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

Percentage Accurate: 97.9% → 95.2%

Time: 8.9s

Alternatives: 11

Speedup: 0.6×

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

Specification

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Initial Program: 97.9% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Alternative 1: 95.2% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -6.5 \cdot 10^{-195} \lor \neg \left(x \leq 1.85 \cdot 10^{-152}\right):\\ \;\;\;\;t + x \cdot \frac{z - t}{y}\\ \mathbf{else}:\\ \;\;\;\;t + \frac{x}{y} \cdot z\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= x -6.5e-195) (not (<= x 1.85e-152)))
   (+ t (* x (/ (- z t) y)))
   (+ t (* (/ x y) z))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((x <= -6.5e-195) || !(x <= 1.85e-152)) {
		tmp = t + (x * ((z - t) / 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 ((x <= (-6.5d-195)) .or. (.not. (x <= 1.85d-152))) then
        tmp = t + (x * ((z - t) / 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 ((x <= -6.5e-195) || !(x <= 1.85e-152)) {
		tmp = t + (x * ((z - t) / y));
	} else {
		tmp = t + ((x / y) * z);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (x <= -6.5e-195) or not (x <= 1.85e-152):
		tmp = t + (x * ((z - t) / y))
	else:
		tmp = t + ((x / y) * z)
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((x <= -6.5e-195) || !(x <= 1.85e-152))
		tmp = Float64(t + Float64(x * Float64(Float64(z - t) / 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 ((x <= -6.5e-195) || ~((x <= 1.85e-152)))
		tmp = t + (x * ((z - t) / y));
	else
		tmp = t + ((x / y) * z);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[x, -6.5e-195], N[Not[LessEqual[x, 1.85e-152]], $MachinePrecision]], N[(t + N[(x * N[(N[(z - t), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(t + N[(N[(x / y), $MachinePrecision] * z), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < -6.50000000000000004e-195 or 1.8499999999999999e-152 < x

   1. Initial program 96.2%

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

   3. Taylor expanded in x around 0 89.4%

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

      1. associate-*r/ 98.9%

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

   5. Simplified 98.9%

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

   if -6.50000000000000004e-195 < x < 1.8499999999999999e-152

   1. Initial program 98.5%

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

   3. Taylor expanded in z around inf 97.9%

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

      1. associate-*l/ 98.5%

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

      2. *-commutative 98.5%

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

   5. Simplified 98.5%

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

4. Final simplification 98.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -6.5 \cdot 10^{-195} \lor \neg \left(x \leq 1.85 \cdot 10^{-152}\right):\\ \;\;\;\;t + x \cdot \frac{z - t}{y}\\ \mathbf{else}:\\ \;\;\;\;t + \frac{x}{y} \cdot z\\ \end{array} \]
5. Add Preprocessing

Alternative 2: 62.1% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;\frac{x}{y} \leq -200000 \lor \neg \left(\frac{x}{y} \leq 10\right):\\ \;\;\;\;\frac{t}{y} \cdot \left(-x\right)\\ \mathbf{else}:\\ \;\;\;\;t\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= (/ x y) -200000.0) (not (<= (/ x y) 10.0))) (* (/ t y) (- x)) t))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (((x / y) <= -200000.0) || !((x / y) <= 10.0)) {
		tmp = (t / y) * -x;
	} 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) <= (-200000.0d0)) .or. (.not. ((x / y) <= 10.0d0))) then
        tmp = (t / y) * -x
    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) <= -200000.0) || !((x / y) <= 10.0)) {
		tmp = (t / y) * -x;
	} else {
		tmp = t;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if ((x / y) <= -200000.0) or not ((x / y) <= 10.0):
		tmp = (t / y) * -x
	else:
		tmp = t
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((Float64(x / y) <= -200000.0) || !(Float64(x / y) <= 10.0))
		tmp = Float64(Float64(t / y) * Float64(-x));
	else
		tmp = t;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (((x / y) <= -200000.0) || ~(((x / y) <= 10.0)))
		tmp = (t / y) * -x;
	else
		tmp = t;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[N[(x / y), $MachinePrecision], -200000.0], N[Not[LessEqual[N[(x / y), $MachinePrecision], 10.0]], $MachinePrecision]], N[(N[(t / y), $MachinePrecision] * (-x)), $MachinePrecision], t]

Derivation

1. Split input into 2 regimes

2. if (/.f64 x y) < -2e5 or 10 < (/.f64 x y)

