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

Percentage Accurate: 97.9% → 98.0%

Time: 8.6s

Alternatives: 12

Speedup: 1.0×

• 24.3% 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: 97.9% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Alternative 1: 98.0% accurate, 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 98.0%

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

3. Taylor expanded in x around 0 94.0%

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

   1. associate-*r/ 94.3%

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

   2. *-commutative 94.3%

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

   3. associate-/r/ 98.2%

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

5. Simplified 98.2%

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

6. Final simplification 98.2%

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

Alternative 2: 63.5% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := t \cdot \frac{x}{-y}\\ \mathbf{if}\;\frac{x}{y} \leq -5000000000000:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;\frac{x}{y} \leq 4 \cdot 10^{-68}:\\ \;\;\;\;t\\ \mathbf{elif}\;\frac{x}{y} \leq 5000000 \lor \neg \left(\frac{x}{y} \leq 5 \cdot 10^{+194}\right):\\ \;\;\;\;\frac{z \cdot x}{y}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (* t (/ x (- y)))))
   (if (<= (/ x y) -5000000000000.0)
     t_1
     (if (<= (/ x y) 4e-68)
       t
       (if (or (<= (/ x y) 5000000.0) (not (<= (/ x y) 5e+194)))
         (/ (* z x) y)
         t_1)))))

C

double code(double x, double y, double z, double t) {
	double t_1 = t * (x / -y);
	double tmp;
	if ((x / y) <= -5000000000000.0) {
		tmp = t_1;
	} else if ((x / y) <= 4e-68) {
		tmp = t;
	} else if (((x / y) <= 5000000.0) || !((x / y) <= 5e+194)) {
		tmp = (z * x) / 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 = t * (x / -y)
    if ((x / y) <= (-5000000000000.0d0)) then
        tmp = t_1
    else if ((x / y) <= 4d-68) then
        tmp = t
    else if (((x / y) <= 5000000.0d0) .or. (.not. ((x / y) <= 5d+194))) then
        tmp = (z * x) / 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 = t * (x / -y);
	double tmp;
	if ((x / y) <= -5000000000000.0) {
		tmp = t_1;
	} else if ((x / y) <= 4e-68) {
		tmp = t;
	} else if (((x / y) <= 5000000.0) || !((x / y) <= 5e+194)) {
		tmp = (z * x) / y;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = t * (x / -y)
	tmp = 0
	if (x / y) <= -5000000000000.0:
		tmp = t_1
	elif (x / y) <= 4e-68:
		tmp = t
	elif ((x / y) <= 5000000.0) or not ((x / y) <= 5e+194):
		tmp = (z * x) / y
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(t * Float64(x / Float64(-y)))
	tmp = 0.0
	if (Float64(x / y) <= -5000000000000.0)
		tmp = t_1;
	elseif (Float64(x / y) <= 4e-68)
		tmp = t;
	elseif ((Float64(x / y) <= 5000000.0) || !(Float64(x / y) <= 5e+194))
		tmp = Float64(Float64(z * x) / y);
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = t * (x / -y);
	tmp = 0.0;
	if ((x / y) <= -5000000000000.0)
		tmp = t_1;
	elseif ((x / y) <= 4e-68)
		tmp = t;
	elseif (((x / y) <= 5000000.0) || ~(((x / y) <= 5e+194)))
		tmp = (z * x) / y;
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(t * N[(x / (-y)), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[N[(x / y), $MachinePrecision], -5000000000000.0], t$95$1, If[LessEqual[N[(x / y), $MachinePrecision], 4e-68], t, If[Or[LessEqual[N[(x / y), $MachinePrecision], 5000000.0], N[Not[LessEqual[N[(x / y), $MachinePrecision], 5e+194]], $MachinePrecision]], N[(N[(z * x), $MachinePrecision] / y), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if (/.f64 x y) < -5e12 or 5e6 < (/.f64 x y) < 4.99999999999999989e194

