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

Percentage Accurate: 97.7% → 97.7%

Time: 7.6s

Alternatives: 9

Speedup: 1.0×

• 25.5% 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: 97.7% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Alternative 1: 97.7% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 98.4%

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

3. Final simplification 98.4%

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

Alternative 2: 63.6% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;\frac{x}{y} \leq -1 \cdot 10^{+14} \lor \neg \left(\frac{x}{y} \leq 5\right):\\ \;\;\;\;\frac{x}{y} \cdot \left(-t\right)\\ \mathbf{else}:\\ \;\;\;\;t\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= (/ x y) -1e+14) (not (<= (/ x y) 5.0))) (* (/ x y) (- t)) t))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (((x / y) <= -1e+14) || !((x / y) <= 5.0)) {
		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) <= (-1d+14)) .or. (.not. ((x / y) <= 5.0d0))) 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) <= -1e+14) || !((x / y) <= 5.0)) {
		tmp = (x / y) * -t;
	} else {
		tmp = t;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if ((x / y) <= -1e+14) or not ((x / y) <= 5.0):
		tmp = (x / y) * -t
	else:
		tmp = t
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((Float64(x / y) <= -1e+14) || !(Float64(x / y) <= 5.0))
		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) <= -1e+14) || ~(((x / y) <= 5.0)))
		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], -1e+14], N[Not[LessEqual[N[(x / y), $MachinePrecision], 5.0]], $MachinePrecision]], N[(N[(x / y), $MachinePrecision] * (-t)), $MachinePrecision], t]

Derivation

1. Split input into 2 regimes

2. if (/.f64 x y) < -1e14 or 5 < (/.f64 x y)

   1. Initial program 98.4%

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

   3. Taylor expanded in z around 0 52.6%

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

      1. *-rgt-identity 52.6%

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

      2. mul-1-neg 52.6%

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

      3. associate-/l* 56.3%

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

      4. distribute-rgt-neg-in 56.3%

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

      5. mul-1-neg 56.3%

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

      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 52.6%

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

      1. mul-1-neg 52.6%

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

      2. distribute-frac-neg 52.6%

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

      3. distribute-rgt-neg-in 52.6%

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

      4. associate-*r/ 56.1%

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

   8. Simplified 56.1%

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

   if -1e14 < (/.f64 x y) < 5

   1. Initial program 98.5%

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

   3. Taylor expanded in x around 0 77.3%

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

4. Final simplification 67.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{x}{y} \leq -1 \cdot 10^{+14} \lor \neg \left(\frac{x}{y} \leq 5\right):\\ \;\;\;\;\frac{x}{y} \cdot \left(-t\right)\\ \mathbf{else}:\\ \;\;\;\;t\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 43.3% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;\frac{x}{y} \leq -5 \cdot 10^{-99}:\\ \;\;\;\;y \cdot \frac{t}{y}\\ \mathbf{elif}\;\frac{x}{y} \leq 2 \cdot 10^{+71}:\\ \;\;\;\;t\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{y} \cdot t\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= (/ x y) -5e-99)
   (* y (/ t y))
   (if (<= (/ x y) 2e+71) t (* (/ x y) t))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((x / y) <= -5e-99) {
		tmp = y * (t / y);
	} else if ((x / y) <= 2e+71) {
		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) <= (-5d-99)) then
        tmp = y * (t / y)
    else if ((x / y) <= 2d+71) 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) <= -5e-99) {
		tmp = y * (t / y);
	} else if ((x / y) <= 2e+71) {
		tmp = t;
	} else {
		tmp = (x / y) * t;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (x / y) <= -5e-99:
		tmp = y * (t / y)
	elif (x / y) <= 2e+71:
		tmp = t
	else:
		tmp = (x / y) * t
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (Float64(x / y) <= -5e-99)
		tmp = Float64(y * Float64(t / y));
	elseif (Float64(x / y) <= 2e+71)
		tmp = t;
	else
		tmp = Float64(Float64(x / y) * t);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((x / y) <= -5e-99)
		tmp = y * (t / y);
	elseif ((x / y) <= 2e+71)
		tmp = t;
	else
		tmp = (x / y) * t;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[N[(x / y), $MachinePrecision], -5e-99], N[(y * N[(t / y), $MachinePrecision]), $MachinePrecision], If[LessEqual[N[(x / y), $MachinePrecision], 2e+71], t, N[(N[(x / y), $MachinePrecision] * t), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if (/.f64 x y) < -4.99999999999999969e-99

