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

Percentage Accurate: 97.5% → 97.6%

Time: 10.0s

Alternatives: 12

Speedup: 1.0×

• 24.5% 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: 97.5% 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: 97.6% accurate, 1.0× 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 98.4%

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

3. Taylor expanded in x around 0 91.2%

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

   1. associate-*r/ 89.7%

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

   2. *-commutative 89.7%

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

   3. associate-/r/ 98.7%

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

5. Simplified 98.7%

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

6. Final simplification 98.7%

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

Alternative 2: 71.9% accurate, 0.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := t \cdot \left(1 - \frac{x}{y}\right)\\ \mathbf{if}\;t \leq -6.1 \cdot 10^{+32}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t \leq -2.5 \cdot 10^{-12}:\\ \;\;\;\;\frac{z \cdot x}{y}\\ \mathbf{elif}\;t \leq -4 \cdot 10^{-88} \lor \neg \left(t \leq 9.6 \cdot 10^{-207}\right) \land \left(t \leq 9.5 \cdot 10^{-150} \lor \neg \left(t \leq 1.12 \cdot 10^{-74}\right)\right):\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;x \cdot \frac{z}{y}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (* t (- 1.0 (/ x y)))))
   (if (<= t -6.1e+32)
     t_1
     (if (<= t -2.5e-12)
       (/ (* z x) y)
       (if (or (<= t -4e-88)
               (and (not (<= t 9.6e-207))
                    (or (<= t 9.5e-150) (not (<= t 1.12e-74)))))
         t_1
         (* x (/ z y)))))))

C

double code(double x, double y, double z, double t) {
	double t_1 = t * (1.0 - (x / y));
	double tmp;
	if (t <= -6.1e+32) {
		tmp = t_1;
	} else if (t <= -2.5e-12) {
		tmp = (z * x) / y;
	} else if ((t <= -4e-88) || (!(t <= 9.6e-207) && ((t <= 9.5e-150) || !(t <= 1.12e-74)))) {
		tmp = t_1;
	} else {
		tmp = x * (z / 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) :: t_1
    real(8) :: tmp
    t_1 = t * (1.0d0 - (x / y))
    if (t <= (-6.1d+32)) then
        tmp = t_1
    else if (t <= (-2.5d-12)) then
        tmp = (z * x) / y
    else if ((t <= (-4d-88)) .or. (.not. (t <= 9.6d-207)) .and. (t <= 9.5d-150) .or. (.not. (t <= 1.12d-74))) then
        tmp = t_1
    else
        tmp = x * (z / y)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double t_1 = t * (1.0 - (x / y));
	double tmp;
	if (t <= -6.1e+32) {
		tmp = t_1;
	} else if (t <= -2.5e-12) {
		tmp = (z * x) / y;
	} else if ((t <= -4e-88) || (!(t <= 9.6e-207) && ((t <= 9.5e-150) || !(t <= 1.12e-74)))) {
		tmp = t_1;
	} else {
		tmp = x * (z / y);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = t * (1.0 - (x / y))
	tmp = 0
	if t <= -6.1e+32:
		tmp = t_1
	elif t <= -2.5e-12:
		tmp = (z * x) / y
	elif (t <= -4e-88) or (not (t <= 9.6e-207) and ((t <= 9.5e-150) or not (t <= 1.12e-74))):
		tmp = t_1
	else:
		tmp = x * (z / y)
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(t * Float64(1.0 - Float64(x / y)))
	tmp = 0.0
	if (t <= -6.1e+32)
		tmp = t_1;
	elseif (t <= -2.5e-12)
		tmp = Float64(Float64(z * x) / y);
	elseif ((t <= -4e-88) || (!(t <= 9.6e-207) && ((t <= 9.5e-150) || !(t <= 1.12e-74))))
		tmp = t_1;
	else
		tmp = Float64(x * Float64(z / y));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = t * (1.0 - (x / y));
	tmp = 0.0;
	if (t <= -6.1e+32)
		tmp = t_1;
	elseif (t <= -2.5e-12)
		tmp = (z * x) / y;
	elseif ((t <= -4e-88) || (~((t <= 9.6e-207)) && ((t <= 9.5e-150) || ~((t <= 1.12e-74)))))
		tmp = t_1;
	else
		tmp = x * (z / y);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(t * N[(1.0 - N[(x / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t, -6.1e+32], t$95$1, If[LessEqual[t, -2.5e-12], N[(N[(z * x), $MachinePrecision] / y), $MachinePrecision], If[Or[LessEqual[t, -4e-88], And[N[Not[LessEqual[t, 9.6e-207]], $MachinePrecision], Or[LessEqual[t, 9.5e-150], N[Not[LessEqual[t, 1.12e-74]], $MachinePrecision]]]], t$95$1, N[(x * N[(z / y), $MachinePrecision]), $MachinePrecision]]]]]

