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

Percentage Accurate: 97.6% → 97.6%

Time: 11.4s

Alternatives: 14

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: 97.6% 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, 0.1× speedup

Math

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

FPCore

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

C

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

Julia

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

Wolfram

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

Derivation

1. Initial program 96.8%

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

   1. fma-define 96.9%

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

3. Simplified 96.9%

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

5. Final simplification 96.9%

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

Alternative 2: 64.6% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;\frac{x}{y} \leq -1 \lor \neg \left(\frac{x}{y} \leq 2 \cdot 10^{+18}\right):\\ \;\;\;\;\frac{x}{y} \cdot \left(-t\right)\\ \mathbf{else}:\\ \;\;\;\;t\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= (/ x y) -1.0) (not (<= (/ x y) 2e+18))) (* (/ x y) (- t)) t))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (((x / y) <= -1.0) || !((x / y) <= 2e+18)) {
		tmp = (x / y) * -t;
	} else {
		tmp = t;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if (((x / y) <= (-1.0d0)) .or. (.not. ((x / y) <= 2d+18))) then
        tmp = (x / y) * -t
    else
        tmp = t
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if (((x / y) <= -1.0) || !((x / y) <= 2e+18)) {
		tmp = (x / y) * -t;
	} else {
		tmp = t;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if ((x / y) <= -1.0) or not ((x / y) <= 2e+18):
		tmp = (x / y) * -t
	else:
		tmp = t
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((Float64(x / y) <= -1.0) || !(Float64(x / y) <= 2e+18))
		tmp = Float64(Float64(x / y) * Float64(-t));
	else
		tmp = t;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (((x / y) <= -1.0) || ~(((x / y) <= 2e+18)))
		tmp = (x / y) * -t;
	else
		tmp = t;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[N[(x / y), $MachinePrecision], -1.0], N[Not[LessEqual[N[(x / y), $MachinePrecision], 2e+18]], $MachinePrecision]], N[(N[(x / y), $MachinePrecision] * (-t)), $MachinePrecision], t]

Derivation

1. Split input into 2 regimes

2. if (/.f64 x y) < -1 or 2e18 < (/.f64 x y)

   1. Initial program 97.3%

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

   3. Taylor expanded in z around 0 44.9%

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

      1. *-rgt-identity 44.9%

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

      2. mul-1-neg 44.9%

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

      3. associate-/l* 46.6%

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

      4. distribute-rgt-neg-in 46.6%

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

      5. mul-1-neg 46.6%

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

      6. distribute-lft-in 46.6%

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

      7. mul-1-neg 46.6%

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

      8. unsub-neg 46.6%

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

   5. Simplified 46.6%

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

   6. Taylor expanded in x around inf 45.9%

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

      1. mul-1-neg 45.9%

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

      2. distribute-frac-neg2 45.9%

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

   8. Simplified 45.9%

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

   if -1 < (/.f64 x y) < 2e18

   1. Initial program 96.5%

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

   3. Taylor expanded in x around 0 70.4%

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

4. Final simplification 60.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{x}{y} \leq -1 \lor \neg \left(\frac{x}{y} \leq 2 \cdot 10^{+18}\right):\\ \;\;\;\;\frac{x}{y} \cdot \left(-t\right)\\ \mathbf{else}:\\ \;\;\;\;t\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 64.5% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;\frac{x}{y} \leq -1:\\ \;\;\;\;\frac{t}{\frac{y}{-x}}\\ \mathbf{elif}\;\frac{x}{y} \leq 2 \cdot 10^{+18}:\\ \;\;\;\;t\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{y} \cdot \left(-t\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= (/ x y) -1.0)
   (/ t (/ y (- x)))
   (if (<= (/ x y) 2e+18) t (* (/ x y) (- t)))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((x / y) <= -1.0) {
		tmp = t / (y / -x);
	} else if ((x / y) <= 2e+18) {
		tmp = t;
	} 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) <= (-1.0d0)) then
        tmp = t / (y / -x)
    else if ((x / y) <= 2d+18) then
        tmp = t
    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) <= -1.0) {
		tmp = t / (y / -x);
	} else if ((x / y) <= 2e+18) {
		tmp = t;
	} else {
		tmp = (x / y) * -t;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (x / y) <= -1.0:
		tmp = t / (y / -x)
	elif (x / y) <= 2e+18:
		tmp = t
	else:
		tmp = (x / y) * -t
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (Float64(x / y) <= -1.0)
		tmp = Float64(t / Float64(y / Float64(-x)));
	elseif (Float64(x / y) <= 2e+18)
		tmp = t;
	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) <= -1.0)
		tmp = t / (y / -x);
	elseif ((x / y) <= 2e+18)
		tmp = t;
	else
		tmp = (x / y) * -t;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[N[(x / y), $MachinePrecision], -1.0], N[(t / N[(y / (-x)), $MachinePrecision]), $MachinePrecision], If[LessEqual[N[(x / y), $MachinePrecision], 2e+18], t, N[(N[(x / y), $MachinePrecision] * (-t)), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