   1. Initial program 99.8%

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

   3. Taylor expanded in z around 0 58.1%

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

      1. *-rgt-identity 58.1%

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

      2. mul-1-neg 58.1%

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

      3. associate-/l* 65.5%

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

      4. distribute-rgt-neg-in 65.5%

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

      5. mul-1-neg 65.5%

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

      6. distribute-lft-in 65.5%

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

      7. mul-1-neg 65.5%

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

      8. unsub-neg 65.5%

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

   5. Simplified 65.5%

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

   6. Taylor expanded in x around inf 65.1%

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

      1. mul-1-neg 65.1%

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

      2. distribute-frac-neg 65.1%

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

   8. Simplified 65.1%

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

   if -5e12 < (/.f64 x y) < 4.00000000000000027e-68

   1. Initial program 97.5%

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

   3. Taylor expanded in x around 0 76.1%

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

   if 4.00000000000000027e-68 < (/.f64 x y) < 5e6 or 4.99999999999999989e194 < (/.f64 x y)

   1. Initial program 96.1%

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

   3. Taylor expanded in z around inf 66.8%

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

      1. associate-/l* 70.3%

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

   5. Simplified 70.3%

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

   6. Taylor expanded in y around 0 64.8%

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

   7. Taylor expanded in t around 0 60.6%

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

4. Final simplification 69.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{x}{y} \leq -5000000000000:\\ \;\;\;\;t \cdot \frac{x}{-y}\\ \mathbf{elif}\;\frac{x}{y} \leq 4 \cdot 10^{-68}:\\ \;\;\;\;t\\ \mathbf{elif}\;\frac{x}{y} \leq 5000000 \lor \neg \left(\frac{x}{y} \leq 5 \cdot 10^{+194}\right):\\ \;\;\;\;\frac{z \cdot x}{y}\\ \mathbf{else}:\\ \;\;\;\;t \cdot \frac{x}{-y}\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 62.2% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;\frac{x}{y} \leq -1 \cdot 10^{-42} \lor \neg \left(\frac{x}{y} \leq 4 \cdot 10^{-68}\right):\\ \;\;\;\;\frac{z \cdot x}{y}\\ \mathbf{else}:\\ \;\;\;\;t\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= (/ x y) -1e-42) (not (<= (/ x y) 4e-68))) (/ (* z x) y) t))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (((x / y) <= -1e-42) || !((x / y) <= 4e-68)) {
		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 (((x / y) <= (-1d-42)) .or. (.not. ((x / y) <= 4d-68))) 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 (((x / y) <= -1e-42) || !((x / y) <= 4e-68)) {
		tmp = (z * x) / y;
	} else {
		tmp = t;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if ((x / y) <= -1e-42) or not ((x / y) <= 4e-68):
		tmp = (z * x) / y
	else:
		tmp = t
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((Float64(x / y) <= -1e-42) || !(Float64(x / y) <= 4e-68))
		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 (((x / y) <= -1e-42) || ~(((x / y) <= 4e-68)))
		tmp = (z * x) / y;
	else
		tmp = t;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[N[(x / y), $MachinePrecision], -1e-42], N[Not[LessEqual[N[(x / y), $MachinePrecision], 4e-68]], $MachinePrecision]], N[(N[(z * x), $MachinePrecision] / y), $MachinePrecision], t]

Derivation

1. Split input into 2 regimes

2. if (/.f64 x y) < -1.00000000000000004e-42 or 4.00000000000000027e-68 < (/.f64 x y)