   1. Initial program 97.5%

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

   3. Taylor expanded in z around 0 61.5%

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

      1. neg-mul-1 61.5%

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

   5. Simplified 61.5%

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

   6. Taylor expanded in y around 0 52.4%

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

      1. mul-1-neg 52.4%

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

      2. distribute-rgt-neg-out 52.4%

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

      3. +-commutative 52.4%

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

      4. distribute-lft-out 52.4%

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

   8. Simplified 52.4%

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

   9. Taylor expanded in y around inf 11.9%

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

       1. *-commutative 11.9%

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

       2. associate-/l* 20.2%

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

   11. Applied egg-rr 20.2%

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

   if -4.99999999999999969e-99 < (/.f64 x y) < 2.0000000000000001e71

   1. Initial program 98.4%

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

   3. Taylor expanded in x around 0 76.6%

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

   if 2.0000000000000001e71 < (/.f64 x y)

   1. Initial program 99.8%

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

   3. Taylor expanded in z around 0 47.3%

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

      1. neg-mul-1 47.3%

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

   5. Simplified 47.3%

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

   6. Taylor expanded in y around 0 45.4%

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

      1. mul-1-neg 45.4%

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

      2. distribute-rgt-neg-out 45.4%

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

      3. +-commutative 45.4%

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

      4. distribute-lft-out 47.3%

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

   8. Simplified 47.3%

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

   9. Taylor expanded in y around 0 47.3%

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

       1. mul-1-neg 47.3%

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

       2. distribute-lft-neg-out 47.3%

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

       3. *-commutative 47.3%

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

   11. Simplified 47.3%

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

       1. distribute-rgt-neg-out 47.3%

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

       2. distribute-lft-neg-in 47.3%

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

       3. associate-*l/ 47.3%

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

       4. div-inv 47.3%

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

       5. associate-*l* 45.5%

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

       6. add-sqr-sqrt 27.8%

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

       7. sqrt-unprod 30.2%

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

       8. sqr-neg 30.2%

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

       9. sqrt-unprod 2.5%

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

       10. add-sqr-sqrt 8.9%

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

       11. associate-*l* 12.6%

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

       12. div-inv 12.6%

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

   13. Applied egg-rr 12.6%

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

Alternative 4: 84.8% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -2.7 \cdot 10^{+58} \lor \neg \left(z \leq 6.5 \cdot 10^{-70}\right):\\ \;\;\;\;t + \frac{x}{y} \cdot z\\ \mathbf{else}:\\ \;\;\;\;t - \frac{x}{y} \cdot t\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= z -2.7e+58) (not (<= z 6.5e-70)))
   (+ t (* (/ x y) z))
   (- t (* (/ x y) t))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((z <= -2.7e+58) || !(z <= 6.5e-70)) {
		tmp = t + ((x / y) * z);
	} else {
		tmp = t - ((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 ((z <= (-2.7d+58)) .or. (.not. (z <= 6.5d-70))) then
        tmp = t + ((x / y) * z)
    else
        tmp = t - ((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 ((z <= -2.7e+58) || !(z <= 6.5e-70)) {
		tmp = t + ((x / y) * z);
	} else {
		tmp = t - ((x / y) * t);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (z <= -2.7e+58) or not (z <= 6.5e-70):
		tmp = t + ((x / y) * z)
	else:
		tmp = t - ((x / y) * t)
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((z <= -2.7e+58) || !(z <= 6.5e-70))
		tmp = Float64(t + Float64(Float64(x / y) * z));
	else
		tmp = Float64(t - Float64(Float64(x / y) * t));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((z <= -2.7e+58) || ~((z <= 6.5e-70)))
		tmp = t + ((x / y) * z);
	else
		tmp = t - ((x / y) * t);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[z, -2.7e+58], N[Not[LessEqual[z, 6.5e-70]], $MachinePrecision]], N[(t + N[(N[(x / y), $MachinePrecision] * z), $MachinePrecision]), $MachinePrecision], N[(t - N[(N[(x / y), $MachinePrecision] * t), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -2.7000000000000001e58 or 6.5000000000000005e-70 < z

