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

Percentage Accurate: 97.7% → 97.7%

Time: 8.7s

Alternatives: 7

Speedup: 1.1×

• 25.1% 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: 97.7% 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: 97.7% 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 97.0%

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

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

   3. lower-fma.f64 97.0

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

4. Applied egg-rr 97.0%

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

Alternative 2: 75.8% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := -\frac{x \cdot t}{y}\\ \mathbf{if}\;\frac{x}{y} \leq -5 \cdot 10^{+293}:\\ \;\;\;\;\frac{x}{y} \cdot z\\ \mathbf{elif}\;\frac{x}{y} \leq -500000000:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;\frac{x}{y} \leq 2 \cdot 10^{+152}:\\ \;\;\;\;\mathsf{fma}\left(\frac{x}{y}, z, t\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (- (/ (* x t) y))))
   (if (<= (/ x y) -5e+293)
     (* (/ x y) z)
     (if (<= (/ x y) -500000000.0)
       t_1
       (if (<= (/ x y) 2e+152) (fma (/ x y) z t) t_1)))))

C

double code(double x, double y, double z, double t) {
	double t_1 = -((x * t) / y);
	double tmp;
	if ((x / y) <= -5e+293) {
		tmp = (x / y) * z;
	} else if ((x / y) <= -500000000.0) {
		tmp = t_1;
	} else if ((x / y) <= 2e+152) {
		tmp = fma((x / y), z, t);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Julia

function code(x, y, z, t)
	t_1 = Float64(-Float64(Float64(x * t) / y))
	tmp = 0.0
	if (Float64(x / y) <= -5e+293)
		tmp = Float64(Float64(x / y) * z);
	elseif (Float64(x / y) <= -500000000.0)
		tmp = t_1;
	elseif (Float64(x / y) <= 2e+152)
		tmp = fma(Float64(x / y), z, t);
	else
		tmp = t_1;
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = (-N[(N[(x * t), $MachinePrecision] / y), $MachinePrecision])}, If[LessEqual[N[(x / y), $MachinePrecision], -5e+293], N[(N[(x / y), $MachinePrecision] * z), $MachinePrecision], If[LessEqual[N[(x / y), $MachinePrecision], -500000000.0], t$95$1, If[LessEqual[N[(x / y), $MachinePrecision], 2e+152], N[(N[(x / y), $MachinePrecision] * z + t), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if (/.f64 x y) < -5.00000000000000033e293

   1. Initial program 90.8%

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

   3. Taylor expanded in z around inf

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

      1. lower-/.f64 N/A

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

      2. lower-*.f64 70.6

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

   5. Simplified 70.6%

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

      1. *-commutative N/A

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

      2. associate-/l* N/A

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

      3. lift-/.f64 N/A

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

      4. lower-*.f64 75.8

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

   7. Applied egg-rr 75.8%

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

   if -5.00000000000000033e293 < (/.f64 x y) < -5e8 or 2.0000000000000001e152 < (/.f64 x y)

