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

Percentage Accurate: 97.8% → 97.8%

Time: 6.2s

Alternatives: 7

Speedup: 1.0×

• 25.7% of points produce a very large (infinite) output. You may want to add a precondition.

Specification

Math

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

FPCore

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

C

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

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    code = ((x / y) * (z - t)) + t
end function

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Initial Program: 97.8% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    code = ((x / y) * (z - t)) + t
end function

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Alternative 1: 97.8% accurate, 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 97.7%

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

3. Final simplification 97.7%

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

Alternative 2: 62.9% accurate, 0.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{x}{y} \cdot z\\ t_2 := t \cdot \frac{x}{-y}\\ \mathbf{if}\;\frac{x}{y} \leq -1 \cdot 10^{+237}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;\frac{x}{y} \leq -10000000:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;\frac{x}{y} \leq 2 \cdot 10^{-75}:\\ \;\;\;\;t\\ \mathbf{elif}\;\frac{x}{y} \leq 2 \cdot 10^{+43} \lor \neg \left(\frac{x}{y} \leq 2 \cdot 10^{+110}\right) \land \frac{x}{y} \leq 5 \cdot 10^{+192}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (* (/ x y) z)) (t_2 (* t (/ x (- y)))))
   (if (<= (/ x y) -1e+237)
     t_1
     (if (<= (/ x y) -10000000.0)
       t_2
       (if (<= (/ x y) 2e-75)
         t
         (if (or (<= (/ x y) 2e+43)
                 (and (not (<= (/ x y) 2e+110)) (<= (/ x y) 5e+192)))
           t_1
           t_2))))))

C

double code(double x, double y, double z, double t) {
	double t_1 = (x / y) * z;
	double t_2 = t * (x / -y);
	double tmp;
	if ((x / y) <= -1e+237) {
		tmp = t_1;
	} else if ((x / y) <= -10000000.0) {
		tmp = t_2;
	} else if ((x / y) <= 2e-75) {
		tmp = t;
	} else if (((x / y) <= 2e+43) || (!((x / y) <= 2e+110) && ((x / y) <= 5e+192))) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	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) :: t_2
    real(8) :: tmp
    t_1 = (x / y) * z
    t_2 = t * (x / -y)
    if ((x / y) <= (-1d+237)) then
        tmp = t_1
    else if ((x / y) <= (-10000000.0d0)) then
        tmp = t_2
    else if ((x / y) <= 2d-75) then
        tmp = t
    else if (((x / y) <= 2d+43) .or. (.not. ((x / y) <= 2d+110)) .and. ((x / y) <= 5d+192)) then
        tmp = t_1
    else
        tmp = t_2
    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 t_2 = t * (x / -y);
	double tmp;
	if ((x / y) <= -1e+237) {
		tmp = t_1;
	} else if ((x / y) <= -10000000.0) {
		tmp = t_2;
	} else if ((x / y) <= 2e-75) {
		tmp = t;
	} else if (((x / y) <= 2e+43) || (!((x / y) <= 2e+110) && ((x / y) <= 5e+192))) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = (x / y) * z
	t_2 = t * (x / -y)
	tmp = 0
	if (x / y) <= -1e+237:
		tmp = t_1
	elif (x / y) <= -10000000.0:
		tmp = t_2
	elif (x / y) <= 2e-75:
		tmp = t
	elif ((x / y) <= 2e+43) or (not ((x / y) <= 2e+110) and ((x / y) <= 5e+192)):
		tmp = t_1
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(Float64(x / y) * z)
	t_2 = Float64(t * Float64(x / Float64(-y)))
	tmp = 0.0
	if (Float64(x / y) <= -1e+237)
		tmp = t_1;
	elseif (Float64(x / y) <= -10000000.0)
		tmp = t_2;
	elseif (Float64(x / y) <= 2e-75)
		tmp = t;
	elseif ((Float64(x / y) <= 2e+43) || (!(Float64(x / y) <= 2e+110) && (Float64(x / y) <= 5e+192)))
		tmp = t_1;
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = (x / y) * z;
	t_2 = t * (x / -y);
	tmp = 0.0;
	if ((x / y) <= -1e+237)
		tmp = t_1;
	elseif ((x / y) <= -10000000.0)
		tmp = t_2;
	elseif ((x / y) <= 2e-75)
		tmp = t;
	elseif (((x / y) <= 2e+43) || (~(((x / y) <= 2e+110)) && ((x / y) <= 5e+192)))
		tmp = t_1;
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(N[(x / y), $MachinePrecision] * z), $MachinePrecision]}, Block[{t$95$2 = N[(t * N[(x / (-y)), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[N[(x / y), $MachinePrecision], -1e+237], t$95$1, If[LessEqual[N[(x / y), $MachinePrecision], -10000000.0], t$95$2, If[LessEqual[N[(x / y), $MachinePrecision], 2e-75], t, If[Or[LessEqual[N[(x / y), $MachinePrecision], 2e+43], And[N[Not[LessEqual[N[(x / y), $MachinePrecision], 2e+110]], $MachinePrecision], LessEqual[N[(x / y), $MachinePrecision], 5e+192]]], t$95$1, t$95$2]]]]]]

