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

Percentage Accurate: 98.0% → 98.0%

Time: 10.5s

Alternatives: 8

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: 98.0% 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: 98.0% accurate, 0.8× speedup

Math

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

FPCore

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

C

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

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

   2. clear-num N/A

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

   3. un-div-inv N/A

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

   4. /-lowering-/.f64 N/A

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

   5. --lowering--.f64 N/A

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

   6. /-lowering-/.f64 97.3

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

4. Applied egg-rr 97.3%

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

5. Final simplification 97.3%

   \[\leadsto t + \frac{z - t}{\frac{y}{x}} \]
6. Add Preprocessing

Alternative 2: 94.9% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x \cdot \frac{z - t}{y}\\ \mathbf{if}\;\frac{x}{y} \leq -2 \cdot 10^{+14}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;\frac{x}{y} \leq 2000000:\\ \;\;\;\;\mathsf{fma}\left(\frac{x}{y}, z, t\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (* x (/ (- z t) y))))
   (if (<= (/ x y) -2e+14)
     t_1
     (if (<= (/ x y) 2000000.0) (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) <= -2e+14) {
		tmp = t_1;
	} else if ((x / y) <= 2000000.0) {
		tmp = fma((x / y), z, t);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Julia

function code(x, y, z, t)
	t_1 = Float64(x * Float64(Float64(z - t) / y))
	tmp = 0.0
	if (Float64(x / y) <= -2e+14)
		tmp = t_1;
	elseif (Float64(x / y) <= 2000000.0)
		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[(x * N[(N[(z - t), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[N[(x / y), $MachinePrecision], -2e+14], t$95$1, If[LessEqual[N[(x / y), $MachinePrecision], 2000000.0], N[(N[(x / y), $MachinePrecision] * z + t), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if (/.f64 x y) < -2e14 or 2e6 < (/.f64 x y)

   1. Initial program 96.0%

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

      1. accelerator-lowering-fma.f64 N/A

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

      2. /-lowering-/.f64 N/A

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

      3. --lowering--.f64 96.1

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

   4. Applied egg-rr 96.1%

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

   5. Taylor expanded in x around inf

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

      1. div-sub N/A

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

      2. sub-neg N/A

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

      3. mul-1-neg N/A

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

      4. associate-/l* N/A

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

      5. /-lowering-/.f64 N/A

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

      6. *-lowering-*.f64 N/A

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

      7. mul-1-neg N/A

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

      8. sub-neg N/A

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

      9. --lowering--.f64 90.3

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

   7. Simplified 90.3%

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

      1. associate-/l* N/A

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

      2. *-commutative N/A

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

      3. *-lowering-*.f64 N/A

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

      4. /-lowering-/.f64 N/A

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

      5. --lowering--.f64 94.7

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

   9. Applied egg-rr 94.7%

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

   if -2e14 < (/.f64 x y) < 2e6

   1. Initial program 97.8%

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

   3. Taylor expanded in z around inf

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

   5. Simplified 94.5%

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

      1. accelerator-lowering-fma.f64 N/A

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

      2. /-lowering-/.f64 94.6

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

   7. Applied egg-rr 94.6%

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

4. Final simplification 94.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{x}{y} \leq -2 \cdot 10^{+14}:\\ \;\;\;\;x \cdot \frac{z - t}{y}\\ \mathbf{elif}\;\frac{x}{y} \leq 2000000:\\ \;\;\;\;\mathsf{fma}\left(\frac{x}{y}, z, t\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \frac{z - t}{y}\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 64.9% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := z \cdot \frac{x}{y}\\ \mathbf{if}\;\frac{x}{y} \leq -4 \cdot 10^{-68}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;\frac{x}{y} \leq 4 \cdot 10^{-42}:\\ \;\;\;\;t\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (* z (/ x y))))
   (if (<= (/ x y) -4e-68) t_1 (if (<= (/ x y) 4e-42) t t_1))))

C

double code(double x, double y, double z, double t) {
	double t_1 = z * (x / y);
	double tmp;
	if ((x / y) <= -4e-68) {
		tmp = t_1;
	} else if ((x / y) <= 4e-42) {
		tmp = 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 = z * (x / y)
    if ((x / y) <= (-4d-68)) then
        tmp = t_1
    else if ((x / y) <= 4d-42) then
        tmp = 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 = z * (x / y);
	double tmp;
	if ((x / y) <= -4e-68) {
		tmp = t_1;
	} else if ((x / y) <= 4e-42) {
		tmp = t;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = z * (x / y)
	tmp = 0
	if (x / y) <= -4e-68:
		tmp = t_1
	elif (x / y) <= 4e-42:
		tmp = t
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(z * Float64(x / y))
	tmp = 0.0
	if (Float64(x / y) <= -4e-68)
		tmp = t_1;
	elseif (Float64(x / y) <= 4e-42)
		tmp = t;
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = z * (x / y);
	tmp = 0.0;
	if ((x / y) <= -4e-68)
		tmp = t_1;
	elseif ((x / y) <= 4e-42)
		tmp = t;
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(z * N[(x / y), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[N[(x / y), $MachinePrecision], -4e-68], t$95$1, If[LessEqual[N[(x / y), $MachinePrecision], 4e-42], t, t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if (/.f64 x y) < -4.00000000000000027e-68 or 4.00000000000000015e-42 < (/.f64 x y)