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

   1. Initial program 96.7%

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

   3. Taylor expanded in z around 0 43.5%

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

      1. *-rgt-identity 43.5%

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

      2. mul-1-neg 43.5%

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

      3. associate-/l* 43.5%

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

      4. distribute-rgt-neg-in 43.5%

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

      5. mul-1-neg 43.5%

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

      6. distribute-lft-in 43.5%

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

      7. mul-1-neg 43.5%

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

      8. unsub-neg 43.5%

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

   5. Simplified 43.5%

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

   6. Taylor expanded in x around inf 42.2%

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

      1. mul-1-neg 42.2%

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

      2. distribute-frac-neg2 42.2%

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

   8. Simplified 42.2%

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

   9. Taylor expanded in t around 0 42.2%

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

       1. associate-*l/ 37.3%

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

       2. associate-/r/ 42.2%

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

       3. associate-*r/ 42.2%

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

       4. neg-mul-1 42.2%

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

   11. Simplified 42.2%

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

   if -1 < (/.f64 x y) < 2e18

   1. Initial program 96.5%

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

   3. Taylor expanded in x around 0 70.4%

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

   if 2e18 < (/.f64 x y)

   1. Initial program 98.0%

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

   3. Taylor expanded in z around 0 46.5%

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

      1. *-rgt-identity 46.5%

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

      2. mul-1-neg 46.5%

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

      3. associate-/l* 50.5%

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

      4. distribute-rgt-neg-in 50.5%

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

      5. mul-1-neg 50.5%

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

      6. distribute-lft-in 50.5%

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

      7. mul-1-neg 50.5%

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

      8. unsub-neg 50.5%

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

   5. Simplified 50.5%

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

   6. Taylor expanded in x around inf 50.5%

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

      1. mul-1-neg 50.5%

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

      2. distribute-frac-neg2 50.5%

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

   8. Simplified 50.5%

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

4. Final simplification 60.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{x}{y} \leq -1:\\ \;\;\;\;\frac{t}{\frac{y}{-x}}\\ \mathbf{elif}\;\frac{x}{y} \leq 2 \cdot 10^{+18}:\\ \;\;\;\;t\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{y} \cdot \left(-t\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 41.4% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;\frac{x}{y} \leq -2.4 \cdot 10^{+270} \lor \neg \left(\frac{x}{y} \leq 0.38\right):\\ \;\;\;\;\frac{x}{y} \cdot t\\ \mathbf{else}:\\ \;\;\;\;t\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= (/ x y) -2.4e+270) (not (<= (/ x y) 0.38))) (* (/ x y) t) t))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (((x / y) <= -2.4e+270) || !((x / y) <= 0.38)) {
		tmp = (x / y) * t;
	} else {
		tmp = t;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if (((x / y) <= (-2.4d+270)) .or. (.not. ((x / y) <= 0.38d0))) then
        tmp = (x / y) * t
    else
        tmp = t
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if (((x / y) <= -2.4e+270) || !((x / y) <= 0.38)) {
		tmp = (x / y) * t;
	} else {
		tmp = t;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if ((x / y) <= -2.4e+270) or not ((x / y) <= 0.38):
		tmp = (x / y) * t
	else:
		tmp = t
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((Float64(x / y) <= -2.4e+270) || !(Float64(x / y) <= 0.38))
		tmp = Float64(Float64(x / y) * t);
	else
		tmp = t;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (((x / y) <= -2.4e+270) || ~(((x / y) <= 0.38)))
		tmp = (x / y) * t;
	else
		tmp = t;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[N[(x / y), $MachinePrecision], -2.4e+270], N[Not[LessEqual[N[(x / y), $MachinePrecision], 0.38]], $MachinePrecision]], N[(N[(x / y), $MachinePrecision] * t), $MachinePrecision], t]

Derivation

1. Split input into 2 regimes

2. if (/.f64 x y) < -2.4000000000000001e270 or 0.38 < (/.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 46.7%

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

      1. *-rgt-identity 46.7%

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

      2. mul-1-neg 46.7%

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

      3. associate-/l* 49.3%

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

      4. distribute-rgt-neg-in 49.3%

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

      5. mul-1-neg 49.3%

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

      6. distribute-lft-in 49.4%

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

      7. mul-1-neg 49.4%

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

      8. unsub-neg 49.4%

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

   5. Simplified 49.4%

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

   6. Taylor expanded in x around inf 45.4%

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

      1. associate-*r/ 45.4%

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

      2. *-commutative 45.4%

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

      3. mul-1-neg 45.4%

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

      4. distribute-neg-frac 45.4%

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

      5. distribute-frac-neg2 45.4%

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

      6. associate-/l* 45.4%

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

   8. Simplified 45.4%

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

      1. add0 45.4%

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

      2. add-sqr-sqrt 28.3%

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

      3. sqrt-unprod 41.4%

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

      4. sqr-neg 41.4%

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

      5. sqrt-unprod 10.5%

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

      6. add-sqr-sqrt 16.4%

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

   10. Applied egg-rr 16.4%

       \[\leadsto \color{blue}{x \cdot \frac{t}{y} + 0} \]
   11. Step-by-step derivation

