.99999999999999983e111 < t < 8.4e18

   1. Initial program 97.1%

      \[\frac{x}{y} \cdot \left(z - t\right) + t \]
   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 60.4

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

   5. Applied rewrites 60.4%

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

4. Final simplification 58.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -4 \cdot 10^{+111} \lor \neg \left(t \leq 8.4 \cdot 10^{+18}\right):\\ \;\;\;\;\frac{-x}{y} \cdot t\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{y} \cdot z\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 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 98.2%

   \[\frac{x}{y} \cdot \left(z - t\right) + t \]
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 46.5

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

5. Applied rewrites 46.5%

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

Alternative 7: 37.6% 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 98.2%

   \[\frac{x}{y} \cdot \left(z - t\right) + t \]
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 65.8

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

5. Applied rewrites 65.8%

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

6. Taylor expanded in z around inf

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

8. Applied rewrites 41.5%

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

Developer Target 1: 97.5% 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 2024326 
(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))