   1. Initial program 96.7%

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

   3. Taylor expanded in z around inf

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

      1. +-rgt-identity N/A

         \[\leadsto \color{blue}{\frac{x \cdot z}{y} + 0} \]

      2. associate-/l* N/A

         \[\leadsto \color{blue}{x \cdot \frac{z}{y}} + 0 \]

      3. accelerator-lowering-fma.f64 N/A

         \[\leadsto \color{blue}{\mathsf{fma}\left(x, \frac{z}{y}, 0\right)} \]

      4. /-lowering-/.f64 48.4

         \[\leadsto \mathsf{fma}\left(x, \color{blue}{\frac{z}{y}}, 0\right) \]

   5. Simplified 48.4%

      \[\leadsto \color{blue}{\mathsf{fma}\left(x, \frac{z}{y}, 0\right)} \]
   6. Step-by-step derivation

      1. +-rgt-identity N/A

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

      2. *-commutative N/A

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

      3. associate-*l/ N/A

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

      4. associate-/l* N/A

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

      5. *-lowering-*.f64 N/A

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

      6. /-lowering-/.f64 50.6

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

   7. Applied egg-rr 50.6%

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

   if -4.00000000000000027e-68 < (/.f64 x y) < 4.00000000000000015e-42

   1. Initial program 97.3%

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

   3. Taylor expanded in x around 0

      \[\leadsto \color{blue}{t} \]
   4. Step-by-step derivation

   5. Simplified 81.5%

      \[\leadsto \color{blue}{t} \]
3. Recombined 2 regimes into one program.
4. Add Preprocessing

Alternative 4: 42.1% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;\frac{x}{y} \leq -2 \cdot 10^{+78}:\\ \;\;\;\;y \cdot \frac{t}{y}\\ \mathbf{else}:\\ \;\;\;\;t\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t) :precision binary64 (if (<= (/ x y) -2e+78) (* y (/ t y)) t))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((x / y) <= -2e+78) {
		tmp = y * (t / y);
	} else {
		tmp = 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+78)) then
        tmp = y * (t / y)
    else
        tmp = 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+78) {
		tmp = y * (t / y);
	} else {
		tmp = t;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (x / y) <= -2e+78:
		tmp = y * (t / y)
	else:
		tmp = t
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (Float64(x / y) <= -2e+78)
		tmp = Float64(y * Float64(t / y));
	else
		tmp = t;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((x / y) <= -2e+78)
		tmp = y * (t / y);
	else
		tmp = t;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[N[(x / y), $MachinePrecision], -2e+78], N[(y * N[(t / y), $MachinePrecision]), $MachinePrecision], t]

Derivation

1. Split input into 2 regimes

2. if (/.f64 x y) < -2.00000000000000002e78

   1. Initial program 96.7%

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

   3. Taylor expanded in y around 0

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

      1. /-lowering-/.f64 N/A

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

      2. distribute-rgt-out-- N/A

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

      3. *-commutative N/A

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

      4. unsub-neg N/A

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

      5. mul-1-neg N/A

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

      6. +-commutative N/A

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

      7. associate-+r+ N/A

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

      8. mul-1-neg N/A

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

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

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

      10. mul-1-neg N/A

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

      11. distribute-lft-out N/A

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

      12. accelerator-lowering-fma.f64 N/A

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

      13. mul-1-neg N/A

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

      14. unsub-neg N/A

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

      15. --lowering--.f64 N/A

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

      16. +-rgt-identity N/A

          \[\leadsto \frac{\mathsf{fma}\left(t, y - x, \color{blue}{x \cdot z + 0}\right)}{y} \]

      17. accelerator-lowering-fma.f64 92.0

          \[\leadsto \frac{\mathsf{fma}\left(t, y - x, \color{blue}{\mathsf{fma}\left(x, z, 0\right)}\right)}{y} \]

   5. Simplified 92.0%

      \[\leadsto \color{blue}{\frac{\mathsf{fma}\left(t, y - x, \mathsf{fma}\left(x, z, 0\right)\right)}{y}} \]

   6. Taylor expanded in y around inf

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

      1. +-rgt-identity N/A

         \[\leadsto \frac{\color{blue}{t \cdot y + 0}}{y} \]