Derivation

1. Split input into 3 regimes

2. if (/.f64 x y) < -9.9999999999999994e236 or 1.9999999999999999e-75 < (/.f64 x y) < 2.00000000000000003e43 or 2e110 < (/.f64 x y) < 5.00000000000000033e192

   1. Initial program 97.0%

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

   3. Taylor expanded in z around inf 69.7%

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

      1. *-commutative 69.7%

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

      2. associate-/l* 74.8%

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

   5. Applied egg-rr 74.8%

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

   if -9.9999999999999994e236 < (/.f64 x y) < -1e7 or 2.00000000000000003e43 < (/.f64 x y) < 2e110 or 5.00000000000000033e192 < (/.f64 x y)

   1. Initial program 97.2%

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

   3. Taylor expanded in x around -inf 91.9%

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

   4. Taylor expanded in z around 0 71.0%

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

      1. mul-1-neg 71.0%

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

      2. distribute-rgt-neg-in 71.0%

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

   6. Simplified 71.0%

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

   7. Taylor expanded in t around 0 71.0%

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

      1. mul-1-neg 71.0%

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

      2. associate-*r/ 78.9%

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

      3. distribute-rgt-neg-in 78.9%

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

      4. distribute-frac-neg2 78.9%

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

   9. Simplified 78.9%

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

   if -1e7 < (/.f64 x y) < 1.9999999999999999e-75

   1. Initial program 98.4%

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

   3. Taylor expanded in x around 0 80.5%

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

4. Final simplification 78.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{x}{y} \leq -1 \cdot 10^{+237}:\\ \;\;\;\;\frac{x}{y} \cdot z\\ \mathbf{elif}\;\frac{x}{y} \leq -10000000:\\ \;\;\;\;t \cdot \frac{x}{-y}\\ \mathbf{elif}\;\frac{x}{y} \leq 2 \cdot 10^{-75}:\\ \;\;\;\;t\\ \mathbf{elif}\;\frac{x}{y} \leq 2 \cdot 10^{+43} \lor \neg \left(\frac{x}{y} \leq 2 \cdot 10^{+110}\right) \land \frac{x}{y} \leq 5 \cdot 10^{+192}:\\ \;\;\;\;\frac{x}{y} \cdot z\\ \mathbf{else}:\\ \;\;\;\;t \cdot \frac{x}{-y}\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 62.9% accurate, 0.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{x}{y} \cdot z\\ t_2 := \frac{t}{\frac{y}{-x}}\\ \mathbf{if}\;\frac{x}{y} \leq -1 \cdot 10^{+237}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;\frac{x}{y} \leq -10000000:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;\frac{x}{y} \leq 2 \cdot 10^{-75}:\\ \;\;\;\;t\\ \mathbf{elif}\;\frac{x}{y} \leq 2 \cdot 10^{+43} \lor \neg \left(\frac{x}{y} \leq 2 \cdot 10^{+110}\right) \land \frac{x}{y} \leq 5 \cdot 10^{+192}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (* (/ x y) z)) (t_2 (/ t (/ y (- x)))))
   (if (<= (/ x y) -1e+237)
     t_1
     (if (<= (/ x y) -10000000.0)
       t_2
       (if (<= (/ x y) 2e-75)
         t
         (if (or (<= (/ x y) 2e+43)
                 (and (not (<= (/ x y) 2e+110)) (<= (/ x y) 5e+192)))
           t_1
           t_2))))))