   1. Initial program 98.5%

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

   3. Taylor expanded in z around inf 55.1%

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

      1. associate-/l* 53.1%

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

   5. Simplified 53.1%

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

   6. Taylor expanded in y around 0 56.3%

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

   7. Taylor expanded in t around 0 50.7%

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

   if -1.00000000000000004e-42 < (/.f64 x y) < 4.00000000000000027e-68

   1. Initial program 97.3%

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

   3. Taylor expanded in x around 0 79.9%

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

4. Final simplification 63.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{x}{y} \leq -1 \cdot 10^{-42} \lor \neg \left(\frac{x}{y} \leq 4 \cdot 10^{-68}\right):\\ \;\;\;\;\frac{z \cdot x}{y}\\ \mathbf{else}:\\ \;\;\;\;t\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 41.5% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;\frac{x}{y} \leq -3.6 \cdot 10^{+290} \lor \neg \left(\frac{x}{y} \leq 2.6 \cdot 10^{+194}\right):\\ \;\;\;\;t \cdot \frac{x}{y}\\ \mathbf{else}:\\ \;\;\;\;t\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= (/ x y) -3.6e+290) (not (<= (/ x y) 2.6e+194))) (* t (/ x y)) t))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (((x / y) <= -3.6e+290) || !((x / y) <= 2.6e+194)) {
		tmp = t * (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 (((x / y) <= (-3.6d+290)) .or. (.not. ((x / y) <= 2.6d+194))) then
        tmp = t * (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 (((x / y) <= -3.6e+290) || !((x / y) <= 2.6e+194)) {
		tmp = t * (x / y);
	} else {
		tmp = t;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if ((x / y) <= -3.6e+290) or not ((x / y) <= 2.6e+194):
		tmp = t * (x / y)
	else:
		tmp = t
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((Float64(x / y) <= -3.6e+290) || !(Float64(x / y) <= 2.6e+194))
		tmp = Float64(t * Float64(x / y));
	else
		tmp = t;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (((x / y) <= -3.6e+290) || ~(((x / y) <= 2.6e+194)))
		tmp = t * (x / y);
	else
		tmp = t;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[N[(x / y), $MachinePrecision], -3.6e+290], N[Not[LessEqual[N[(x / y), $MachinePrecision], 2.6e+194]], $MachinePrecision]], N[(t * N[(x / y), $MachinePrecision]), $MachinePrecision], t]

Derivation

1. Split input into 2 regimes

2. if (/.f64 x y) < -3.59999999999999988e290 or 2.5999999999999999e194 < (/.f64 x y)

   1. Initial program 96.0%

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

   3. Taylor expanded in z around 0 50.2%

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

      1. *-rgt-identity 50.2%

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

      2. mul-1-neg 50.2%

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

      3. associate-/l* 56.2%

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

      4. distribute-rgt-neg-in 56.2%

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

      5. mul-1-neg 56.2%

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

      6. distribute-lft-in 56.2%

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

      7. mul-1-neg 56.2%

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

      8. unsub-neg 56.2%

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

   5. Simplified 56.2%

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

   6. Taylor expanded in x around inf 56.2%

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

      1. mul-1-neg 56.2%

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

      2. distribute-frac-neg 56.2%

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

   8. Simplified 56.2%

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

      1. div-inv 56.2%

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

      2. add-sqr-sqrt 24.0%

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

      3. sqrt-unprod 32.8%

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

      4. sqr-neg 32.8%

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

      5. sqrt-unprod 8.8%

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

      6. add-sqr-sqrt 23.8%

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

   10. Applied egg-rr 23.8%

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

       1. associate-*r/ 23.8%

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

       2. *-rgt-identity 23.8%

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

   12. Simplified 23.8%

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

   if -3.59999999999999988e290 < (/.f64 x y) < 2.5999999999999999e194

   1. Initial program 98.4%

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

   3. Taylor expanded in x around 0 46.6%

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

4. Final simplification 42.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{x}{y} \leq -3.6 \cdot 10^{+290} \lor \neg \left(\frac{x}{y} \leq 2.6 \cdot 10^{+194}\right):\\ \;\;\;\;t \cdot \frac{x}{y}\\ \mathbf{else}:\\ \;\;\;\;t\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 43.8% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;\frac{x}{y} \leq -5 \cdot 10^{+41}:\\ \;\;\;\;y \cdot \frac{t}{y}\\ \mathbf{elif}\;\frac{x}{y} \leq 5 \cdot 10^{+194}:\\ \;\;\;\;t\\ \mathbf{else}:\\ \;\;\;\;t \cdot \frac{x}{y}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= (/ x y) -5e+41)
   (* y (/ t y))
   (if (<= (/ x y) 5e+194) t (* t (/ x y)))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((x / y) <= -5e+41) {
		tmp = y * (t / y);
	} else if ((x / y) <= 5e+194) {
		tmp = t;
	} else {
		tmp = t * (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+41)) then
        tmp = y * (t / y)
    else if ((x / y) <= 5d+194) then
        tmp = t
    else
        tmp = t * (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+41) {
		tmp = y * (t / y);
	} else if ((x / y) <= 5e+194) {
		tmp = t;
	} else {
		tmp = t * (x / y);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (x / y) <= -5e+41:
		tmp = y * (t / y)
	elif (x / y) <= 5e+194:
		tmp = t
	else:
		tmp = t * (x / y)
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (Float64(x / y) <= -5e+41)
		tmp = Float64(y * Float64(t / y));
	elseif (Float64(x / y) <= 5e+194)
		tmp = t;
	else
		tmp = Float64(t * Float64(x / y));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((x / y) <= -5e+41)
		tmp = y * (t / y);
	elseif ((x / y) <= 5e+194)
		tmp = t;
	else
		tmp = t * (x / y);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[N[(x / y), $MachinePrecision], -5e+41], N[(y * N[(t / y), $MachinePrecision]), $MachinePrecision], If[LessEqual[N[(x / y), $MachinePrecision], 5e+194], t, N[(t * N[(x / y), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if (/.f64 x y) < -5.00000000000000022e41