   1. Initial program 96.6%

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

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

      3. lower--.f64 N/A

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

      4. lower-/.f64 N/A

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

      5. lower-*.f64 65.1

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

   5. Simplified 65.1%

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

   6. Taylor expanded in x around inf

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

      1. associate-*r/ N/A

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

      2. lower-/.f64 N/A

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

      3. neg-mul-1 N/A

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

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

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

      5. mul-1-neg N/A

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

      6. lower-*.f64 N/A

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

      7. mul-1-neg N/A

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

      8. lower-neg.f64 64.6

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

   8. Simplified 64.6%

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

   if -5e8 < (/.f64 x y) < 2.0000000000000001e152

   1. Initial program 98.0%

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

   3. Taylor expanded in z around inf

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

      1. lower-/.f64 N/A

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

      2. lower-*.f64 87.6

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

   5. Simplified 87.6%

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

      1. associate-/l* N/A

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

      2. lift-/.f64 N/A

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

      3. *-commutative N/A

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

      4. lift-/.f64 N/A

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

      5. associate-*l/ N/A

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

      6. associate-*r/ N/A

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

      7. lift-/.f64 N/A

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

      8. *-commutative N/A

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

      9. lower-fma.f64 89.5

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

   7. Applied egg-rr 89.5%

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

4. Final simplification 80.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{x}{y} \leq -5 \cdot 10^{+293}:\\ \;\;\;\;\frac{x}{y} \cdot z\\ \mathbf{elif}\;\frac{x}{y} \leq -500000000:\\ \;\;\;\;-\frac{x \cdot t}{y}\\ \mathbf{elif}\;\frac{x}{y} \leq 2 \cdot 10^{+152}:\\ \;\;\;\;\mathsf{fma}\left(\frac{x}{y}, z, t\right)\\ \mathbf{else}:\\ \;\;\;\;-\frac{x \cdot t}{y}\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 94.1% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{x \cdot \left(z - t\right)}{y}\\ \mathbf{if}\;\frac{x}{y} \leq -20:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;\frac{x}{y} \leq 5 \cdot 10^{-16}:\\ \;\;\;\;\mathsf{fma}\left(\frac{x}{y}, z, t\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (/ (* x (- z t)) y)))
   (if (<= (/ x y) -20.0) t_1 (if (<= (/ x y) 5e-16) (fma (/ x y) z t) t_1))))

C

double code(double x, double y, double z, double t) {
	double t_1 = (x * (z - t)) / y;
	double tmp;
	if ((x / y) <= -20.0) {
		tmp = t_1;
	} else if ((x / y) <= 5e-16) {
		tmp = fma((x / y), z, t);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Julia

function code(x, y, z, t)
	t_1 = Float64(Float64(x * Float64(z - t)) / y)
	tmp = 0.0
	if (Float64(x / y) <= -20.0)
		tmp = t_1;
	elseif (Float64(x / y) <= 5e-16)
		tmp = fma(Float64(x / y), z, t);
	else
		tmp = t_1;
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(N[(x * N[(z - t), $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision]}, If[LessEqual[N[(x / y), $MachinePrecision], -20.0], t$95$1, If[LessEqual[N[(x / y), $MachinePrecision], 5e-16], N[(N[(x / y), $MachinePrecision] * z + t), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if (/.f64 x y) < -20 or 5.0000000000000004e-16 < (/.f64 x y)

   1. Initial program 96.3%

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

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

      3. lower-/.f64 N/A

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

      4. lower-*.f64 N/A

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

      5. lower--.f64 94.5

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

   5. Simplified 94.5%

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

   if -20 < (/.f64 x y) < 5.0000000000000004e-16

   1. Initial program 97.7%

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

   3. Taylor expanded in z around inf

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

      1. lower-/.f64 N/A

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

      2. lower-*.f64 94.3

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

   5. Simplified 94.3%

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

      1. associate-/l* N/A

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

      2. lift-/.f64 N/A

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

      3. *-commutative N/A

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

      4. lift-/.f64 N/A

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

      5. associate-*l/ N/A

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

      6. associate-*r/ N/A

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

      7. lift-/.f64 N/A

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

      8. *-commutative N/A

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

      9. lower-fma.f64 96.0

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

   7. Applied egg-rr 96.0%

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

Alternative 4: 54.9% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{x}{y} \cdot z\\ \mathbf{if}\;\frac{x}{y} \leq -1 \cdot 10^{-53}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;\frac{x}{y} \leq 10^{-92}:\\ \;\;\;\;\frac{y \cdot t}{y}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (* (/ x y) z)))
   (if (<= (/ x y) -1e-53) t_1 (if (<= (/ x y) 1e-92) (/ (* y t) y) t_1))))