Derivation

1. Split input into 3 regimes

2. if t < -6.10000000000000027e32 or -2.49999999999999985e-12 < t < -3.99999999999999974e-88 or 9.59999999999999956e-207 < t < 9.50000000000000013e-150 or 1.11999999999999999e-74 < t

   1. Initial program 98.8%

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

   3. Taylor expanded in z around 0 76.9%

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

      1. mul-1-neg 76.9%

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

      2. *-lft-identity 76.9%

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

      3. *-commutative 76.9%

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

      4. associate-*l/ 83.3%

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

      5. distribute-lft-neg-in 83.3%

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

      6. mul-1-neg 83.3%

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

      7. distribute-rgt-in 83.3%

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

      8. mul-1-neg 83.3%

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

      9. unsub-neg 83.3%

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

   5. Simplified 83.3%

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

   if -6.10000000000000027e32 < t < -2.49999999999999985e-12

   1. Initial program 100.0%

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

   3. Taylor expanded in x around inf 84.5%

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

   4. Taylor expanded in z around inf 100.0%

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

   if -3.99999999999999974e-88 < t < 9.59999999999999956e-207 or 9.50000000000000013e-150 < t < 1.11999999999999999e-74

   1. Initial program 97.5%

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

   3. Taylor expanded in x around inf 80.4%

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

   4. Taylor expanded in z around inf 68.2%

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

      1. associate-*r/ 71.6%

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

   6. Simplified 71.6%

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

4. Final simplification 79.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -6.1 \cdot 10^{+32}:\\ \;\;\;\;t \cdot \left(1 - \frac{x}{y}\right)\\ \mathbf{elif}\;t \leq -2.5 \cdot 10^{-12}:\\ \;\;\;\;\frac{z \cdot x}{y}\\ \mathbf{elif}\;t \leq -4 \cdot 10^{-88} \lor \neg \left(t \leq 9.6 \cdot 10^{-207}\right) \land \left(t \leq 9.5 \cdot 10^{-150} \lor \neg \left(t \leq 1.12 \cdot 10^{-74}\right)\right):\\ \;\;\;\;t \cdot \left(1 - \frac{x}{y}\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \frac{z}{y}\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 62.7% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;\frac{x}{y} \leq -4 \cdot 10^{-27}:\\ \;\;\;\;x \cdot \frac{z}{y}\\ \mathbf{elif}\;\frac{x}{y} \leq 2 \cdot 10^{-24}:\\ \;\;\;\;t\\ \mathbf{elif}\;\frac{x}{y} \leq 2 \cdot 10^{+70}:\\ \;\;\;\;\frac{z \cdot x}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{y} \cdot \left(-t\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= (/ x y) -4e-27)
   (* x (/ z y))
   (if (<= (/ x y) 2e-24)
     t
     (if (<= (/ x y) 2e+70) (/ (* z x) y) (* (/ x y) (- t))))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((x / y) <= -4e-27) {
		tmp = x * (z / y);
	} else if ((x / y) <= 2e-24) {
		tmp = t;
	} else if ((x / y) <= 2e+70) {
		tmp = (z * x) / y;
	} else {
		tmp = (x / y) * -t;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if ((x / y) <= (-4d-27)) then
        tmp = x * (z / y)
    else if ((x / y) <= 2d-24) then
        tmp = t
    else if ((x / y) <= 2d+70) then
        tmp = (z * x) / y
    else
        tmp = (x / y) * -t
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if ((x / y) <= -4e-27) {
		tmp = x * (z / y);
	} else if ((x / y) <= 2e-24) {
		tmp = t;
	} else if ((x / y) <= 2e+70) {
		tmp = (z * x) / y;
	} else {
		tmp = (x / y) * -t;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (x / y) <= -4e-27:
		tmp = x * (z / y)
	elif (x / y) <= 2e-24:
		tmp = t
	elif (x / y) <= 2e+70:
		tmp = (z * x) / y
	else:
		tmp = (x / y) * -t
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (Float64(x / y) <= -4e-27)
		tmp = Float64(x * Float64(z / y));
	elseif (Float64(x / y) <= 2e-24)
		tmp = t;
	elseif (Float64(x / y) <= 2e+70)
		tmp = Float64(Float64(z * x) / y);
	else
		tmp = Float64(Float64(x / y) * Float64(-t));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((x / y) <= -4e-27)
		tmp = x * (z / y);
	elseif ((x / y) <= 2e-24)
		tmp = t;
	elseif ((x / y) <= 2e+70)
		tmp = (z * x) / y;
	else
		tmp = (x / y) * -t;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[N[(x / y), $MachinePrecision], -4e-27], N[(x * N[(z / y), $MachinePrecision]), $MachinePrecision], If[LessEqual[N[(x / y), $MachinePrecision], 2e-24], t, If[LessEqual[N[(x / y), $MachinePrecision], 2e+70], N[(N[(z * x), $MachinePrecision] / y), $MachinePrecision], N[(N[(x / y), $MachinePrecision] * (-t)), $MachinePrecision]]]]