   1. Initial program 99.9%

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

   3. Taylor expanded in z around inf 54.2%

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

      1. associate-/l* 52.6%

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

   5. Simplified 52.6%

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

   6. Taylor expanded in y around 0 59.4%

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

   7. Taylor expanded in t around inf 9.4%

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

      1. *-commutative 9.4%

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

      2. associate-/l* 23.7%

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

   9. Applied egg-rr 23.7%

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

   if -5.00000000000000022e41 < (/.f64 x y) < 4.99999999999999989e194

   1. Initial program 98.2%

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

   3. Taylor expanded in x around 0 55.3%

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

   if 4.99999999999999989e194 < (/.f64 x y)

   1. Initial program 93.7%

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

   3. Taylor expanded in z around 0 45.0%

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

      1. *-rgt-identity 45.0%

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

      2. mul-1-neg 45.0%

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

      3. associate-/l* 48.0%

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

      4. distribute-rgt-neg-in 48.0%

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

      5. mul-1-neg 48.0%

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

      6. distribute-lft-in 48.0%

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

      7. mul-1-neg 48.0%

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

      8. unsub-neg 48.0%

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

   5. Simplified 48.0%

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

   6. Taylor expanded in x around inf 48.0%

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

      1. mul-1-neg 48.0%

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

      2. distribute-frac-neg 48.0%

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

   8. Simplified 48.0%

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

      1. div-inv 48.0%

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

      2. add-sqr-sqrt 20.9%

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

      3. sqrt-unprod 28.0%

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

      4. sqr-neg 28.0%

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

      5. sqrt-unprod 7.2%

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

      6. add-sqr-sqrt 20.7%

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

   10. Applied egg-rr 20.7%

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

       1. associate-*r/ 20.7%

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

       2. *-rgt-identity 20.7%

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

   12. Simplified 20.7%

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

Alternative 6: 84.7% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -23000 \lor \neg \left(t \leq 5.2 \cdot 10^{+42}\right):\\ \;\;\;\;t \cdot \frac{y - x}{y}\\ \mathbf{else}:\\ \;\;\;\;t + \frac{x}{\frac{y}{z}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= t -23000.0) (not (<= t 5.2e+42)))
   (* t (/ (- y x) y))
   (+ t (/ x (/ y z)))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((t <= -23000.0) || !(t <= 5.2e+42)) {
		tmp = t * ((y - x) / y);
	} else {
		tmp = t + (x / (y / z));
	}
	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 <= (-23000.0d0)) .or. (.not. (t <= 5.2d+42))) then
        tmp = t * ((y - x) / y)
    else
        tmp = t + (x / (y / z))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if ((t <= -23000.0) || !(t <= 5.2e+42)) {
		tmp = t * ((y - x) / y);
	} else {
		tmp = t + (x / (y / z));
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (t <= -23000.0) or not (t <= 5.2e+42):
		tmp = t * ((y - x) / y)
	else:
		tmp = t + (x / (y / z))
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((t <= -23000.0) || !(t <= 5.2e+42))
		tmp = Float64(t * Float64(Float64(y - x) / y));
	else
		tmp = Float64(t + Float64(x / Float64(y / z)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((t <= -23000.0) || ~((t <= 5.2e+42)))
		tmp = t * ((y - x) / y);
	else
		tmp = t + (x / (y / z));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[t, -23000.0], N[Not[LessEqual[t, 5.2e+42]], $MachinePrecision]], N[(t * N[(N[(y - x), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision], N[(t + N[(x / N[(y / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if t < -23000 or 5.1999999999999998e42 < t