       1. add0 16.4%

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

       2. associate-*r/ 17.9%

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

       3. *-commutative 17.9%

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

       4. associate-*r/ 17.9%

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

   12. Simplified 17.9%

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

   if -2.4000000000000001e270 < (/.f64 x y) < 0.38

   1. Initial program 97.2%

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

   3. Taylor expanded in x around 0 57.4%

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

4. Final simplification 46.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{x}{y} \leq -2.4 \cdot 10^{+270} \lor \neg \left(\frac{x}{y} \leq 0.38\right):\\ \;\;\;\;\frac{x}{y} \cdot t\\ \mathbf{else}:\\ \;\;\;\;t\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 41.3% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;\frac{x}{y} \leq -2 \cdot 10^{+285}:\\ \;\;\;\;\frac{x}{y} \cdot t\\ \mathbf{elif}\;\frac{x}{y} \leq 5 \cdot 10^{-7}:\\ \;\;\;\;t\\ \mathbf{else}:\\ \;\;\;\;\frac{t}{\frac{y}{x}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= (/ x y) -2e+285)
   (* (/ x y) t)
   (if (<= (/ x y) 5e-7) t (/ t (/ y x)))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((x / y) <= -2e+285) {
		tmp = (x / y) * t;
	} else if ((x / y) <= 5e-7) {
		tmp = t;
	} else {
		tmp = t / (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) <= (-2d+285)) then
        tmp = (x / y) * t
    else if ((x / y) <= 5d-7) then
        tmp = t
    else
        tmp = t / (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) <= -2e+285) {
		tmp = (x / y) * t;
	} else if ((x / y) <= 5e-7) {
		tmp = t;
	} else {
		tmp = t / (y / x);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (x / y) <= -2e+285:
		tmp = (x / y) * t
	elif (x / y) <= 5e-7:
		tmp = t
	else:
		tmp = t / (y / x)
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (Float64(x / y) <= -2e+285)
		tmp = Float64(Float64(x / y) * t);
	elseif (Float64(x / y) <= 5e-7)
		tmp = t;
	else
		tmp = Float64(t / Float64(y / x));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((x / y) <= -2e+285)
		tmp = (x / y) * t;
	elseif ((x / y) <= 5e-7)
		tmp = t;
	else
		tmp = t / (y / x);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[N[(x / y), $MachinePrecision], -2e+285], N[(N[(x / y), $MachinePrecision] * t), $MachinePrecision], If[LessEqual[N[(x / y), $MachinePrecision], 5e-7], t, N[(t / N[(y / x), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if (/.f64 x y) < -2e285

   1. Initial program 90.7%

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

   3. Taylor expanded in z around 0 51.1%

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

      1. *-rgt-identity 51.1%

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

      2. mul-1-neg 51.1%

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

      3. associate-/l* 51.1%

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

      4. distribute-rgt-neg-in 51.1%

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

      5. mul-1-neg 51.1%

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

      6. distribute-lft-in 51.1%

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

      7. mul-1-neg 51.1%

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

      8. unsub-neg 51.1%

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

   5. Simplified 51.1%

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

   6. Taylor expanded in x around inf 51.1%

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

      1. associate-*r/ 51.1%

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

      2. *-commutative 51.1%

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

      3. mul-1-neg 51.1%

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

      4. distribute-neg-frac 51.1%

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

      5. distribute-frac-neg2 51.1%

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

      6. associate-/l* 51.1%

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

   8. Simplified 51.1%

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

      1. add0 51.1%

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

      2. add-sqr-sqrt 20.7%

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

      3. sqrt-unprod 50.5%

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

      4. sqr-neg 50.5%

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

      5. sqrt-unprod 15.6%

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

      6. add-sqr-sqrt 20.6%

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

   10. Applied egg-rr 20.6%

       \[\leadsto \color{blue}{x \cdot \frac{t}{y} + 0} \]
   11. Step-by-step derivation

       1. add0 20.6%

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

       2. associate-*r/ 20.6%

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

       3. *-commutative 20.6%

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

       4. associate-*r/ 25.3%

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

   12. Simplified 25.3%

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

   if -2e285 < (/.f64 x y) < 4.99999999999999977e-7

   1. Initial program 97.2%

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

   3. Taylor expanded in x around 0 57.4%

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

   if 4.99999999999999977e-7 < (/.f64 x y)

   1. Initial program 98.0%

      \[\frac{x}{y} \cdot \left(z - t\right) + t \]
   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* 48.6%