C

double code(double x, double y, double z, double t) {
	double t_1 = (x / y) * z;
	double t_2 = t / (y / -x);
	double tmp;
	if ((x / y) <= -1e+237) {
		tmp = t_1;
	} else if ((x / y) <= -10000000.0) {
		tmp = t_2;
	} else if ((x / y) <= 2e-75) {
		tmp = t;
	} else if (((x / y) <= 2e+43) || (!((x / y) <= 2e+110) && ((x / y) <= 5e+192))) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	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) :: t_2
    real(8) :: tmp
    t_1 = (x / y) * z
    t_2 = t / (y / -x)
    if ((x / y) <= (-1d+237)) then
        tmp = t_1
    else if ((x / y) <= (-10000000.0d0)) then
        tmp = t_2
    else if ((x / y) <= 2d-75) then
        tmp = t
    else if (((x / y) <= 2d+43) .or. (.not. ((x / y) <= 2d+110)) .and. ((x / y) <= 5d+192)) then
        tmp = t_1
    else
        tmp = t_2
    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 t_2 = t / (y / -x);
	double tmp;
	if ((x / y) <= -1e+237) {
		tmp = t_1;
	} else if ((x / y) <= -10000000.0) {
		tmp = t_2;
	} else if ((x / y) <= 2e-75) {
		tmp = t;
	} else if (((x / y) <= 2e+43) || (!((x / y) <= 2e+110) && ((x / y) <= 5e+192))) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = (x / y) * z
	t_2 = t / (y / -x)
	tmp = 0
	if (x / y) <= -1e+237:
		tmp = t_1
	elif (x / y) <= -10000000.0:
		tmp = t_2
	elif (x / y) <= 2e-75:
		tmp = t
	elif ((x / y) <= 2e+43) or (not ((x / y) <= 2e+110) and ((x / y) <= 5e+192)):
		tmp = t_1
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(Float64(x / y) * z)
	t_2 = Float64(t / Float64(y / Float64(-x)))
	tmp = 0.0
	if (Float64(x / y) <= -1e+237)
		tmp = t_1;
	elseif (Float64(x / y) <= -10000000.0)
		tmp = t_2;
	elseif (Float64(x / y) <= 2e-75)
		tmp = t;
	elseif ((Float64(x / y) <= 2e+43) || (!(Float64(x / y) <= 2e+110) && (Float64(x / y) <= 5e+192)))
		tmp = t_1;
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = (x / y) * z;
	t_2 = t / (y / -x);
	tmp = 0.0;
	if ((x / y) <= -1e+237)
		tmp = t_1;
	elseif ((x / y) <= -10000000.0)
		tmp = t_2;
	elseif ((x / y) <= 2e-75)
		tmp = t;
	elseif (((x / y) <= 2e+43) || (~(((x / y) <= 2e+110)) && ((x / y) <= 5e+192)))
		tmp = t_1;
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(N[(x / y), $MachinePrecision] * z), $MachinePrecision]}, Block[{t$95$2 = N[(t / N[(y / (-x)), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[N[(x / y), $MachinePrecision], -1e+237], t$95$1, If[LessEqual[N[(x / y), $MachinePrecision], -10000000.0], t$95$2, If[LessEqual[N[(x / y), $MachinePrecision], 2e-75], t, If[Or[LessEqual[N[(x / y), $MachinePrecision], 2e+43], And[N[Not[LessEqual[N[(x / y), $MachinePrecision], 2e+110]], $MachinePrecision], LessEqual[N[(x / y), $MachinePrecision], 5e+192]]], t$95$1, t$95$2]]]]]]

