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

Percentage Accurate: 97.7% → 94.4%

Time: 6.6s

Alternatives: 8

Speedup: 1.1×

• 24.6% 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: 94.4% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{x}{y} \cdot \left(z - t\right)\\ \mathbf{if}\;\frac{x}{y} \leq -5 \cdot 10^{-30}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;\frac{x}{y} \leq 50:\\ \;\;\;\;t + \frac{x \cdot z}{y}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (* (/ x y) (- z t))))
   (if (<= (/ x y) -5e-30)
     t_1
     (if (<= (/ x y) 50.0) (+ t (/ (* x z) y)) t_1))))

C

double code(double x, double y, double z, double t) {
	double t_1 = (x / y) * (z - t);
	double tmp;
	if ((x / y) <= -5e-30) {
		tmp = t_1;
	} else if ((x / y) <= 50.0) {
		tmp = t + ((x * z) / 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 - t)
    if ((x / y) <= (-5d-30)) then
        tmp = t_1
    else if ((x / y) <= 50.0d0) then
        tmp = t + ((x * z) / 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 - t);
	double tmp;
	if ((x / y) <= -5e-30) {
		tmp = t_1;
	} else if ((x / y) <= 50.0) {
		tmp = t + ((x * z) / y);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = (x / y) * (z - t)
	tmp = 0
	if (x / y) <= -5e-30:
		tmp = t_1
	elif (x / y) <= 50.0:
		tmp = t + ((x * z) / y)
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(Float64(x / y) * Float64(z - t))
	tmp = 0.0
	if (Float64(x / y) <= -5e-30)
		tmp = t_1;
	elseif (Float64(x / y) <= 50.0)
		tmp = Float64(t + Float64(Float64(x * z) / y));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = (x / y) * (z - t);
	tmp = 0.0;
	if ((x / y) <= -5e-30)
		tmp = t_1;
	elseif ((x / y) <= 50.0)
		tmp = t + ((x * z) / 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] * N[(z - t), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[N[(x / y), $MachinePrecision], -5e-30], t$95$1, If[LessEqual[N[(x / y), $MachinePrecision], 50.0], N[(t + N[(N[(x * z), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if (/.f64 x y) < -4.99999999999999972e-30 or 50 < (/.f64 x y)

   1. Initial program 96.8%

      \[\frac{x}{y} \cdot \left(z - t\right) + t \]
   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. 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 92.0

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

   5. Simplified 92.0%

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

      1. lift--.f64 N/A

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

      2. associate-*l/ N/A

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

      3. lift-/.f64 N/A

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

      4. lower-*.f64 95.2

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

   7. Applied egg-rr 95.2%

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

   if -4.99999999999999972e-30 < (/.f64 x y) < 50

   1. Initial program 96.3%

      \[\frac{x}{y} \cdot \left(z - t\right) + t \]
   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 98.5

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

   5. Simplified 98.5%

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

4. Final simplification 96.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{x}{y} \leq -5 \cdot 10^{-30}:\\ \;\;\;\;\frac{x}{y} \cdot \left(z - t\right)\\ \mathbf{elif}\;\frac{x}{y} \leq 50:\\ \;\;\;\;t + \frac{x \cdot z}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{y} \cdot \left(z - t\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 2: 95.3% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{x}{y} \cdot \left(z - t\right)\\ \mathbf{if}\;\frac{x}{y} \leq -5 \cdot 10^{+31}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;\frac{x}{y} \leq 5 \cdot 10^{-18}:\\ \;\;\;\;\mathsf{fma}\left(z, \frac{x}{y}, t\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (* (/ x y) (- z t))))
   (if (<= (/ x y) -5e+31) t_1 (if (<= (/ x y) 5e-18) (fma z (/ x y) t) t_1))))