C

double code(double x, double y, double z, double t) {
	double t_1 = (x / y) * z;
	double tmp;
	if ((x / y) <= -1e-53) {
		tmp = t_1;
	} else if ((x / y) <= 1e-92) {
		tmp = (y * t) / 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 = (x / y) * z
    if ((x / y) <= (-1d-53)) then
        tmp = t_1
    else if ((x / y) <= 1d-92) then
        tmp = (y * t) / 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 = (x / y) * z;
	double tmp;
	if ((x / y) <= -1e-53) {
		tmp = t_1;
	} else if ((x / y) <= 1e-92) {
		tmp = (y * t) / y;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = (x / y) * z
	tmp = 0
	if (x / y) <= -1e-53:
		tmp = t_1
	elif (x / y) <= 1e-92:
		tmp = (y * t) / y
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(Float64(x / y) * z)
	tmp = 0.0
	if (Float64(x / y) <= -1e-53)
		tmp = t_1;
	elseif (Float64(x / y) <= 1e-92)
		tmp = Float64(Float64(y * t) / y);
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = (x / y) * z;
	tmp = 0.0;
	if ((x / y) <= -1e-53)
		tmp = t_1;
	elseif ((x / y) <= 1e-92)
		tmp = (y * t) / y;
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(N[(x / y), $MachinePrecision] * z), $MachinePrecision]}, If[LessEqual[N[(x / y), $MachinePrecision], -1e-53], t$95$1, If[LessEqual[N[(x / y), $MachinePrecision], 1e-92], N[(N[(y * t), $MachinePrecision] / y), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if (/.f64 x y) < -1.00000000000000003e-53 or 9.99999999999999988e-93 < (/.f64 x y)

   1. Initial program 97.0%

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

   3. Taylor expanded in z around inf

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

      1. lower-/.f64 N/A

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

      2. lower-*.f64 44.4

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

   5. Simplified 44.4%

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

      1. *-commutative N/A

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

      2. associate-/l* N/A

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

      3. lift-/.f64 N/A

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

      4. lower-*.f64 49.7

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

   7. Applied egg-rr 49.7%

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

   if -1.00000000000000003e-53 < (/.f64 x y) < 9.99999999999999988e-93

   1. Initial program 97.0%

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

      1. lift--.f64 N/A

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

      2. associate-*l/ N/A

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

      3. associate-/l* N/A

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

      4. *-commutative N/A

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

      5. lower-fma.f64 N/A

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

      6. lower-/.f64 94.9

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

   4. Applied egg-rr 94.9%

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

   5. Taylor expanded in z around 0

      \[\leadsto \mathsf{fma}\left(\frac{\color{blue}{-1 \cdot t}}{y}, x, t\right) \]
   6. Step-by-step derivation

      1. mul-1-neg N/A

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

      2. lower-neg.f64 79.0

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

   7. Simplified 79.0%

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

   8. Taylor expanded in y around 0

      \[\leadsto \color{blue}{\frac{-1 \cdot \left(t \cdot x\right) + t \cdot y}{y}} \]
   9. Step-by-step derivation

      1. lower-/.f64 N/A

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

      2. mul-1-neg N/A

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

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

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

      4. mul-1-neg N/A

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

      5. distribute-lft-out N/A

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

      6. lower-*.f64 N/A

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

      7. +-commutative N/A

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

      8. mul-1-neg N/A

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

      9. sub-neg N/A

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

      10. lower--.f64 54.0

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

   10. Simplified 54.0%

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

   11. Taylor expanded in y around inf

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

       1. lower-*.f64 54.0

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

   13. Simplified 54.0%

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

4. Final simplification 51.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{x}{y} \leq -1 \cdot 10^{-53}:\\ \;\;\;\;\frac{x}{y} \cdot z\\ \mathbf{elif}\;\frac{x}{y} \leq 10^{-92}:\\ \;\;\;\;\frac{y \cdot t}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{y} \cdot z\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 81.5% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -6 \cdot 10^{+96}:\\ \;\;\;\;\mathsf{fma}\left(\frac{z}{y}, x, t\right)\\ \mathbf{elif}\;z \leq 1.8 \cdot 10^{-22}:\\ \;\;\;\;t - \frac{x \cdot t}{y}\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(\frac{x}{y}, z, t\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= z -6e+96)
   (fma (/ z y) x t)
   (if (<= z 1.8e-22) (- t (/ (* x t) y)) (fma (/ x y) z t))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (z <= -6e+96) {
		tmp = fma((z / y), x, t);
	} else if (z <= 1.8e-22) {
		tmp = t - ((x * t) / y);
	} else {
		tmp = fma((x / y), z, t);
	}
	return tmp;
}