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

      4. distribute-rgt-neg-in 48.6%

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

      5. mul-1-neg 48.6%

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

      6. distribute-lft-in 48.7%

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

      7. mul-1-neg 48.7%

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

      8. unsub-neg 48.7%

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

   5. Simplified 48.7%

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

   6. Taylor expanded in x around inf 46.8%

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

      1. mul-1-neg 46.8%

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

      2. distribute-frac-neg2 46.8%

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

   8. Simplified 46.8%

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

      1. associate-*r/ 43.2%

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

      2. add-sqr-sqrt 29.4%

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

      3. sqrt-unprod 37.9%

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

      4. sqr-neg 37.9%

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

      5. sqrt-unprod 8.8%

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

      6. add-sqr-sqrt 16.8%

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

      7. associate-*l/ 14.9%

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

      8. associate-/r/ 15.1%

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

   10. Applied egg-rr 15.1%

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

4. Final simplification 46.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{x}{y} \leq -2 \cdot 10^{+285}:\\ \;\;\;\;\frac{x}{y} \cdot t\\ \mathbf{elif}\;\frac{x}{y} \leq 5 \cdot 10^{-7}:\\ \;\;\;\;t\\ \mathbf{else}:\\ \;\;\;\;\frac{t}{\frac{y}{x}}\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 40.8% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;\frac{x}{y} \leq -2 \cdot 10^{+285}:\\ \;\;\;\;\frac{x}{y} \cdot t\\ \mathbf{elif}\;\frac{x}{y} \leq 5 \cdot 10^{-7}:\\ \;\;\;\;t\\ \mathbf{else}:\\ \;\;\;\;\frac{x \cdot t}{y}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= (/ x y) -2e+285)
   (* (/ x y) t)
   (if (<= (/ x y) 5e-7) t (/ (* x t) y))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((x / y) <= -2e+285) {
		tmp = (x / y) * t;
	} else if ((x / y) <= 5e-7) {
		tmp = t;
	} else {
		tmp = (x * 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) <= (-2d+285)) then
        tmp = (x / y) * t
    else if ((x / y) <= 5d-7) then
        tmp = t
    else
        tmp = (x * 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) <= -2e+285) {
		tmp = (x / y) * t;
	} else if ((x / y) <= 5e-7) {
		tmp = t;
	} else {
		tmp = (x * t) / y;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (x / y) <= -2e+285:
		tmp = (x / y) * t
	elif (x / y) <= 5e-7:
		tmp = t
	else:
		tmp = (x * t) / y
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (Float64(x / y) <= -2e+285)
		tmp = Float64(Float64(x / y) * t);
	elseif (Float64(x / y) <= 5e-7)
		tmp = t;
	else
		tmp = Float64(Float64(x * t) / y);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((x / y) <= -2e+285)
		tmp = (x / y) * t;
	elseif ((x / y) <= 5e-7)
		tmp = t;
	else
		tmp = (x * t) / y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[N[(x / y), $MachinePrecision], -2e+285], N[(N[(x / y), $MachinePrecision] * t), $MachinePrecision], If[LessEqual[N[(x / y), $MachinePrecision], 5e-7], t, N[(N[(x * t), $MachinePrecision] / y), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if (/.f64 x y) < -2e285

   1. Initial program 90.7%

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

   3. Taylor expanded in z around 0 51.1%

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

      1. *-rgt-identity 51.1%

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

      2. mul-1-neg 51.1%

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

      3. associate-/l* 51.1%

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

      4. distribute-rgt-neg-in 51.1%

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

      5. mul-1-neg 51.1%

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

      6. distribute-lft-in 51.1%

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

      7. mul-1-neg 51.1%

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

      8. unsub-neg 51.1%

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

   5. Simplified 51.1%

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

   6. Taylor expanded in x around inf 51.1%

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

      1. associate-*r/ 51.1%

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

      2. *-commutative 51.1%

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

      3. mul-1-neg 51.1%

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

      4. distribute-neg-frac 51.1%

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

      5. distribute-frac-neg2 51.1%

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

      6. associate-/l* 51.1%

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

   8. Simplified 51.1%

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

      1. add0 51.1%

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

      2. add-sqr-sqrt 20.7%

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

      3. sqrt-unprod 50.5%

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

      4. sqr-neg 50.5%

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

      5. sqrt-unprod 15.6%

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

      6. add-sqr-sqrt 20.6%

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

   10. Applied egg-rr 20.6%

       \[\leadsto \color{blue}{x \cdot \frac{t}{y} + 0} \]
   11. Step-by-step derivation

       1. add0 20.6%

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

       2. associate-*r/ 20.6%

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

       3. *-commutative 20.6%

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

       4. associate-*r/ 25.3%

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

   12. Simplified 25.3%

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

   if -2e285 < (/.f64 x y) < 4.99999999999999977e-7

   1. Initial program 97.2%

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

   3. Taylor expanded in x around 0 57.4%

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

   if 4.99999999999999977e-7 < (/.f64 x y)

   1. Initial program 98.0%

      \[\frac{x}{y} \cdot \left(z - t\right) + t \]
   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* 48.6%