   1. Initial program 99.9%

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

   3. Taylor expanded in z around 0 83.1%

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

      1. *-rgt-identity 83.1%

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

      2. mul-1-neg 83.1%

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

      3. associate-/l* 90.7%

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

      4. distribute-rgt-neg-in 90.7%

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

      5. mul-1-neg 90.7%

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

      6. distribute-lft-in 90.7%

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

      7. mul-1-neg 90.7%

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

      8. unsub-neg 90.7%

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

   5. Simplified 90.7%

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

   6. Taylor expanded in y around 0 90.7%

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

   if -23000 < t < 5.1999999999999998e42

   1. Initial program 96.3%

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

   3. Taylor expanded in z around inf 90.6%

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

      1. associate-/l* 91.4%

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

   5. Simplified 91.4%

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

      1. clear-num 91.3%

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

      2. un-div-inv 91.4%

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

   7. Applied egg-rr 91.4%

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

4. Final simplification 91.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -23000 \lor \neg \left(t \leq 5.2 \cdot 10^{+42}\right):\\ \;\;\;\;t \cdot \frac{y - x}{y}\\ \mathbf{else}:\\ \;\;\;\;t + \frac{x}{\frac{y}{z}}\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 84.6% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -53000 \lor \neg \left(t \leq 2.5 \cdot 10^{+44}\right):\\ \;\;\;\;t \cdot \frac{y - x}{y}\\ \mathbf{else}:\\ \;\;\;\;t + x \cdot \frac{z}{y}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= t -53000.0) (not (<= t 2.5e+44)))
   (* t (/ (- y x) y))
   (+ t (* x (/ z y)))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((t <= -53000.0) || !(t <= 2.5e+44)) {
		tmp = t * ((y - x) / 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 ((t <= (-53000.0d0)) .or. (.not. (t <= 2.5d+44))) then
        tmp = t * ((y - x) / 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 ((t <= -53000.0) || !(t <= 2.5e+44)) {
		tmp = t * ((y - x) / y);
	} else {
		tmp = t + (x * (z / y));
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (t <= -53000.0) or not (t <= 2.5e+44):
		tmp = t * ((y - x) / y)
	else:
		tmp = t + (x * (z / y))
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((t <= -53000.0) || !(t <= 2.5e+44))
		tmp = Float64(t * Float64(Float64(y - x) / 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 ((t <= -53000.0) || ~((t <= 2.5e+44)))
		tmp = t * ((y - x) / y);
	else
		tmp = t + (x * (z / y));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[t, -53000.0], N[Not[LessEqual[t, 2.5e+44]], $MachinePrecision]], N[(t * N[(N[(y - x), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision], N[(t + N[(x * N[(z / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if t < -53000 or 2.4999999999999998e44 < t

   1. Initial program 99.9%

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

   3. Taylor expanded in z around 0 83.1%

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

      1. *-rgt-identity 83.1%

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

      2. mul-1-neg 83.1%

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

      3. associate-/l* 90.7%

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

      4. distribute-rgt-neg-in 90.7%

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

      5. mul-1-neg 90.7%

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

      6. distribute-lft-in 90.7%

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

      7. mul-1-neg 90.7%

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

      8. unsub-neg 90.7%

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

   5. Simplified 90.7%

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

   6. Taylor expanded in y around 0 90.7%

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

   if -53000 < t < 2.4999999999999998e44

   1. Initial program 96.3%

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

   3. Taylor expanded in z around inf 90.6%

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

      1. associate-/l* 91.4%

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

   5. Simplified 91.4%

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

4. Final simplification 91.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -53000 \lor \neg \left(t \leq 2.5 \cdot 10^{+44}\right):\\ \;\;\;\;t \cdot \frac{y - x}{y}\\ \mathbf{else}:\\ \;\;\;\;t + x \cdot \frac{z}{y}\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 73.7% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -1.44 \cdot 10^{-83} \lor \neg \left(t \leq 3 \cdot 10^{-81}\right):\\ \;\;\;\;t \cdot \frac{y - x}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{z \cdot x}{y}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= t -1.44e-83) (not (<= t 3e-81)))
   (* t (/ (- y x) y))
   (/ (* z x) y)))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((t <= -1.44e-83) || !(t <= 3e-81)) {
		tmp = t * ((y - x) / y);
	} else {
		tmp = (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 ((t <= (-1.44d-83)) .or. (.not. (t <= 3d-81))) then
        tmp = t * ((y - x) / y)
    else
        tmp = (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 ((t <= -1.44e-83) || !(t <= 3e-81)) {
		tmp = t * ((y - x) / y);
	} else {
		tmp = (z * x) / y;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (t <= -1.44e-83) or not (t <= 3e-81):
		tmp = t * ((y - x) / y)
	else:
		tmp = (z * x) / y
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((t <= -1.44e-83) || !(t <= 3e-81))
		tmp = Float64(t * Float64(Float64(y - x) / y));
	else
		tmp = Float64(Float64(z * x) / y);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((t <= -1.44e-83) || ~((t <= 3e-81)))
		tmp = t * ((y - x) / y);
	else
		tmp = (z * x) / y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[t, -1.44e-83], N[Not[LessEqual[t, 3e-81]], $MachinePrecision]], N[(t * N[(N[(y - x), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision], N[(N[(z * x), $MachinePrecision] / y), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if t < -1.44000000000000001e-83 or 2.9999999999999999e-81 < t