Derivation

1. Split input into 4 regimes

2. if (/.f64 x y) < -4.0000000000000002e-27

   1. Initial program 95.8%

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

   3. Taylor expanded in x around inf 83.1%

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

   4. Taylor expanded in z around inf 55.1%

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

      1. associate-*r/ 57.9%

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

   6. Simplified 57.9%

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

   if -4.0000000000000002e-27 < (/.f64 x y) < 1.99999999999999985e-24

   1. Initial program 99.9%

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

   3. Taylor expanded in x around 0 75.6%

      \[\leadsto \color{blue}{t} \]

   if 1.99999999999999985e-24 < (/.f64 x y) < 2.00000000000000015e70

   1. Initial program 99.4%

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

   3. Taylor expanded in x around inf 58.4%

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

   4. Taylor expanded in z around inf 63.8%

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

   if 2.00000000000000015e70 < (/.f64 x y)

   1. Initial program 98.2%

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

   3. Taylor expanded in x around inf 89.5%

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

   4. Taylor expanded in z around 0 54.6%

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

      1. mul-1-neg 54.6%

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

      2. associate-*r/ 69.6%

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

   6. Simplified 69.6%

      \[\leadsto \color{blue}{-t \cdot \frac{x}{y}} \]
3. Recombined 4 regimes into one program.

4. Final simplification 68.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{x}{y} \leq -4 \cdot 10^{-27}:\\ \;\;\;\;x \cdot \frac{z}{y}\\ \mathbf{elif}\;\frac{x}{y} \leq 2 \cdot 10^{-24}:\\ \;\;\;\;t\\ \mathbf{elif}\;\frac{x}{y} \leq 2 \cdot 10^{+70}:\\ \;\;\;\;\frac{z \cdot x}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{y} \cdot \left(-t\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 94.3% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;\frac{x}{y} \leq -5 \cdot 10^{+17} \lor \neg \left(\frac{x}{y} \leq 10^{+20}\right):\\ \;\;\;\;x \cdot \frac{z - t}{y}\\ \mathbf{else}:\\ \;\;\;\;t + \frac{z}{\frac{y}{x}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= (/ x y) -5e+17) (not (<= (/ x y) 1e+20)))
   (* x (/ (- z t) y))
   (+ t (/ z (/ y x)))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (((x / y) <= -5e+17) || !((x / y) <= 1e+20)) {
		tmp = x * ((z - t) / y);
	} else {
		tmp = t + (z / (y / x));
	}
	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) <= (-5d+17)) .or. (.not. ((x / y) <= 1d+20))) then
        tmp = x * ((z - t) / y)
    else
        tmp = t + (z / (y / x))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if (((x / y) <= -5e+17) || !((x / y) <= 1e+20)) {
		tmp = x * ((z - t) / y);
	} else {
		tmp = t + (z / (y / x));
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if ((x / y) <= -5e+17) or not ((x / y) <= 1e+20):
		tmp = x * ((z - t) / y)
	else:
		tmp = t + (z / (y / x))
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((Float64(x / y) <= -5e+17) || !(Float64(x / y) <= 1e+20))
		tmp = Float64(x * Float64(Float64(z - t) / y));
	else
		tmp = Float64(t + Float64(z / Float64(y / x)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (((x / y) <= -5e+17) || ~(((x / y) <= 1e+20)))
		tmp = x * ((z - t) / y);
	else
		tmp = t + (z / (y / x));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[N[(x / y), $MachinePrecision], -5e+17], N[Not[LessEqual[N[(x / y), $MachinePrecision], 1e+20]], $MachinePrecision]], N[(x * N[(N[(z - t), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision], N[(t + N[(z / N[(y / x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if (/.f64 x y) < -5e17 or 1e20 < (/.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 88.9%