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

      4. distribute-rgt-neg-in 48.6%

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

      5. mul-1-neg 48.6%

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

      6. distribute-lft-in 48.7%

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

      7. mul-1-neg 48.7%

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

      8. unsub-neg 48.7%

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

   5. Simplified 48.7%

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

   6. Taylor expanded in x around inf 43.2%

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

      1. associate-*r/ 43.2%

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

      2. *-commutative 43.2%

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

      3. mul-1-neg 43.2%

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

      4. distribute-neg-frac 43.2%

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

      5. distribute-frac-neg2 43.2%

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

      6. associate-/l* 43.2%

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

   8. Simplified 43.2%

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

      1. associate-*r/ 43.2%

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

      2. add-sqr-sqrt 29.4%

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

      3. sqrt-unprod 37.9%

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

      4. sqr-neg 37.9%

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

      5. sqrt-unprod 8.8%

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

      6. add-sqr-sqrt 16.8%

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

   10. Applied egg-rr 16.8%

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

4. Final simplification 46.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{x}{y} \leq -2 \cdot 10^{+285}:\\ \;\;\;\;\frac{x}{y} \cdot t\\ \mathbf{elif}\;\frac{x}{y} \leq 5 \cdot 10^{-7}:\\ \;\;\;\;t\\ \mathbf{else}:\\ \;\;\;\;\frac{x \cdot t}{y}\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 83.3% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -2 \cdot 10^{-140} \lor \neg \left(z \leq 5.5 \cdot 10^{-99}\right):\\ \;\;\;\;t + x \cdot \frac{z}{y}\\ \mathbf{else}:\\ \;\;\;\;t \cdot \left(1 - \frac{x}{y}\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= z -2e-140) (not (<= z 5.5e-99)))
   (+ t (* x (/ z y)))
   (* t (- 1.0 (/ x y)))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((z <= -2e-140) || !(z <= 5.5e-99)) {
		tmp = t + (x * (z / 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 ((z <= (-2d-140)) .or. (.not. (z <= 5.5d-99))) then
        tmp = t + (x * (z / 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 ((z <= -2e-140) || !(z <= 5.5e-99)) {
		tmp = t + (x * (z / y));
	} else {
		tmp = t * (1.0 - (x / y));
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (z <= -2e-140) or not (z <= 5.5e-99):
		tmp = t + (x * (z / y))
	else:
		tmp = t * (1.0 - (x / y))
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((z <= -2e-140) || !(z <= 5.5e-99))
		tmp = Float64(t + Float64(x * Float64(z / 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 ((z <= -2e-140) || ~((z <= 5.5e-99)))
		tmp = t + (x * (z / y));
	else
		tmp = t * (1.0 - (x / y));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[z, -2e-140], N[Not[LessEqual[z, 5.5e-99]], $MachinePrecision]], N[(t + N[(x * N[(z / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(t * N[(1.0 - N[(x / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -2e-140 or 5.49999999999999991e-99 < z

   1. Initial program 96.8%

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

   3. Taylor expanded in z around inf 87.3%

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

      1. associate-/l* 86.5%

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

   5. Simplified 86.5%

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

   if -2e-140 < z < 5.49999999999999991e-99

   1. Initial program 97.1%

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

   3. Taylor expanded in z around 0 90.1%

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

      1. *-rgt-identity 90.1%

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

      2. mul-1-neg 90.1%

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

      3. associate-/l* 91.5%

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

      4. distribute-rgt-neg-in 91.5%

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

      5. mul-1-neg 91.5%

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

      6. distribute-lft-in 91.5%

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

      7. mul-1-neg 91.5%

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

      8. unsub-neg 91.5%

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

   5. Simplified 91.5%

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

4. Final simplification 87.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -2 \cdot 10^{-140} \lor \neg \left(z \leq 5.5 \cdot 10^{-99}\right):\\ \;\;\;\;t + x \cdot \frac{z}{y}\\ \mathbf{else}:\\ \;\;\;\;t \cdot \left(1 - \frac{x}{y}\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 85.6% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -4.2 \cdot 10^{-143} \lor \neg \left(z \leq 5 \cdot 10^{-101}\right):\\ \;\;\;\;t + \frac{x}{y} \cdot z\\ \mathbf{else}:\\ \;\;\;\;t \cdot \left(1 - \frac{x}{y}\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= z -4.2e-143) (not (<= z 5e-101)))
   (+ t (* (/ x y) z))
   (* t (- 1.0 (/ x y)))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((z <= -4.2e-143) || !(z <= 5e-101)) {
		tmp = t + ((x / y) * z);
	} 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 ((z <= (-4.2d-143)) .or. (.not. (z <= 5d-101))) then
        tmp = t + ((x / y) * z)
    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 ((z <= -4.2e-143) || !(z <= 5e-101)) {
		tmp = t + ((x / y) * z);
	} else {
		tmp = t * (1.0 - (x / y));
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (z <= -4.2e-143) or not (z <= 5e-101):
		tmp = t + ((x / y) * z)
	else:
		tmp = t * (1.0 - (x / y))
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((z <= -4.2e-143) || !(z <= 5e-101))
		tmp = Float64(t + Float64(Float64(x / y) * z));
	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 ((z <= -4.2e-143) || ~((z <= 5e-101)))
		tmp = t + ((x / y) * z);
	else
		tmp = t * (1.0 - (x / y));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[z, -4.2e-143], N[Not[LessEqual[z, 5e-101]], $MachinePrecision]], N[(t + N[(N[(x / y), $MachinePrecision] * z), $MachinePrecision]), $MachinePrecision], N[(t * N[(1.0 - N[(x / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -4.2000000000000002e-143 or 5.0000000000000001e-101 < z