Derivation

1. Split input into 3 regimes

2. if (/.f64 x y) < -9.9999999999999994e236 or 1.9999999999999999e-75 < (/.f64 x y) < 2.00000000000000003e43 or 2e110 < (/.f64 x y) < 5.00000000000000033e192

   1. Initial program 97.0%

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

   3. Taylor expanded in z around inf 69.7%

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

      1. *-commutative 69.7%

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

      2. associate-/l* 74.8%

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

   5. Applied egg-rr 74.8%

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

   if -9.9999999999999994e236 < (/.f64 x y) < -1e7 or 2.00000000000000003e43 < (/.f64 x y) < 2e110 or 5.00000000000000033e192 < (/.f64 x y)

   1. Initial program 97.2%

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

   3. Taylor expanded in x around -inf 91.9%

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

   4. Taylor expanded in z around 0 71.0%

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

      1. mul-1-neg 71.0%

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

      2. distribute-rgt-neg-in 71.0%

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

   6. Simplified 71.0%

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

      1. frac-2neg 71.0%

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

      2. distribute-frac-neg 71.0%

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

      3. associate-*r/ 78.9%

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

      4. frac-2neg 78.9%

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

      5. clear-num 78.8%

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

      6. div-inv 77.5%

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

   8. Applied egg-rr 77.5%

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

   if -1e7 < (/.f64 x y) < 1.9999999999999999e-75

   1. Initial program 98.4%

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

   3. Taylor expanded in x around 0 80.5%

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

4. Final simplification 78.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{x}{y} \leq -1 \cdot 10^{+237}:\\ \;\;\;\;\frac{x}{y} \cdot z\\ \mathbf{elif}\;\frac{x}{y} \leq -10000000:\\ \;\;\;\;\frac{t}{\frac{y}{-x}}\\ \mathbf{elif}\;\frac{x}{y} \leq 2 \cdot 10^{-75}:\\ \;\;\;\;t\\ \mathbf{elif}\;\frac{x}{y} \leq 2 \cdot 10^{+43} \lor \neg \left(\frac{x}{y} \leq 2 \cdot 10^{+110}\right) \land \frac{x}{y} \leq 5 \cdot 10^{+192}:\\ \;\;\;\;\frac{x}{y} \cdot z\\ \mathbf{else}:\\ \;\;\;\;\frac{t}{\frac{y}{-x}}\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 85.1% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;\frac{x}{y} \leq -1 \cdot 10^{-24} \lor \neg \left(\frac{x}{y} \leq 2 \cdot 10^{-75}\right):\\ \;\;\;\;\frac{x}{y} \cdot \left(z - t\right)\\ \mathbf{else}:\\ \;\;\;\;t\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= (/ x y) -1e-24) (not (<= (/ x y) 2e-75))) (* (/ x y) (- z t)) t))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (((x / y) <= -1e-24) || !((x / y) <= 2e-75)) {
		tmp = (x / y) * (z - t);
	} 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) <= (-1d-24)) .or. (.not. ((x / y) <= 2d-75))) then
        tmp = (x / y) * (z - t)
    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) <= -1e-24) || !((x / y) <= 2e-75)) {
		tmp = (x / y) * (z - t);
	} else {
		tmp = t;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if ((x / y) <= -1e-24) or not ((x / y) <= 2e-75):
		tmp = (x / y) * (z - t)
	else:
		tmp = t
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((Float64(x / y) <= -1e-24) || !(Float64(x / y) <= 2e-75))
		tmp = Float64(Float64(x / y) * Float64(z - t));
	else
		tmp = t;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (((x / y) <= -1e-24) || ~(((x / y) <= 2e-75)))
		tmp = (x / y) * (z - t);
	else
		tmp = t;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[N[(x / y), $MachinePrecision], -1e-24], N[Not[LessEqual[N[(x / y), $MachinePrecision], 2e-75]], $MachinePrecision]], N[(N[(x / y), $MachinePrecision] * N[(z - t), $MachinePrecision]), $MachinePrecision], t]