C

double code(double x, double y, double z, double t) {
	double t_1 = (x / y) * (z - t);
	double tmp;
	if ((x / y) <= -5e+31) {
		tmp = t_1;
	} else if ((x / y) <= 5e-18) {
		tmp = fma(z, (x / y), t);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Julia

function code(x, y, z, t)
	t_1 = Float64(Float64(x / y) * Float64(z - t))
	tmp = 0.0
	if (Float64(x / y) <= -5e+31)
		tmp = t_1;
	elseif (Float64(x / y) <= 5e-18)
		tmp = fma(z, Float64(x / y), t);
	else
		tmp = t_1;
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(N[(x / y), $MachinePrecision] * N[(z - t), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[N[(x / y), $MachinePrecision], -5e+31], t$95$1, If[LessEqual[N[(x / y), $MachinePrecision], 5e-18], N[(z * N[(x / y), $MachinePrecision] + t), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if (/.f64 x y) < -5.00000000000000027e31 or 5.00000000000000036e-18 < (/.f64 x y)

   1. Initial program 96.6%

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

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

   5. Simplified 94.7%

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

      1. lift--.f64 N/A

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

      2. associate-*l/ N/A

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

      3. lift-/.f64 N/A

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

      4. lower-*.f64 96.4

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

   7. Applied egg-rr 96.4%

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

   if -5.00000000000000027e31 < (/.f64 x y) < 5.00000000000000036e-18

   1. Initial program 96.4%

      \[\frac{x}{y} \cdot \left(z - t\right) + t \]
   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 96.8

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

   5. Simplified 96.8%

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

      1. lift-*.f64 N/A

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

      2. div-inv N/A

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

      3. lift-*.f64 N/A

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

      4. *-commutative N/A

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

      5. associate-*l* N/A

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

      6. div-inv N/A

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

      7. lift-/.f64 N/A

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

      8. lower-fma.f64 96.0

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

   7. Applied egg-rr 96.0%

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

Alternative 3: 76.2% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := -\frac{x}{y} \cdot t\\ \mathbf{if}\;\frac{x}{y} \leq -5 \cdot 10^{+60}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;\frac{x}{y} \leq 10^{+26}:\\ \;\;\;\;\mathsf{fma}\left(z, \frac{x}{y}, t\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (- (* (/ x y) t))))
   (if (<= (/ x y) -5e+60) t_1 (if (<= (/ x y) 1e+26) (fma z (/ x y) t) t_1))))

C

double code(double x, double y, double z, double t) {
	double t_1 = -((x / y) * t);
	double tmp;
	if ((x / y) <= -5e+60) {
		tmp = t_1;
	} else if ((x / y) <= 1e+26) {
		tmp = fma(z, (x / y), t);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Julia

function code(x, y, z, t)
	t_1 = Float64(-Float64(Float64(x / y) * t))
	tmp = 0.0
	if (Float64(x / y) <= -5e+60)
		tmp = t_1;
	elseif (Float64(x / y) <= 1e+26)
		tmp = fma(z, Float64(x / y), t);
	else
		tmp = t_1;
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = (-N[(N[(x / y), $MachinePrecision] * t), $MachinePrecision])}, If[LessEqual[N[(x / y), $MachinePrecision], -5e+60], t$95$1, If[LessEqual[N[(x / y), $MachinePrecision], 1e+26], N[(z * N[(x / y), $MachinePrecision] + t), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if (/.f64 x y) < -4.99999999999999975e60 or 1.00000000000000005e26 < (/.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 97.0