   1. Initial program 96.8%

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

   3. Taylor expanded in z around inf 87.3%

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

      1. associate-/l* 86.5%

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

   5. Simplified 86.5%

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

      1. *-commutative 86.5%

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

      2. associate-*l/ 87.3%

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

   7. Applied egg-rr 87.3%

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

      1. associate-/l* 87.0%

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

      2. *-commutative 87.0%

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

   9. Applied egg-rr 87.0%

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

   if -4.2000000000000002e-143 < z < 5.0000000000000001e-101

   1. Initial program 97.1%

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

   3. Taylor expanded in z around 0 90.1%

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

      1. *-rgt-identity 90.1%

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

      2. mul-1-neg 90.1%

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

      3. associate-/l* 91.5%

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

      4. distribute-rgt-neg-in 91.5%

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

      5. mul-1-neg 91.5%

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

      6. distribute-lft-in 91.5%

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

      7. mul-1-neg 91.5%

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

      8. unsub-neg 91.5%

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

   5. Simplified 91.5%

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

4. Final simplification 88.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -4.2 \cdot 10^{-143} \lor \neg \left(z \leq 5 \cdot 10^{-101}\right):\\ \;\;\;\;t + \frac{x}{y} \cdot z\\ \mathbf{else}:\\ \;\;\;\;t \cdot \left(1 - \frac{x}{y}\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 84.4% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -8 \cdot 10^{-139}:\\ \;\;\;\;t + \frac{x}{\frac{y}{z}}\\ \mathbf{elif}\;z \leq 1.42 \cdot 10^{-102}:\\ \;\;\;\;t \cdot \left(1 - \frac{x}{y}\right)\\ \mathbf{else}:\\ \;\;\;\;t + \frac{x}{y} \cdot z\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= z -8e-139)
   (+ t (/ x (/ y z)))
   (if (<= z 1.42e-102) (* t (- 1.0 (/ x y))) (+ t (* (/ x y) z)))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (z <= -8e-139) {
		tmp = t + (x / (y / z));
	} else if (z <= 1.42e-102) {
		tmp = t * (1.0 - (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 (z <= (-8d-139)) then
        tmp = t + (x / (y / z))
    else if (z <= 1.42d-102) then
        tmp = t * (1.0d0 - (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 (z <= -8e-139) {
		tmp = t + (x / (y / z));
	} else if (z <= 1.42e-102) {
		tmp = t * (1.0 - (x / y));
	} else {
		tmp = t + ((x / y) * z);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if z <= -8e-139:
		tmp = t + (x / (y / z))
	elif z <= 1.42e-102:
		tmp = t * (1.0 - (x / y))
	else:
		tmp = t + ((x / y) * z)
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (z <= -8e-139)
		tmp = Float64(t + Float64(x / Float64(y / z)));
	elseif (z <= 1.42e-102)
		tmp = Float64(t * Float64(1.0 - Float64(x / y)));
	else
		tmp = Float64(t + Float64(Float64(x / y) * z));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (z <= -8e-139)
		tmp = t + (x / (y / z));
	elseif (z <= 1.42e-102)
		tmp = t * (1.0 - (x / y));
	else
		tmp = t + ((x / y) * z);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[z, -8e-139], N[(t + N[(x / N[(y / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 1.42e-102], N[(t * N[(1.0 - N[(x / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(t + N[(N[(x / y), $MachinePrecision] * z), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if z < -8.00000000000000024e-139

   1. Initial program 95.9%

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

      1. associate-*l/ 95.8%

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

      2. associate-*r/ 92.7%

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

      3. clear-num 92.7%

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

      4. un-div-inv 93.1%

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

   4. Applied egg-rr 93.1%

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

   5. Taylor expanded in z around inf 83.1%

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

   if -8.00000000000000024e-139 < z < 1.42000000000000009e-102

   1. Initial program 97.1%

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

   3. Taylor expanded in z around 0 90.1%

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

      1. *-rgt-identity 90.1%

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

      2. mul-1-neg 90.1%

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

      3. associate-/l* 91.5%

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

      4. distribute-rgt-neg-in 91.5%

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

      5. mul-1-neg 91.5%

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

      6. distribute-lft-in 91.5%

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

      7. mul-1-neg 91.5%

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

      8. unsub-neg 91.5%

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

   5. Simplified 91.5%

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

   if 1.42000000000000009e-102 < z

   1. Initial program 97.7%

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

   3. Taylor expanded in z around inf 90.5%

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

      1. associate-/l* 90.4%

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

   5. Simplified 90.4%

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

      1. *-commutative 90.4%

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

      2. associate-*l/ 90.5%

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

   7. Applied egg-rr 90.5%

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

      1. associate-/l* 91.3%

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

      2. *-commutative 91.3%

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

   9. Applied egg-rr 91.3%

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

4. Final simplification 88.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -8 \cdot 10^{-139}:\\ \;\;\;\;t + \frac{x}{\frac{y}{z}}\\ \mathbf{elif}\;z \leq 1.42 \cdot 10^{-102}:\\ \;\;\;\;t \cdot \left(1 - \frac{x}{y}\right)\\ \mathbf{else}:\\ \;\;\;\;t + \frac{x}{y} \cdot z\\ \end{array} \]
5. Add Preprocessing