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

   4. Taylor expanded in z around 0 78.6%

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

      1. associate-*r/ 80.9%

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

      2. +-commutative 80.9%

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

      3. associate-*l/ 81.6%

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

      4. associate-*r* 81.6%

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

      5. mul-1-neg 81.6%

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

      6. distribute-frac-neg 81.6%

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

      7. *-commutative 81.6%

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

      8. distribute-lft-out 88.9%

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

      9. distribute-frac-neg 88.9%

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

      10. sub-neg 88.9%

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

      11. div-sub 93.8%

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

   6. Simplified 93.8%

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

   if -5e17 < (/.f64 x y) < 1e20

   1. Initial program 99.8%

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

   3. Taylor expanded in z around inf 90.8%

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

      1. associate-/l* 89.4%

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

   5. Simplified 89.4%

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

      1. *-commutative 89.4%

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

      2. associate-/r/ 96.5%

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

   7. Applied egg-rr 96.5%

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

4. Final simplification 95.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{x}{y} \leq -5 \cdot 10^{+17} \lor \neg \left(\frac{x}{y} \leq 10^{+20}\right):\\ \;\;\;\;x \cdot \frac{z - t}{y}\\ \mathbf{else}:\\ \;\;\;\;t + \frac{z}{\frac{y}{x}}\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 94.4% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;\frac{x}{y} \leq -5 \cdot 10^{+17} \lor \neg \left(\frac{x}{y} \leq 10^{+20}\right):\\ \;\;\;\;x \cdot \frac{z - t}{y}\\ \mathbf{else}:\\ \;\;\;\;t + z \cdot \frac{x}{y}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= (/ x y) -5e+17) (not (<= (/ x y) 1e+20)))
   (* x (/ (- z t) y))
   (+ t (* z (/ x y)))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (((x / y) <= -5e+17) || !((x / y) <= 1e+20)) {
		tmp = x * ((z - t) / y);
	} else {
		tmp = t + (z * (x / 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) <= (-5d+17)) .or. (.not. ((x / y) <= 1d+20))) then
        tmp = x * ((z - t) / y)
    else
        tmp = t + (z * (x / 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) <= -5e+17) || !((x / y) <= 1e+20)) {
		tmp = x * ((z - t) / y);
	} else {
		tmp = t + (z * (x / y));
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if ((x / y) <= -5e+17) or not ((x / y) <= 1e+20):
		tmp = x * ((z - t) / y)
	else:
		tmp = t + (z * (x / y))
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((Float64(x / y) <= -5e+17) || !(Float64(x / y) <= 1e+20))
		tmp = Float64(x * Float64(Float64(z - t) / y));
	else
		tmp = Float64(t + Float64(z * Float64(x / y)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (((x / y) <= -5e+17) || ~(((x / y) <= 1e+20)))
		tmp = x * ((z - t) / y);
	else
		tmp = t + (z * (x / y));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[N[(x / y), $MachinePrecision], -5e+17], N[Not[LessEqual[N[(x / y), $MachinePrecision], 1e+20]], $MachinePrecision]], N[(x * N[(N[(z - t), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision], N[(t + N[(z * N[(x / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if (/.f64 x y) < -5e17 or 1e20 < (/.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 88.9%