   1. Initial program 99.9%

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

   3. Taylor expanded in z around 0 81.8%

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

      1. *-rgt-identity 81.8%

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

      2. mul-1-neg 81.8%

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

      3. associate-/l* 87.7%

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

      4. distribute-rgt-neg-in 87.7%

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

      5. mul-1-neg 87.7%

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

      6. distribute-lft-in 87.7%

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

      7. mul-1-neg 87.7%

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

      8. unsub-neg 87.7%

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

   5. Simplified 87.7%

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

   6. Taylor expanded in y around 0 87.7%

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

   if -1.44000000000000001e-83 < t < 2.9999999999999999e-81

   1. Initial program 95.1%

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

   3. Taylor expanded in z around inf 90.4%

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

      1. associate-/l* 89.5%

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

   5. Simplified 89.5%

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

   6. Taylor expanded in y around 0 90.4%

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

   7. Taylor expanded in t around 0 67.7%

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

4. Final simplification 79.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -1.44 \cdot 10^{-83} \lor \neg \left(t \leq 3 \cdot 10^{-81}\right):\\ \;\;\;\;t \cdot \frac{y - x}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{z \cdot x}{y}\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 73.5% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -2.55 \cdot 10^{-76} \lor \neg \left(t \leq 6.5 \cdot 10^{-78}\right):\\ \;\;\;\;t \cdot \left(1 - \frac{x}{y}\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{z \cdot x}{y}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= t -2.55e-76) (not (<= t 6.5e-78)))
   (* t (- 1.0 (/ x y)))
   (/ (* z x) y)))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((t <= -2.55e-76) || !(t <= 6.5e-78)) {
		tmp = t * (1.0 - (x / y));
	} else {
		tmp = (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 ((t <= (-2.55d-76)) .or. (.not. (t <= 6.5d-78))) then
        tmp = t * (1.0d0 - (x / y))
    else
        tmp = (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 ((t <= -2.55e-76) || !(t <= 6.5e-78)) {
		tmp = t * (1.0 - (x / y));
	} else {
		tmp = (z * x) / y;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (t <= -2.55e-76) or not (t <= 6.5e-78):
		tmp = t * (1.0 - (x / y))
	else:
		tmp = (z * x) / y
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((t <= -2.55e-76) || !(t <= 6.5e-78))
		tmp = Float64(t * Float64(1.0 - Float64(x / y)));
	else
		tmp = Float64(Float64(z * x) / y);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((t <= -2.55e-76) || ~((t <= 6.5e-78)))
		tmp = t * (1.0 - (x / y));
	else
		tmp = (z * x) / y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[t, -2.55e-76], N[Not[LessEqual[t, 6.5e-78]], $MachinePrecision]], N[(t * N[(1.0 - N[(x / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(z * x), $MachinePrecision] / y), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if t < -2.54999999999999993e-76 or 6.5000000000000003e-78 < t

   1. Initial program 99.9%

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

   3. Taylor expanded in z around 0 81.8%

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

      1. *-rgt-identity 81.8%

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

      2. mul-1-neg 81.8%

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

      3. associate-/l* 87.7%

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

      4. distribute-rgt-neg-in 87.7%

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

      5. mul-1-neg 87.7%

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

      6. distribute-lft-in 87.7%

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

      7. mul-1-neg 87.7%

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

      8. unsub-neg 87.7%

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

   5. Simplified 87.7%

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

   if -2.54999999999999993e-76 < t < 6.5000000000000003e-78

   1. Initial program 95.1%

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

   3. Taylor expanded in z around inf 90.4%

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

      1. associate-/l* 89.5%

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

   5. Simplified 89.5%

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

   6. Taylor expanded in y around 0 90.4%

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

   7. Taylor expanded in t around 0 67.7%

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

4. Final simplification 79.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -2.55 \cdot 10^{-76} \lor \neg \left(t \leq 6.5 \cdot 10^{-78}\right):\\ \;\;\;\;t \cdot \left(1 - \frac{x}{y}\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{z \cdot x}{y}\\ \end{array} \]
5. Add Preprocessing