Derivation

1. Split input into 2 regimes

2. if (/.f64 x y) < -9.99999999999999924e-25 or 1.9999999999999999e-75 < (/.f64 x y)

   1. Initial program 97.2%

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

   3. Taylor expanded in x around -inf 87.6%

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

      1. *-commutative 87.6%

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

      2. associate-/l* 91.9%

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

      3. *-commutative 91.9%

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

   5. Applied egg-rr 91.9%

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

   if -9.99999999999999924e-25 < (/.f64 x y) < 1.9999999999999999e-75

   1. Initial program 98.3%

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

   3. Taylor expanded in x around 0 83.2%

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

4. Final simplification 88.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{x}{y} \leq -1 \cdot 10^{-24} \lor \neg \left(\frac{x}{y} \leq 2 \cdot 10^{-75}\right):\\ \;\;\;\;\frac{x}{y} \cdot \left(z - t\right)\\ \mathbf{else}:\\ \;\;\;\;t\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 93.8% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;\frac{x}{y} \leq -10000000:\\ \;\;\;\;\frac{x}{y} \cdot \left(z - t\right)\\ \mathbf{elif}\;\frac{x}{y} \leq 0.04:\\ \;\;\;\;t + \frac{x \cdot z}{y}\\ \mathbf{else}:\\ \;\;\;\;x \cdot \frac{z - t}{y}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= (/ x y) -10000000.0)
   (* (/ x y) (- z t))
   (if (<= (/ x y) 0.04) (+ t (/ (* x z) y)) (* x (/ (- z t) y)))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((x / y) <= -10000000.0) {
		tmp = (x / y) * (z - t);
	} else if ((x / y) <= 0.04) {
		tmp = t + ((x * z) / y);
	} else {
		tmp = x * ((z - t) / y);
	}
	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) <= (-10000000.0d0)) then
        tmp = (x / y) * (z - t)
    else if ((x / y) <= 0.04d0) then
        tmp = t + ((x * z) / y)
    else
        tmp = x * ((z - t) / y)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if ((x / y) <= -10000000.0) {
		tmp = (x / y) * (z - t);
	} else if ((x / y) <= 0.04) {
		tmp = t + ((x * z) / y);
	} else {
		tmp = x * ((z - t) / y);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (x / y) <= -10000000.0:
		tmp = (x / y) * (z - t)
	elif (x / y) <= 0.04:
		tmp = t + ((x * z) / y)
	else:
		tmp = x * ((z - t) / y)
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (Float64(x / y) <= -10000000.0)
		tmp = Float64(Float64(x / y) * Float64(z - t));
	elseif (Float64(x / y) <= 0.04)
		tmp = Float64(t + Float64(Float64(x * z) / y));
	else
		tmp = Float64(x * Float64(Float64(z - t) / y));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((x / y) <= -10000000.0)
		tmp = (x / y) * (z - t);
	elseif ((x / y) <= 0.04)
		tmp = t + ((x * z) / y);
	else
		tmp = x * ((z - t) / y);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[N[(x / y), $MachinePrecision], -10000000.0], N[(N[(x / y), $MachinePrecision] * N[(z - t), $MachinePrecision]), $MachinePrecision], If[LessEqual[N[(x / y), $MachinePrecision], 0.04], N[(t + N[(N[(x * z), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision], N[(x * N[(N[(z - t), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if (/.f64 x y) < -1e7