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

   4. Taylor expanded in z around 0 78.6%

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

      1. associate-*r/ 80.9%

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

      2. +-commutative 80.9%

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

      3. associate-*l/ 81.6%

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

      4. associate-*r* 81.6%

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

      5. mul-1-neg 81.6%

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

      6. distribute-frac-neg 81.6%

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

      7. *-commutative 81.6%

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

      8. distribute-lft-out 88.9%

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

      9. distribute-frac-neg 88.9%

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

      10. sub-neg 88.9%

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

      11. div-sub 93.8%

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

   6. Simplified 93.8%

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

   if -5e17 < (/.f64 x y) < 1e20

   1. Initial program 99.8%

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

   3. Taylor expanded in z around inf 96.5%

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

4. Final simplification 95.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{x}{y} \leq -5 \cdot 10^{+17} \lor \neg \left(\frac{x}{y} \leq 10^{+20}\right):\\ \;\;\;\;x \cdot \frac{z - t}{y}\\ \mathbf{else}:\\ \;\;\;\;t + z \cdot \frac{x}{y}\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 93.3% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;\frac{x}{y} \leq -500 \lor \neg \left(\frac{x}{y} \leq 4 \cdot 10^{-6}\right):\\ \;\;\;\;x \cdot \frac{z - t}{y}\\ \mathbf{else}:\\ \;\;\;\;t + x \cdot \frac{z}{y}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= (/ x y) -500.0) (not (<= (/ x y) 4e-6)))
   (* x (/ (- z t) y))
   (+ t (* x (/ z y)))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (((x / y) <= -500.0) || !((x / y) <= 4e-6)) {
		tmp = x * ((z - t) / y);
	} else {
		tmp = t + (x * (z / 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) <= (-500.0d0)) .or. (.not. ((x / y) <= 4d-6))) then
        tmp = x * ((z - t) / y)
    else
        tmp = t + (x * (z / 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) <= -500.0) || !((x / y) <= 4e-6)) {
		tmp = x * ((z - t) / y);
	} else {
		tmp = t + (x * (z / y));
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if ((x / y) <= -500.0) or not ((x / y) <= 4e-6):
		tmp = x * ((z - t) / y)
	else:
		tmp = t + (x * (z / y))
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((Float64(x / y) <= -500.0) || !(Float64(x / y) <= 4e-6))
		tmp = Float64(x * Float64(Float64(z - t) / y));
	else
		tmp = Float64(t + Float64(x * Float64(z / y)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (((x / y) <= -500.0) || ~(((x / y) <= 4e-6)))
		tmp = x * ((z - t) / y);
	else
		tmp = t + (x * (z / y));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[N[(x / y), $MachinePrecision], -500.0], N[Not[LessEqual[N[(x / y), $MachinePrecision], 4e-6]], $MachinePrecision]], N[(x * N[(N[(z - t), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision], N[(t + N[(x * N[(z / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if (/.f64 x y) < -500 or 3.99999999999999982e-6 < (/.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 inf 84.8%