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

   5. Simplified 97.0%

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

   6. Taylor expanded in z around 0

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

      1. mul-1-neg N/A

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

      2. lower-neg.f64 65.4

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

   8. Simplified 65.4%

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

      1. distribute-rgt-neg-out N/A

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

      2. distribute-lft-neg-in N/A

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

      3. lift-neg.f64 N/A

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

      4. associate-*r/ N/A

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

      5. clear-num N/A

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

      6. associate-/r/ N/A

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

      7. lift-/.f64 N/A

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

      8. associate-*r* N/A

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

      9. lift-/.f64 N/A

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

      10. div-inv N/A

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

      11. lower-*.f64 N/A

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

      12. lower-/.f64 69.6

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

   10. Applied egg-rr 69.6%

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

   if -4.99999999999999975e60 < (/.f64 x y) < 1.00000000000000005e26

   1. Initial program 96.7%

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

   3. Taylor expanded in z around inf

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

      1. lower-/.f64 N/A

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

      2. lower-*.f64 93.8

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

   5. Simplified 93.8%

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

      1. lift-*.f64 N/A

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

      2. div-inv N/A

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

      3. lift-*.f64 N/A

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

      4. *-commutative N/A

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

      5. associate-*l* N/A

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

      6. div-inv N/A

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

      7. lift-/.f64 N/A

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

      8. lower-fma.f64 94.4

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

   7. Applied egg-rr 94.4%

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

4. Final simplification 84.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{x}{y} \leq -5 \cdot 10^{+60}:\\ \;\;\;\;-\frac{x}{y} \cdot t\\ \mathbf{elif}\;\frac{x}{y} \leq 10^{+26}:\\ \;\;\;\;\mathsf{fma}\left(z, \frac{x}{y}, t\right)\\ \mathbf{else}:\\ \;\;\;\;-\frac{x}{y} \cdot t\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 74.9% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := -x \cdot \frac{t}{y}\\ \mathbf{if}\;\frac{x}{y} \leq -2 \cdot 10^{+95}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;\frac{x}{y} \leq 10^{+29}:\\ \;\;\;\;\mathsf{fma}\left(z, \frac{x}{y}, t\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (- (* x (/ t y)))))
   (if (<= (/ x y) -2e+95) t_1 (if (<= (/ x y) 1e+29) (fma z (/ x y) 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) <= -2e+95) {
		tmp = t_1;
	} else if ((x / y) <= 1e+29) {
		tmp = fma(z, (x / y), t);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Julia

function code(x, y, z, t)
	t_1 = Float64(-Float64(x * Float64(t / y)))
	tmp = 0.0
	if (Float64(x / y) <= -2e+95)
		tmp = t_1;
	elseif (Float64(x / y) <= 1e+29)
		tmp = fma(z, Float64(x / y), t);
	else
		tmp = t_1;
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = (-N[(x * N[(t / y), $MachinePrecision]), $MachinePrecision])}, If[LessEqual[N[(x / y), $MachinePrecision], -2e+95], t$95$1, If[LessEqual[N[(x / y), $MachinePrecision], 1e+29], N[(z * N[(x / y), $MachinePrecision] + t), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if (/.f64 x y) < -2.00000000000000004e95 or 9.99999999999999914e28 < (/.f64 x y)

   1. Initial program 96.0%

      \[\frac{x}{y} \cdot \left(z - t\right) + t \]
   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. 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 96.7

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

   5. Simplified 96.7%

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

   6. Taylor expanded in z around 0

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

      1. mul-1-neg N/A

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

      2. lower-neg.f64 65.8

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

   8. Simplified 65.8%

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

      1. lift-neg.f64 N/A

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

      2. associate-/l* N/A

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

      3. *-commutative N/A

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

      4. lower-*.f64 N/A

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

      5. frac-2neg N/A

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

      6. lift-neg.f64 N/A

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

      7. remove-double-neg N/A

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

      8. lower-/.f64 N/A

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

      9. lower-neg.f64 66.9

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

   10. Applied egg-rr 66.9%

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

   if -2.00000000000000004e95 < (/.f64 x y) < 9.99999999999999914e28

   1. Initial program 96.9%

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

   3. Taylor expanded in z around inf

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

      1. lower-/.f64 N/A

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

      2. lower-*.f64 90.7

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

   5. Simplified 90.7%

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

      1. lift-*.f64 N/A

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

      2. div-inv N/A

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

      3. lift-*.f64 N/A

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

      4. *-commutative N/A

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

      5. associate-*l* N/A

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

      6. div-inv N/A

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

      7. lift-/.f64 N/A

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

      8. lower-fma.f64 91.2

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

   7. Applied egg-rr 91.2%

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

4. Final simplification 82.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{x}{y} \leq -2 \cdot 10^{+95}:\\ \;\;\;\;-x \cdot \frac{t}{y}\\ \mathbf{elif}\;\frac{x}{y} \leq 10^{+29}:\\ \;\;\;\;\mathsf{fma}\left(z, \frac{x}{y}, t\right)\\ \mathbf{else}:\\ \;\;\;\;-x \cdot \frac{t}{y}\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 97.7% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 96.5%