   1. Initial program 98.5%

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

   3. Taylor expanded in z around inf 93.2%

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

   if -2.7000000000000001e58 < z < 6.5000000000000005e-70

   1. Initial program 98.4%

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

   3. Taylor expanded in z around 0 87.4%

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

      1. *-rgt-identity 87.4%

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

      2. mul-1-neg 87.4%

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

      3. associate-/l* 90.4%

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

      4. distribute-rgt-neg-in 90.4%

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

      5. mul-1-neg 90.4%

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

      6. distribute-lft-in 90.4%

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

      7. mul-1-neg 90.4%

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

      8. unsub-neg 90.4%

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

   5. Simplified 90.4%

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

      1. sub-neg 90.4%

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

      2. distribute-lft-in 90.4%

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

      3. *-commutative 90.4%

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

      4. distribute-neg-frac 90.4%

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

      5. add-sqr-sqrt 46.8%

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

      6. sqrt-unprod 67.1%

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

      7. sqr-neg 67.1%

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

      8. sqrt-unprod 28.2%

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

      9. add-sqr-sqrt 51.7%

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

      10. clear-num 51.7%

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

      11. associate-/r/ 51.7%

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

      12. associate-*l* 49.2%

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

      13. div-inv 49.2%

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

      14. *-commutative 49.2%

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

      15. add-sqr-sqrt 26.5%

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

      16. sqrt-unprod 65.3%

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

      17. sqr-neg 65.3%

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

      18. sqrt-unprod 46.8%

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

      19. add-sqr-sqrt 87.1%

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

      20. *-un-lft-identity 87.1%

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

      21. cancel-sign-sub-inv 87.1%

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

      22. *-commutative 87.1%

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

   7. Applied egg-rr 90.4%

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

4. Final simplification 91.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -2.7 \cdot 10^{+58} \lor \neg \left(z \leq 6.5 \cdot 10^{-70}\right):\\ \;\;\;\;t + \frac{x}{y} \cdot z\\ \mathbf{else}:\\ \;\;\;\;t - \frac{x}{y} \cdot t\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 84.8% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -2.5 \cdot 10^{+58} \lor \neg \left(z \leq 7.6 \cdot 10^{-70}\right):\\ \;\;\;\;t + \frac{x}{y} \cdot z\\ \mathbf{else}:\\ \;\;\;\;t \cdot \left(1 - \frac{x}{y}\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= z -2.5e+58) (not (<= z 7.6e-70)))
   (+ t (* (/ x y) z))
   (* t (- 1.0 (/ x y)))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((z <= -2.5e+58) || !(z <= 7.6e-70)) {
		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 <= (-2.5d+58)) .or. (.not. (z <= 7.6d-70))) 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 <= -2.5e+58) || !(z <= 7.6e-70)) {
		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 <= -2.5e+58) or not (z <= 7.6e-70):
		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 <= -2.5e+58) || !(z <= 7.6e-70))
		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 <= -2.5e+58) || ~((z <= 7.6e-70)))
		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, -2.5e+58], N[Not[LessEqual[z, 7.6e-70]], $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 < -2.49999999999999993e58 or 7.5999999999999995e-70 < z

   1. Initial program 98.5%

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

   3. Taylor expanded in z around inf 93.2%

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

   if -2.49999999999999993e58 < z < 7.5999999999999995e-70

   1. Initial program 98.4%

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

   3. Taylor expanded in z around 0 87.4%

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

      1. *-rgt-identity 87.4%

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

      2. mul-1-neg 87.4%

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

      3. associate-/l* 90.4%

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

      4. distribute-rgt-neg-in 90.4%

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

      5. mul-1-neg 90.4%

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

      6. distribute-lft-in 90.4%

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

      7. mul-1-neg 90.4%

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

      8. unsub-neg 90.4%

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

   5. Simplified 90.4%

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

4. Final simplification 91.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -2.5 \cdot 10^{+58} \lor \neg \left(z \leq 7.6 \cdot 10^{-70}\right):\\ \;\;\;\;t + \frac{x}{y} \cdot z\\ \mathbf{else}:\\ \;\;\;\;t \cdot \left(1 - \frac{x}{y}\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 82.5% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -2.5 \cdot 10^{+58} \lor \neg \left(z \leq 1.1 \cdot 10^{-41}\right):\\ \;\;\;\;t + x \cdot \frac{z}{y}\\ \mathbf{else}:\\ \;\;\;\;t \cdot \left(1 - \frac{x}{y}\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= z -2.5e+58) (not (<= z 1.1e-41)))
   (+ t (* x (/ z y)))
   (* t (- 1.0 (/ x y)))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((z <= -2.5e+58) || !(z <= 1.1e-41)) {
		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 <= (-2.5d+58)) .or. (.not. (z <= 1.1d-41))) 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 <= -2.5e+58) || !(z <= 1.1e-41)) {
		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 <= -2.5e+58) or not (z <= 1.1e-41):
		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 <= -2.5e+58) || !(z <= 1.1e-41))
		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 <= -2.5e+58) || ~((z <= 1.1e-41)))
		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, -2.5e+58], N[Not[LessEqual[z, 1.1e-41]], $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 < -2.49999999999999993e58 or 1.1e-41 < z