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

   4. Taylor expanded in z around 0 78.5%

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

      1. associate-*r/ 78.6%

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

      2. +-commutative 78.6%

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

      3. associate-*l/ 78.0%

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

      4. associate-*r* 78.0%

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

      5. mul-1-neg 78.0%

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

      6. distribute-frac-neg 78.0%

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

      7. *-commutative 78.0%

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

      8. distribute-lft-out 84.8%

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

      9. distribute-frac-neg 84.8%

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

      10. sub-neg 84.8%

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

      11. div-sub 89.4%

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

   6. Simplified 89.4%

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

   if -500 < (/.f64 x y) < 3.99999999999999982e-6

   1. Initial program 99.9%

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

   3. Taylor expanded in z around inf 93.1%

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

      1. associate-/l* 93.8%

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

   5. Simplified 93.8%

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

4. Final simplification 91.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{x}{y} \leq -500 \lor \neg \left(\frac{x}{y} \leq 4 \cdot 10^{-6}\right):\\ \;\;\;\;x \cdot \frac{z - t}{y}\\ \mathbf{else}:\\ \;\;\;\;t + x \cdot \frac{z}{y}\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 83.0% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;\frac{x}{y} \leq -1000000 \lor \neg \left(\frac{x}{y} \leq 2 \cdot 10^{+26}\right):\\ \;\;\;\;x \cdot \frac{z - t}{y}\\ \mathbf{else}:\\ \;\;\;\;t \cdot \left(1 - \frac{x}{y}\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= (/ x y) -1000000.0) (not (<= (/ x y) 2e+26)))
   (* x (/ (- z t) y))
   (* t (- 1.0 (/ x y)))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (((x / y) <= -1000000.0) || !((x / y) <= 2e+26)) {
		tmp = x * ((z - t) / y);
	} else {
		tmp = t * (1.0 - (x / 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) <= (-1000000.0d0)) .or. (.not. ((x / y) <= 2d+26))) then
        tmp = x * ((z - t) / y)
    else
        tmp = t * (1.0d0 - (x / 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) <= -1000000.0) || !((x / y) <= 2e+26)) {
		tmp = x * ((z - t) / y);
	} else {
		tmp = t * (1.0 - (x / y));
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if ((x / y) <= -1000000.0) or not ((x / y) <= 2e+26):
		tmp = x * ((z - t) / y)
	else:
		tmp = t * (1.0 - (x / y))
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((Float64(x / y) <= -1000000.0) || !(Float64(x / y) <= 2e+26))
		tmp = Float64(x * Float64(Float64(z - t) / y));
	else
		tmp = Float64(t * Float64(1.0 - Float64(x / y)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (((x / y) <= -1000000.0) || ~(((x / y) <= 2e+26)))
		tmp = x * ((z - t) / y);
	else
		tmp = t * (1.0 - (x / y));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[N[(x / y), $MachinePrecision], -1000000.0], N[Not[LessEqual[N[(x / y), $MachinePrecision], 2e+26]], $MachinePrecision]], N[(x * N[(N[(z - t), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision], N[(t * N[(1.0 - N[(x / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if (/.f64 x y) < -1e6 or 2.0000000000000001e26 < (/.f64 x y)