      2. accelerator-lowering-fma.f64 5.5

         \[\leadsto \frac{\color{blue}{\mathsf{fma}\left(t, y, 0\right)}}{y} \]

   8. Simplified 5.5%

      \[\leadsto \frac{\color{blue}{\mathsf{fma}\left(t, y, 0\right)}}{y} \]
   9. Step-by-step derivation

      1. +-rgt-identity N/A

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

      2. *-commutative N/A

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

      3. associate-/l* N/A

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

      4. *-lowering-*.f64 N/A

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

      5. /-lowering-/.f64 23.5

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

   10. Applied egg-rr 23.5%

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

   if -2.00000000000000002e78 < (/.f64 x y)

   1. Initial program 97.0%

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

   3. Taylor expanded in x around 0

      \[\leadsto \color{blue}{t} \]
   4. Step-by-step derivation

   5. Simplified 48.5%

      \[\leadsto \color{blue}{t} \]
3. Recombined 2 regimes into one program.
4. Add Preprocessing

Alternative 5: 85.8% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \mathsf{fma}\left(\frac{x}{y}, z, t\right)\\ \mathbf{if}\;z \leq -5.6 \cdot 10^{-32}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq 6.2 \cdot 10^{+52}:\\ \;\;\;\;t \cdot \left(1 - \frac{x}{y}\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (fma (/ x y) z t)))
   (if (<= z -5.6e-32) t_1 (if (<= z 6.2e+52) (* t (- 1.0 (/ x y))) t_1))))

C

double code(double x, double y, double z, double t) {
	double t_1 = fma((x / y), z, t);
	double tmp;
	if (z <= -5.6e-32) {
		tmp = t_1;
	} else if (z <= 6.2e+52) {
		tmp = t * (1.0 - (x / y));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Julia

function code(x, y, z, t)
	t_1 = fma(Float64(x / y), z, t)
	tmp = 0.0
	if (z <= -5.6e-32)
		tmp = t_1;
	elseif (z <= 6.2e+52)
		tmp = Float64(t * Float64(1.0 - Float64(x / y)));
	else
		tmp = t_1;
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(N[(x / y), $MachinePrecision] * z + t), $MachinePrecision]}, If[LessEqual[z, -5.6e-32], t$95$1, If[LessEqual[z, 6.2e+52], N[(t * N[(1.0 - N[(x / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if z < -5.5999999999999998e-32 or 6.2e52 < z

   1. Initial program 97.6%

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

   3. Taylor expanded in z around inf

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

   5. Simplified 85.5%

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

      1. accelerator-lowering-fma.f64 N/A

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

      2. /-lowering-/.f64 85.5

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

   7. Applied egg-rr 85.5%

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

   if -5.5999999999999998e-32 < z < 6.2e52

   1. Initial program 96.3%

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

      1. accelerator-lowering-fma.f64 N/A

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

      2. /-lowering-/.f64 N/A

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

      3. --lowering--.f64 96.4

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

   4. Applied egg-rr 96.4%

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

   5. Taylor expanded in z around 0

      \[\leadsto \color{blue}{t + -1 \cdot \frac{t \cdot x}{y}} \]
   6. 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. *-rgt-identity N/A

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

      4. associate-/l* N/A

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

      5. distribute-lft-out-- N/A

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

      6. *-inverses N/A

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

      7. div-sub N/A

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

      8. *-lowering-*.f64 N/A

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

      9. div-sub N/A

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

      10. *-inverses N/A

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

      11. --lowering--.f64 N/A

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

      12. /-lowering-/.f64 85.4

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

   7. Simplified 85.4%

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

Alternative 6: 98.0% 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. accelerator-lowering-fma.f64 N/A

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

   2. /-lowering-/.f64 N/A

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

   3. --lowering--.f64 96.9

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

4. Applied egg-rr 96.9%

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

Alternative 7: 77.0% 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 96.9%

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

3. Taylor expanded in z around inf

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

5. Simplified 72.1%

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

   1. accelerator-lowering-fma.f64 N/A

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

   2. /-lowering-/.f64 72.1

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

7. Applied egg-rr 72.1%

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

Alternative 8: 38.6% accurate, 23.0× speedup

Math

\[\begin{array}{l} \\ t \end{array} \]

FPCore

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

C

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

Java

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

Python

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

Julia

function code(x, y, z, t)
	return t
end

MATLAB

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

Wolfram

code[x_, y_, z_, t_] := t

Derivation

1. Initial program 96.9%

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

3. Taylor expanded in x around 0

   \[\leadsto \color{blue}{t} \]
4. Step-by-step derivation

5. Simplified 37.7%

   \[\leadsto \color{blue}{t} \]
6. Add Preprocessing

Developer Target 1: 97.7% 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 2024196 
(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))