   1. Initial program 97.1%

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

   3. Taylor expanded in x around -inf 91.4%

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

      1. *-commutative 91.4%

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

      2. associate-/l* 96.4%

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

      3. *-commutative 96.4%

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

   5. Applied egg-rr 96.4%

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

   if -1e7 < (/.f64 x y) < 0.0400000000000000008

   1. Initial program 98.5%

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

   3. Taylor expanded in z around inf 96.2%

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

   if 0.0400000000000000008 < (/.f64 x y)

   1. Initial program 96.7%

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

   3. Taylor expanded in x around -inf 92.5%

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

      1. associate-/l* 96.7%

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

      2. *-commutative 96.7%

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

   5. Applied egg-rr 96.7%

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

4. Final simplification 96.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{x}{y} \leq -10000000:\\ \;\;\;\;\frac{x}{y} \cdot \left(z - t\right)\\ \mathbf{elif}\;\frac{x}{y} \leq 0.04:\\ \;\;\;\;t + \frac{x \cdot z}{y}\\ \mathbf{else}:\\ \;\;\;\;x \cdot \frac{z - t}{y}\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 65.4% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;\frac{x}{y} \leq -1 \cdot 10^{-24} \lor \neg \left(\frac{x}{y} \leq 2 \cdot 10^{-75}\right):\\ \;\;\;\;\frac{x}{y} \cdot z\\ \mathbf{else}:\\ \;\;\;\;t\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= (/ x y) -1e-24) (not (<= (/ x y) 2e-75))) (* (/ x y) z) t))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (((x / y) <= -1e-24) || !((x / y) <= 2e-75)) {
		tmp = (x / y) * z;
	} 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) <= (-1d-24)) .or. (.not. ((x / y) <= 2d-75))) then
        tmp = (x / y) * z
    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) <= -1e-24) || !((x / y) <= 2e-75)) {
		tmp = (x / y) * z;
	} else {
		tmp = t;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if ((x / y) <= -1e-24) or not ((x / y) <= 2e-75):
		tmp = (x / y) * z
	else:
		tmp = t
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((Float64(x / y) <= -1e-24) || !(Float64(x / y) <= 2e-75))
		tmp = Float64(Float64(x / y) * z);
	else
		tmp = t;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (((x / y) <= -1e-24) || ~(((x / y) <= 2e-75)))
		tmp = (x / y) * z;
	else
		tmp = t;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[N[(x / y), $MachinePrecision], -1e-24], N[Not[LessEqual[N[(x / y), $MachinePrecision], 2e-75]], $MachinePrecision]], N[(N[(x / y), $MachinePrecision] * z), $MachinePrecision], t]

Derivation

1. Split input into 2 regimes

2. if (/.f64 x y) < -9.99999999999999924e-25 or 1.9999999999999999e-75 < (/.f64 x y)

   1. Initial program 97.2%

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

   3. Taylor expanded in z around inf 51.6%

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

      1. *-commutative 51.6%

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

      2. associate-/l* 55.3%

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

   5. Applied egg-rr 55.3%

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

   if -9.99999999999999924e-25 < (/.f64 x y) < 1.9999999999999999e-75

   1. Initial program 98.3%

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

   3. Taylor expanded in x around 0 83.2%

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

4. Final simplification 67.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{x}{y} \leq -1 \cdot 10^{-24} \lor \neg \left(\frac{x}{y} \leq 2 \cdot 10^{-75}\right):\\ \;\;\;\;\frac{x}{y} \cdot z\\ \mathbf{else}:\\ \;\;\;\;t\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 37.7% accurate, 9.0× 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 97.7%

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

3. Taylor expanded in x around 0 40.6%

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

Developer target: 97.5% accurate, 0.5× 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 2024097 
(FPCore (x y z t)
  :name "Numeric.Signal.Multichannel:$cget from hsignal-0.2.7.1"
  :precision binary64

  :alt
  (if (< z 2.759456554562692e-282) (+ (* (/ x y) (- z t)) t) (if (< z 2.326994450874436e-110) (+ (* x (/ (- z t) y)) t) (+ (* (/ x y) (- z t)) t)))

  (+ (* (/ x y) (- z t)) t))