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

3. Final simplification 96.5%

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

Alternative 6: 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 96.5%

   \[\frac{x}{y} \cdot \left(z - t\right) + t \]
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 96.5

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

4. Applied egg-rr 96.5%

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

Alternative 7: 77.5% accurate, 1.3× speedup

Math

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

FPCore

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

C

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

Julia

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

Wolfram

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

Derivation

1. Initial program 96.5%

   \[\frac{x}{y} \cdot \left(z - t\right) + t \]
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 72.8

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

5. Simplified 72.8%

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

   1. lift-*.f64 N/A

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

   2. div-inv N/A

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

   3. lift-*.f64 N/A

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

   4. *-commutative N/A

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

   5. associate-*l* N/A

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

   6. div-inv N/A

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

   7. lift-/.f64 N/A

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

   8. lower-fma.f64 74.6

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

7. Applied egg-rr 74.6%

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

Alternative 8: 41.5% 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 96.5%

   \[\frac{x}{y} \cdot \left(z - t\right) + t \]
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 35.6

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

5. Simplified 35.6%

   \[\leadsto \color{blue}{\frac{x \cdot z}{y}} \]
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 37.2

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

7. Applied egg-rr 37.2%

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

8. Final simplification 37.2%

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

Developer Target 1: 97.4% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{x}{y} \cdot \left(z - t\right) + t\\ \mathbf{if}\;z < 2.759456554562692 \cdot 10^{-282}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z < 2.326994450874436 \cdot 10^{-110}:\\ \;\;\;\;x \cdot \frac{z - t}{y} + t\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (+ (* (/ x y) (- z t)) t)))
   (if (< z 2.759456554562692e-282)
     t_1
     (if (< z 2.326994450874436e-110) (+ (* x (/ (- z t) y)) t) t_1))))

C

double code(double x, double y, double z, double t) {
	double t_1 = ((x / y) * (z - t)) + t;
	double tmp;
	if (z < 2.759456554562692e-282) {
		tmp = t_1;
	} else if (z < 2.326994450874436e-110) {
		tmp = (x * ((z - t) / y)) + t;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: t_1
    real(8) :: tmp
    t_1 = ((x / y) * (z - t)) + t
    if (z < 2.759456554562692d-282) then
        tmp = t_1
    else if (z < 2.326994450874436d-110) then
        tmp = (x * ((z - t) / y)) + t
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double t_1 = ((x / y) * (z - t)) + t;
	double tmp;
	if (z < 2.759456554562692e-282) {
		tmp = t_1;
	} else if (z < 2.326994450874436e-110) {
		tmp = (x * ((z - t) / y)) + t;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = ((x / y) * (z - t)) + t
	tmp = 0
	if z < 2.759456554562692e-282:
		tmp = t_1
	elif z < 2.326994450874436e-110:
		tmp = (x * ((z - t) / y)) + t
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(Float64(Float64(x / y) * Float64(z - t)) + t)
	tmp = 0.0
	if (z < 2.759456554562692e-282)
		tmp = t_1;
	elseif (z < 2.326994450874436e-110)
		tmp = Float64(Float64(x * Float64(Float64(z - t) / y)) + t);
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = ((x / y) * (z - t)) + t;
	tmp = 0.0;
	if (z < 2.759456554562692e-282)
		tmp = t_1;
	elseif (z < 2.326994450874436e-110)
		tmp = (x * ((z - t) / y)) + t;
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(N[(N[(x / y), $MachinePrecision] * N[(z - t), $MachinePrecision]), $MachinePrecision] + t), $MachinePrecision]}, If[Less[z, 2.759456554562692e-282], t$95$1, If[Less[z, 2.326994450874436e-110], N[(N[(x * N[(N[(z - t), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision] + t), $MachinePrecision], t$95$1]]]

Reproduce

herbie shell --seed 2024207 
(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))