Alternative 10: 84.1% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -3.4 \cdot 10^{-138}:\\ \;\;\;\;t + \frac{x \cdot z}{y}\\ \mathbf{elif}\;z \leq 6.2 \cdot 10^{-95}:\\ \;\;\;\;t \cdot \left(1 - \frac{x}{y}\right)\\ \mathbf{else}:\\ \;\;\;\;t + \frac{x}{y} \cdot z\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= z -3.4e-138)
   (+ t (/ (* x z) y))
   (if (<= z 6.2e-95) (* t (- 1.0 (/ x y))) (+ t (* (/ x y) z)))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (z <= -3.4e-138) {
		tmp = t + ((x * z) / y);
	} else if (z <= 6.2e-95) {
		tmp = t * (1.0 - (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 (z <= (-3.4d-138)) then
        tmp = t + ((x * z) / y)
    else if (z <= 6.2d-95) then
        tmp = t * (1.0d0 - (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 (z <= -3.4e-138) {
		tmp = t + ((x * z) / y);
	} else if (z <= 6.2e-95) {
		tmp = t * (1.0 - (x / y));
	} else {
		tmp = t + ((x / y) * z);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if z <= -3.4e-138:
		tmp = t + ((x * z) / y)
	elif z <= 6.2e-95:
		tmp = t * (1.0 - (x / y))
	else:
		tmp = t + ((x / y) * z)
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (z <= -3.4e-138)
		tmp = Float64(t + Float64(Float64(x * z) / y));
	elseif (z <= 6.2e-95)
		tmp = Float64(t * Float64(1.0 - Float64(x / y)));
	else
		tmp = Float64(t + Float64(Float64(x / y) * z));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (z <= -3.4e-138)
		tmp = t + ((x * z) / y);
	elseif (z <= 6.2e-95)
		tmp = t * (1.0 - (x / y));
	else
		tmp = t + ((x / y) * z);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[z, -3.4e-138], N[(t + N[(N[(x * z), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 6.2e-95], N[(t * N[(1.0 - N[(x / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(t + N[(N[(x / y), $MachinePrecision] * z), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if z < -3.4000000000000001e-138

   1. Initial program 95.9%

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

   3. Taylor expanded in z around inf 84.0%

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

   if -3.4000000000000001e-138 < z < 6.19999999999999983e-95

   1. Initial program 97.1%

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

   3. Taylor expanded in z around 0 90.1%

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

      1. *-rgt-identity 90.1%

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

      2. mul-1-neg 90.1%

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

      3. associate-/l* 91.5%

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

      4. distribute-rgt-neg-in 91.5%

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

      5. mul-1-neg 91.5%

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

      6. distribute-lft-in 91.5%

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

      7. mul-1-neg 91.5%

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

      8. unsub-neg 91.5%

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

   5. Simplified 91.5%

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

   if 6.19999999999999983e-95 < z

   1. Initial program 97.7%

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

   3. Taylor expanded in z around inf 90.5%

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

      1. associate-/l* 90.4%

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

   5. Simplified 90.4%

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

      1. *-commutative 90.4%

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

      2. associate-*l/ 90.5%

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

   7. Applied egg-rr 90.5%

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

      1. associate-/l* 91.3%

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

      2. *-commutative 91.3%

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

   9. Applied egg-rr 91.3%

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

4. Final simplification 88.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -3.4 \cdot 10^{-138}:\\ \;\;\;\;t + \frac{x \cdot z}{y}\\ \mathbf{elif}\;z \leq 6.2 \cdot 10^{-95}:\\ \;\;\;\;t \cdot \left(1 - \frac{x}{y}\right)\\ \mathbf{else}:\\ \;\;\;\;t + \frac{x}{y} \cdot z\\ \end{array} \]
5. Add Preprocessing