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (z <= -6e+96)
		tmp = fma(Float64(z / y), x, t);
	elseif (z <= 1.8e-22)
		tmp = Float64(t - Float64(Float64(x * t) / y));
	else
		tmp = fma(Float64(x / y), z, t);
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[z, -6e+96], N[(N[(z / y), $MachinePrecision] * x + t), $MachinePrecision], If[LessEqual[z, 1.8e-22], N[(t - N[(N[(x * t), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision], N[(N[(x / y), $MachinePrecision] * z + t), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if z < -6.0000000000000001e96

   1. Initial program 95.8%

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

      1. lift--.f64 N/A

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

      2. associate-*l/ N/A

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

      3. associate-/l* N/A

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

      4. *-commutative N/A

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

      5. lower-fma.f64 N/A

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

      6. lower-/.f64 93.7

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

   4. Applied egg-rr 93.7%

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

   5. Taylor expanded in z around inf

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

      1. lower-/.f64 91.4

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

   7. Simplified 91.4%

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

   if -6.0000000000000001e96 < z < 1.7999999999999999e-22

   1. Initial program 96.6%

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

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

      3. lower--.f64 N/A

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

      4. lower-/.f64 N/A

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

      5. lower-*.f64 81.0

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

   5. Simplified 81.0%

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

   if 1.7999999999999999e-22 < 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

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

      1. lower-/.f64 N/A

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

      2. lower-*.f64 86.1

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

   5. Simplified 86.1%

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

      1. associate-/l* N/A

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

      2. lift-/.f64 N/A

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

      3. *-commutative N/A

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

      4. lift-/.f64 N/A

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

      5. associate-*l/ N/A

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

      6. associate-*r/ N/A

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

      7. lift-/.f64 N/A

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

      8. *-commutative N/A

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

      9. lower-fma.f64 88.8

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

   7. Applied egg-rr 88.8%

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

4. Final simplification 85.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -6 \cdot 10^{+96}:\\ \;\;\;\;\mathsf{fma}\left(\frac{z}{y}, x, t\right)\\ \mathbf{elif}\;z \leq 1.8 \cdot 10^{-22}:\\ \;\;\;\;t - \frac{x \cdot t}{y}\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(\frac{x}{y}, z, t\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 76.1% accurate, 1.3× speedup

Math

\[\begin{array}{l} \\ \mathsf{fma}\left(\frac{x}{y}, z, t\right) \end{array} \]

FPCore

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

C

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

Julia

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

Wolfram

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

Derivation

1. Initial program 97.0%

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

3. Taylor expanded in z around inf

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

   1. lower-/.f64 N/A

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

   2. lower-*.f64 69.3

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

5. Simplified 69.3%

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

   1. associate-/l* N/A

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

   2. lift-/.f64 N/A

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

   3. *-commutative N/A

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

   4. lift-/.f64 N/A

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

   5. associate-*l/ N/A

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

   6. associate-*r/ N/A

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

   7. lift-/.f64 N/A

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

   8. *-commutative N/A

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

   9. lower-fma.f64 72.0

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

7. Applied egg-rr 72.0%

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

Alternative 7: 40.1% 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 97.0%

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

3. Taylor expanded in z around inf

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

   1. lower-/.f64 N/A

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

   2. lower-*.f64 35.1

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

5. Simplified 35.1%

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

   1. *-commutative N/A

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

   2. associate-/l* N/A

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

   3. lift-/.f64 N/A

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

   4. lower-*.f64 37.4

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

7. Applied egg-rr 37.4%

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

8. Final simplification 37.4%

   \[\leadsto \frac{x}{y} \cdot z \]
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 2024212 
(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))