   1. Initial program 96.9%

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

   3. Taylor expanded in x around inf 88.3%

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

   4. Taylor expanded in z around 0 78.9%

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

      1. associate-*r/ 80.5%

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

      2. +-commutative 80.5%

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

      3. associate-*l/ 81.2%

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

      4. associate-*r* 81.2%

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

      5. mul-1-neg 81.2%

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

      6. distribute-frac-neg 81.2%

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

      7. *-commutative 81.2%

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

      8. distribute-lft-out 88.3%

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

      9. distribute-frac-neg 88.3%

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

      10. sub-neg 88.3%

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

      11. div-sub 93.2%

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

   6. Simplified 93.2%

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

   if -1e6 < (/.f64 x y) < 2.0000000000000001e26

   1. Initial program 99.9%

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

   3. Taylor expanded in z around 0 68.9%

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

      1. mul-1-neg 68.9%

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

      2. *-lft-identity 68.9%

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

      3. *-commutative 68.9%

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

      4. associate-*l/ 73.6%

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

      5. distribute-lft-neg-in 73.6%

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

      6. mul-1-neg 73.6%

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

      7. distribute-rgt-in 73.6%

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

      8. mul-1-neg 73.6%

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

      9. unsub-neg 73.6%

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

   5. Simplified 73.6%

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

4. Final simplification 83.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{x}{y} \leq -1000000 \lor \neg \left(\frac{x}{y} \leq 2 \cdot 10^{+26}\right):\\ \;\;\;\;x \cdot \frac{z - t}{y}\\ \mathbf{else}:\\ \;\;\;\;t \cdot \left(1 - \frac{x}{y}\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 94.1% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;\frac{x}{y} \leq -500:\\ \;\;\;\;\frac{\left(z - t\right) \cdot x}{y}\\ \mathbf{elif}\;\frac{x}{y} \leq 10^{+20}:\\ \;\;\;\;t + \frac{z}{\frac{y}{x}}\\ \mathbf{else}:\\ \;\;\;\;x \cdot \frac{z - t}{y}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= (/ x y) -500.0)
   (/ (* (- z t) x) y)
   (if (<= (/ x y) 1e+20) (+ t (/ z (/ y x))) (* x (/ (- z t) y)))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((x / y) <= -500.0) {
		tmp = ((z - t) * x) / y;
	} else if ((x / y) <= 1e+20) {
		tmp = t + (z / (y / x));
	} 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) <= (-500.0d0)) then
        tmp = ((z - t) * x) / y
    else if ((x / y) <= 1d+20) then
        tmp = t + (z / (y / x))
    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) <= -500.0) {
		tmp = ((z - t) * x) / y;
	} else if ((x / y) <= 1e+20) {
		tmp = t + (z / (y / x));
	} else {
		tmp = x * ((z - t) / y);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (x / y) <= -500.0:
		tmp = ((z - t) * x) / y
	elif (x / y) <= 1e+20:
		tmp = t + (z / (y / x))
	else:
		tmp = x * ((z - t) / y)
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (Float64(x / y) <= -500.0)
		tmp = Float64(Float64(Float64(z - t) * x) / y);
	elseif (Float64(x / y) <= 1e+20)
		tmp = Float64(t + Float64(z / Float64(y / x)));
	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) <= -500.0)
		tmp = ((z - t) * x) / y;
	elseif ((x / y) <= 1e+20)
		tmp = t + (z / (y / x));
	else
		tmp = x * ((z - t) / y);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[N[(x / y), $MachinePrecision], -500.0], N[(N[(N[(z - t), $MachinePrecision] * x), $MachinePrecision] / y), $MachinePrecision], If[LessEqual[N[(x / y), $MachinePrecision], 1e+20], N[(t + N[(z / N[(y / x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x * N[(N[(z - t), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if (/.f64 x y) < -500

   1. Initial program 95.6%

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

   3. Taylor expanded in x around inf 84.1%

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

      1. *-commutative 84.1%

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

      2. sub-div 90.3%

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

      3. associate-*l/ 92.1%

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

   5. Applied egg-rr 92.1%

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

   if -500 < (/.f64 x y) < 1e20

   1. Initial program 99.9%

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

   3. Taylor expanded in z around inf 92.5%

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

      1. associate-/l* 91.8%

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

   5. Simplified 91.8%

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

      1. *-commutative 91.8%

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

      2. associate-/r/ 98.4%

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

   7. Applied egg-rr 98.4%

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

   if 1e20 < (/.f64 x y)

   1. Initial program 98.3%

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

   3. Taylor expanded in x around inf 89.3%

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

   4. Taylor expanded in z around 0 79.8%

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

      1. associate-*r/ 81.5%

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

      2. +-commutative 81.5%

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

      3. associate-*l/ 84.5%

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

      4. associate-*r* 84.5%

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

      5. mul-1-neg 84.5%

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

      6. distribute-frac-neg 84.5%

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

      7. *-commutative 84.5%

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

      8. distribute-lft-out 89.3%

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

      9. distribute-frac-neg 89.3%

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

      10. sub-neg 89.3%

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

      11. div-sub 92.5%

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

   6. Simplified 92.5%

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

4. Final simplification 95.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{x}{y} \leq -500:\\ \;\;\;\;\frac{\left(z - t\right) \cdot x}{y}\\ \mathbf{elif}\;\frac{x}{y} \leq 10^{+20}:\\ \;\;\;\;t + \frac{z}{\frac{y}{x}}\\ \mathbf{else}:\\ \;\;\;\;x \cdot \frac{z - t}{y}\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 53.5% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -8.6 \cdot 10^{+68}:\\ \;\;\;\;t\\ \mathbf{elif}\;y \leq 1.95 \cdot 10^{+57}:\\ \;\;\;\;\frac{z \cdot x}{y}\\ \mathbf{else}:\\ \;\;\;\;t\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= y -8.6e+68) t (if (<= y 1.95e+57) (/ (* z x) y) t)))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (y <= -8.6e+68) {
		tmp = t;
	} else if (y <= 1.95e+57) {
		tmp = (z * x) / 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 (y <= (-8.6d+68)) then
        tmp = t
    else if (y <= 1.95d+57) then
        tmp = (z * x) / 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 (y <= -8.6e+68) {
		tmp = t;
	} else if (y <= 1.95e+57) {
		tmp = (z * x) / y;
	} else {
		tmp = t;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if y <= -8.6e+68:
		tmp = t
	elif y <= 1.95e+57:
		tmp = (z * x) / y
	else:
		tmp = t
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (y <= -8.6e+68)
		tmp = t;
	elseif (y <= 1.95e+57)
		tmp = Float64(Float64(z * x) / y);
	else
		tmp = t;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (y <= -8.6e+68)
		tmp = t;
	elseif (y <= 1.95e+57)
		tmp = (z * x) / y;
	else
		tmp = t;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[y, -8.6e+68], t, If[LessEqual[y, 1.95e+57], N[(N[(z * x), $MachinePrecision] / y), $MachinePrecision], t]]