Alternative 11: 84.1% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -1.65 \cdot 10^{-138}:\\ \;\;\;\;t + \frac{x \cdot z}{y}\\ \mathbf{elif}\;z \leq 2.4 \cdot 10^{-93}:\\ \;\;\;\;t - \frac{t}{\frac{y}{x}}\\ \mathbf{else}:\\ \;\;\;\;t + \frac{x}{y} \cdot z\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= z -1.65e-138)
   (+ t (/ (* x z) y))
   (if (<= z 2.4e-93) (- t (/ t (/ y x))) (+ t (* (/ x y) z)))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (z <= -1.65e-138) {
		tmp = t + ((x * z) / y);
	} else if (z <= 2.4e-93) {
		tmp = t - (t / (y / x));
	} 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 (z <= (-1.65d-138)) then
        tmp = t + ((x * z) / y)
    else if (z <= 2.4d-93) then
        tmp = t - (t / (y / x))
    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 (z <= -1.65e-138) {
		tmp = t + ((x * z) / y);
	} else if (z <= 2.4e-93) {
		tmp = t - (t / (y / x));
	} else {
		tmp = t + ((x / y) * z);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if z <= -1.65e-138:
		tmp = t + ((x * z) / y)
	elif z <= 2.4e-93:
		tmp = t - (t / (y / x))
	else:
		tmp = t + ((x / y) * z)
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (z <= -1.65e-138)
		tmp = Float64(t + Float64(Float64(x * z) / y));
	elseif (z <= 2.4e-93)
		tmp = Float64(t - Float64(t / Float64(y / x)));
	else
		tmp = Float64(t + Float64(Float64(x / y) * z));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (z <= -1.65e-138)
		tmp = t + ((x * z) / y);
	elseif (z <= 2.4e-93)
		tmp = t - (t / (y / x));
	else
		tmp = t + ((x / y) * z);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[z, -1.65e-138], N[(t + N[(N[(x * z), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 2.4e-93], N[(t - N[(t / N[(y / x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(t + N[(N[(x / y), $MachinePrecision] * z), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if z < -1.64999999999999991e-138

   1. Initial program 95.9%

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

   3. Taylor expanded in z around inf 84.0%

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

   if -1.64999999999999991e-138 < z < 2.4000000000000001e-93

   1. Initial program 97.1%

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

   3. Taylor expanded in z around 0 90.1%

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

      1. *-rgt-identity 90.1%

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

      2. mul-1-neg 90.1%

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

      3. associate-/l* 91.5%

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

      4. distribute-rgt-neg-in 91.5%

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

      5. mul-1-neg 91.5%

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

      6. distribute-lft-in 91.5%

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

      7. mul-1-neg 91.5%

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

      8. unsub-neg 91.5%

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

   5. Simplified 91.5%

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

      1. distribute-rgt-out-- 91.5%

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

      2. *-un-lft-identity 91.5%

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

      3. *-commutative 91.5%

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

      4. clear-num 91.5%

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

      5. un-div-inv 91.6%

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

   7. Applied egg-rr 91.6%

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

   if 2.4000000000000001e-93 < z

   1. Initial program 97.7%

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

   3. Taylor expanded in z around inf 90.5%

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

      1. associate-/l* 90.4%

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

   5. Simplified 90.4%

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

      1. *-commutative 90.4%

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

      2. associate-*l/ 90.5%

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

   7. Applied egg-rr 90.5%

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

      1. associate-/l* 91.3%

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

      2. *-commutative 91.3%

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

   9. Applied egg-rr 91.3%

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

4. Final simplification 88.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.65 \cdot 10^{-138}:\\ \;\;\;\;t + \frac{x \cdot z}{y}\\ \mathbf{elif}\;z \leq 2.4 \cdot 10^{-93}:\\ \;\;\;\;t - \frac{t}{\frac{y}{x}}\\ \mathbf{else}:\\ \;\;\;\;t + \frac{x}{y} \cdot z\\ \end{array} \]
5. Add Preprocessing

Alternative 12: 97.6% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 96.8%

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

3. Final simplification 96.8%

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

Alternative 13: 66.1% accurate, 1.3× speedup

Math

\[\begin{array}{l} \\ t \cdot \left(1 - \frac{x}{y}\right) \end{array} \]

FPCore

(FPCore (x y z t) :precision binary64 (* t (- 1.0 (/ x y))))

C

double code(double x, double y, double z, double t) {
	return t * (1.0 - (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 * (1.0d0 - (x / y))
end function

Java

public static double code(double x, double y, double z, double t) {
	return t * (1.0 - (x / y));
}

Python

def code(x, y, z, t):
	return t * (1.0 - (x / y))

Julia

function code(x, y, z, t)
	return Float64(t * Float64(1.0 - Float64(x / y)))
end

MATLAB

function tmp = code(x, y, z, t)
	tmp = t * (1.0 - (x / y));
end

Wolfram

code[x_, y_, z_, t_] := N[(t * N[(1.0 - N[(x / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]

Derivation

1. Initial program 96.8%

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

3. Taylor expanded in z around 0 59.2%

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

   1. *-rgt-identity 59.2%

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

   2. mul-1-neg 59.2%

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

   3. associate-/l* 61.5%

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

   4. distribute-rgt-neg-in 61.5%

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

   5. mul-1-neg 61.5%

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

   6. distribute-lft-in 61.5%

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

   7. mul-1-neg 61.5%

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

   8. unsub-neg 61.5%

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

5. Simplified 61.5%

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

6. Final simplification 61.5%

   \[\leadsto t \cdot \left(1 - \frac{x}{y}\right) \]
7. Add Preprocessing

Alternative 14: 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 96.8%

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

3. Taylor expanded in x around 0 41.7%

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

4. Final simplification 41.7%

   \[\leadsto t \]
5. Add Preprocessing

Developer target: 97.4% 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 2024046 
(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))