   1. Initial program 98.4%

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

   3. Taylor expanded in z around inf 90.8%

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

      1. associate-/l* 91.5%

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

   5. Simplified 91.5%

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

   if -2.49999999999999993e58 < z < 1.1e-41

   1. Initial program 98.5%

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

   3. Taylor expanded in z around 0 87.2%

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

      1. *-rgt-identity 87.2%

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

      2. mul-1-neg 87.2%

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

      3. associate-/l* 90.1%

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

      4. distribute-rgt-neg-in 90.1%

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

      5. mul-1-neg 90.1%

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

      6. distribute-lft-in 90.0%

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

      7. mul-1-neg 90.0%

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

      8. unsub-neg 90.0%

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

   5. Simplified 90.0%

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

4. Final simplification 90.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -2.5 \cdot 10^{+58} \lor \neg \left(z \leq 1.1 \cdot 10^{-41}\right):\\ \;\;\;\;t + x \cdot \frac{z}{y}\\ \mathbf{else}:\\ \;\;\;\;t \cdot \left(1 - \frac{x}{y}\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 93.4% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -1 \cdot 10^{+213}:\\ \;\;\;\;t \cdot \left(1 - \frac{x}{y}\right)\\ \mathbf{else}:\\ \;\;\;\;t + x \cdot \frac{z - t}{y}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= t -1e+213) (* t (- 1.0 (/ x y))) (+ t (* x (/ (- z t) y)))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (t <= -1e+213) {
		tmp = t * (1.0 - (x / y));
	} else {
		tmp = t + (x * ((z - t) / y));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if (t <= (-1d+213)) then
        tmp = t * (1.0d0 - (x / y))
    else
        tmp = t + (x * ((z - t) / y))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if (t <= -1e+213) {
		tmp = t * (1.0 - (x / y));
	} else {
		tmp = t + (x * ((z - t) / y));
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if t <= -1e+213:
		tmp = t * (1.0 - (x / y))
	else:
		tmp = t + (x * ((z - t) / y))
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (t <= -1e+213)
		tmp = Float64(t * Float64(1.0 - Float64(x / y)));
	else
		tmp = Float64(t + Float64(x * Float64(Float64(z - t) / y)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (t <= -1e+213)
		tmp = t * (1.0 - (x / y));
	else
		tmp = t + (x * ((z - t) / y));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[t, -1e+213], N[(t * N[(1.0 - N[(x / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(t + N[(x * N[(N[(z - t), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if t < -9.99999999999999984e212

   1. Initial program 100.0%

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

   3. Taylor expanded in z around 0 100.0%

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

      1. *-rgt-identity 100.0%

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

      2. mul-1-neg 100.0%

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

      3. associate-/l* 100.0%

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

      4. distribute-rgt-neg-in 100.0%

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

      5. mul-1-neg 100.0%

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

      6. distribute-lft-in 100.0%

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

      7. mul-1-neg 100.0%

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

      8. unsub-neg 100.0%

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

   5. Simplified 100.0%

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

   if -9.99999999999999984e212 < t

   1. Initial program 98.3%

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

   3. Taylor expanded in x around 0 94.3%

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

      1. associate-*r/ 96.3%

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

   5. Simplified 96.3%

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

4. Final simplification 96.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -1 \cdot 10^{+213}:\\ \;\;\;\;t \cdot \left(1 - \frac{x}{y}\right)\\ \mathbf{else}:\\ \;\;\;\;t + x \cdot \frac{z - t}{y}\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 64.9% 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 98.4%

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

3. Taylor expanded in z around 0 65.2%

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

   1. *-rgt-identity 65.2%

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

   2. mul-1-neg 65.2%

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

   3. associate-/l* 68.4%

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

   4. distribute-rgt-neg-in 68.4%

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

   5. mul-1-neg 68.4%

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

   6. distribute-lft-in 68.4%

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

   7. mul-1-neg 68.4%

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

   8. unsub-neg 68.4%

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

5. Simplified 68.4%

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

Alternative 9: 38.2% accurate, 9.0× speedup

Math

\[\begin{array}{l} \\ t \end{array} \]

FPCore

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

C

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

Fortran

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

Java

public static double code(double x, double y, double z, double t) {
	return t;
}

Python

def code(x, y, z, t):
	return t

Julia

function code(x, y, z, t)
	return t
end

MATLAB

function tmp = code(x, y, z, t)
	tmp = t;
end

Wolfram

code[x_, y_, z_, t_] := t

Derivation

1. Initial program 98.4%

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

3. Taylor expanded in x around 0 42.4%

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

Developer Target 1: 97.3% 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 2024157 
(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))