Derivation

1. Split input into 2 regimes

2. if y < -8.6000000000000002e68 or 1.94999999999999984e57 < y

   1. Initial program 99.9%

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

   3. Taylor expanded in x around 0 64.6%

      \[\leadsto \color{blue}{t} \]

   if -8.6000000000000002e68 < y < 1.94999999999999984e57

   1. Initial program 97.4%

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

   3. Taylor expanded in x around inf 68.8%

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

   4. Taylor expanded in z around inf 52.4%

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

4. Final simplification 57.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -8.6 \cdot 10^{+68}:\\ \;\;\;\;t\\ \mathbf{elif}\;y \leq 1.95 \cdot 10^{+57}:\\ \;\;\;\;\frac{z \cdot x}{y}\\ \mathbf{else}:\\ \;\;\;\;t\\ \end{array} \]
5. Add Preprocessing

Alternative 10: 49.5% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -1.8 \cdot 10^{+124}:\\ \;\;\;\;t\\ \mathbf{elif}\;t \leq 6.6 \cdot 10^{-57}:\\ \;\;\;\;x \cdot \frac{z}{y}\\ \mathbf{else}:\\ \;\;\;\;t\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= t -1.8e+124) t (if (<= t 6.6e-57) (* x (/ z y)) t)))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (t <= -1.8e+124) {
		tmp = t;
	} else if (t <= 6.6e-57) {
		tmp = x * (z / 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 (t <= (-1.8d+124)) then
        tmp = t
    else if (t <= 6.6d-57) then
        tmp = x * (z / 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 (t <= -1.8e+124) {
		tmp = t;
	} else if (t <= 6.6e-57) {
		tmp = x * (z / y);
	} else {
		tmp = t;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if t <= -1.8e+124:
		tmp = t
	elif t <= 6.6e-57:
		tmp = x * (z / y)
	else:
		tmp = t
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (t <= -1.8e+124)
		tmp = t;
	elseif (t <= 6.6e-57)
		tmp = Float64(x * Float64(z / y));
	else
		tmp = t;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (t <= -1.8e+124)
		tmp = t;
	elseif (t <= 6.6e-57)
		tmp = x * (z / y);
	else
		tmp = t;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[t, -1.8e+124], t, If[LessEqual[t, 6.6e-57], N[(x * N[(z / y), $MachinePrecision]), $MachinePrecision], t]]

Derivation

1. Split input into 2 regimes

2. if t < -1.79999999999999993e124 or 6.5999999999999997e-57 < t

   1. Initial program 99.9%

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

   3. Taylor expanded in x around 0 53.5%

      \[\leadsto \color{blue}{t} \]

   if -1.79999999999999993e124 < t < 6.5999999999999997e-57

   1. Initial program 97.1%

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

   3. Taylor expanded in x around inf 68.0%

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

   4. Taylor expanded in z around inf 60.0%

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

      1. associate-*r/ 59.4%

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

   6. Simplified 59.4%

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

Alternative 11: 97.5% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

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) * (x / y))
end function

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 98.4%

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

3. Final simplification 98.4%

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

Alternative 12: 38.1% 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 98.4%

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

3. Taylor expanded in x around 0 36.8%

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

Developer target: 97.2% 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 2024110 
(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))