Alternative 10: 84.7% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -1950:\\ \;\;\;\;t - t \cdot \frac{x}{y}\\ \mathbf{elif}\;t \leq 1.9 \cdot 10^{+45}:\\ \;\;\;\;t + \frac{x}{\frac{y}{z}}\\ \mathbf{else}:\\ \;\;\;\;t \cdot \frac{y - x}{y}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= t -1950.0)
   (- t (* t (/ x y)))
   (if (<= t 1.9e+45) (+ t (/ x (/ y z))) (* t (/ (- y x) y)))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (t <= -1950.0) {
		tmp = t - (t * (x / y));
	} else if (t <= 1.9e+45) {
		tmp = t + (x / (y / z));
	} else {
		tmp = t * ((y - 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 (t <= (-1950.0d0)) then
        tmp = t - (t * (x / y))
    else if (t <= 1.9d+45) then
        tmp = t + (x / (y / z))
    else
        tmp = t * ((y - x) / y)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if (t <= -1950.0) {
		tmp = t - (t * (x / y));
	} else if (t <= 1.9e+45) {
		tmp = t + (x / (y / z));
	} else {
		tmp = t * ((y - x) / y);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if t <= -1950.0:
		tmp = t - (t * (x / y))
	elif t <= 1.9e+45:
		tmp = t + (x / (y / z))
	else:
		tmp = t * ((y - x) / y)
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (t <= -1950.0)
		tmp = Float64(t - Float64(t * Float64(x / y)));
	elseif (t <= 1.9e+45)
		tmp = Float64(t + Float64(x / Float64(y / z)));
	else
		tmp = Float64(t * Float64(Float64(y - x) / y));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (t <= -1950.0)
		tmp = t - (t * (x / y));
	elseif (t <= 1.9e+45)
		tmp = t + (x / (y / z));
	else
		tmp = t * ((y - x) / y);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[t, -1950.0], N[(t - N[(t * N[(x / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 1.9e+45], N[(t + N[(x / N[(y / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(t * N[(N[(y - x), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if t < -1950

   1. Initial program 99.9%

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

   3. Taylor expanded in x around 0 94.4%

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

      1. associate-*r/ 91.4%

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

      2. *-commutative 91.4%

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

      3. associate-/r/ 99.9%

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

   5. Simplified 99.9%

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

   6. Taylor expanded in z around 0 88.5%

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

      1. mul-1-neg 88.5%

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

      2. associate-*r/ 94.1%

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

      3. sub-neg 94.1%

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

   8. Simplified 94.1%

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

   if -1950 < t < 1.9000000000000001e45

   1. Initial program 96.3%

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

   3. Taylor expanded in z around inf 90.6%

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

      1. associate-/l* 91.4%

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

   5. Simplified 91.4%

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

      1. clear-num 91.3%

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

      2. un-div-inv 91.4%

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

   7. Applied egg-rr 91.4%

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

   if 1.9000000000000001e45 < t

   1. Initial program 99.8%

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

   3. Taylor expanded in z around 0 76.6%

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

      1. *-rgt-identity 76.6%

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

      2. mul-1-neg 76.6%

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

      3. associate-/l* 86.7%

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

      4. distribute-rgt-neg-in 86.7%

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

      5. mul-1-neg 86.7%

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

      6. distribute-lft-in 86.8%

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

      7. mul-1-neg 86.8%

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

      8. unsub-neg 86.8%

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

   5. Simplified 86.8%

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

   6. Taylor expanded in y around 0 86.8%

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

4. Final simplification 91.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -1950:\\ \;\;\;\;t - t \cdot \frac{x}{y}\\ \mathbf{elif}\;t \leq 1.9 \cdot 10^{+45}:\\ \;\;\;\;t + \frac{x}{\frac{y}{z}}\\ \mathbf{else}:\\ \;\;\;\;t \cdot \frac{y - x}{y}\\ \end{array} \]
5. Add Preprocessing

Alternative 11: 97.9% 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 98.0%

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

3. Final simplification 98.0%

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

Alternative 12: 38.8% 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 98.0%

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

3. Taylor expanded in x around 0 38.4%

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

Developer Target 1: 97.6% 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 2024186 
(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))