   1. Initial program 94.4%

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

   3. Taylor expanded in z around 0 52.0%

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

      1. mul-1-neg 52.0%

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

      2. unsub-neg 52.0%

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

      3. *-rgt-identity 52.0%

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

      4. associate-*r/ 52.7%

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

      5. distribute-lft-out-- 52.7%

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

   5. Simplified 52.7%

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

   6. Taylor expanded in x around inf 51.8%

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

      1. mul-1-neg 51.8%

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

      2. distribute-neg-frac 51.8%

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

   8. Simplified 51.8%

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

      1. add-sqr-sqrt 30.0%

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

      2. sqrt-unprod 32.7%

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

      3. sqr-neg 32.7%

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

      4. sqrt-unprod 3.9%

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

      5. add-sqr-sqrt 7.9%

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

      6. clear-num 7.9%

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

      7. div-inv 7.9%

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

      8. frac-2neg 7.9%

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

      9. distribute-neg-frac 7.9%

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

      10. add-sqr-sqrt 3.9%

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

      11. sqrt-unprod 32.0%

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

      12. sqr-neg 32.0%

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

      13. sqrt-unprod 29.2%

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

      14. add-sqr-sqrt 51.3%

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

      15. frac-2neg 51.3%

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

   10. Applied egg-rr 51.3%

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

       1. distribute-frac-neg 51.3%

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

       2. associate-/r/ 53.1%

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

       3. add-sqr-sqrt 24.2%

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

       4. sqrt-unprod 23.4%

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

       5. sqr-neg 23.4%

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

       6. sqrt-unprod 4.0%

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

       7. add-sqr-sqrt 7.1%

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

       8. *-commutative 7.1%

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

       9. add-sqr-sqrt 4.0%

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

       10. sqrt-unprod 23.4%

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

       11. sqr-neg 23.4%

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

       12. sqrt-unprod 24.2%

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

       13. add-sqr-sqrt 53.1%

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

   12. Applied egg-rr 53.1%

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

   if -2e5 < (/.f64 x y) < 10

   1. Initial program 98.7%

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

   3. Taylor expanded in x around 0 69.3%

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

4. Final simplification 61.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{x}{y} \leq -200000 \lor \neg \left(\frac{x}{y} \leq 10\right):\\ \;\;\;\;\frac{t}{y} \cdot \left(-x\right)\\ \mathbf{else}:\\ \;\;\;\;t\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 63.0% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;\frac{x}{y} \leq -200000:\\ \;\;\;\;t \cdot \frac{-x}{y}\\ \mathbf{elif}\;\frac{x}{y} \leq 10:\\ \;\;\;\;t\\ \mathbf{else}:\\ \;\;\;\;\frac{t}{y} \cdot \left(-x\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= (/ x y) -200000.0)
   (* t (/ (- x) y))
   (if (<= (/ x y) 10.0) t (* (/ t y) (- x)))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((x / y) <= -200000.0) {
		tmp = t * (-x / y);
	} else if ((x / y) <= 10.0) {
		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) <= (-200000.0d0)) then
        tmp = t * (-x / y)
    else if ((x / y) <= 10.0d0) 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) <= -200000.0) {
		tmp = t * (-x / y);
	} else if ((x / y) <= 10.0) {
		tmp = t;
	} else {
		tmp = (t / y) * -x;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (x / y) <= -200000.0:
		tmp = t * (-x / y)
	elif (x / y) <= 10.0:
		tmp = t
	else:
		tmp = (t / y) * -x
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (Float64(x / y) <= -200000.0)
		tmp = Float64(t * Float64(Float64(-x) / y));
	elseif (Float64(x / y) <= 10.0)
		tmp = t;
	else
		tmp = Float64(Float64(t / y) * Float64(-x));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((x / y) <= -200000.0)
		tmp = t * (-x / y);
	elseif ((x / y) <= 10.0)
		tmp = t;
	else
		tmp = (t / y) * -x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[N[(x / y), $MachinePrecision], -200000.0], N[(t * N[((-x) / y), $MachinePrecision]), $MachinePrecision], If[LessEqual[N[(x / y), $MachinePrecision], 10.0], t, N[(N[(t / y), $MachinePrecision] * (-x)), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if (/.f64 x y) < -2e5

   1. Initial program 96.1%

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

   3. Taylor expanded in z around 0 48.6%

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

      1. mul-1-neg 48.6%

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

      2. unsub-neg 48.6%

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

      3. *-rgt-identity 48.6%

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

      4. associate-*r/ 50.3%

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

      5. distribute-lft-out-- 50.3%

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

   5. Simplified 50.3%

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

   6. Taylor expanded in x around inf 49.3%

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

      1. mul-1-neg 49.3%

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

      2. distribute-neg-frac 49.3%

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

   8. Simplified 49.3%

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

   if -2e5 < (/.f64 x y) < 10

   1. Initial program 98.7%

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

   3. Taylor expanded in x around 0 69.3%

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

   if 10 < (/.f64 x y)

   1. Initial program 93.2%

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

   3. Taylor expanded in z around 0 54.4%

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

      1. mul-1-neg 54.4%

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

      2. unsub-neg 54.4%

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

      3. *-rgt-identity 54.4%

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

      4. associate-*r/ 54.5%

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

      5. distribute-lft-out-- 54.5%

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

   5. Simplified 54.5%

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

   6. Taylor expanded in x around inf 53.6%

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

      1. mul-1-neg 53.6%

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

      2. distribute-neg-frac 53.6%

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

   8. Simplified 53.6%

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

      1. add-sqr-sqrt 32.4%

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

      2. sqrt-unprod 34.8%

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

      3. sqr-neg 34.8%

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

      4. sqrt-unprod 3.2%

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

      5. add-sqr-sqrt 8.1%

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

      6. clear-num 8.1%

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

      7. div-inv 8.1%

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

      8. frac-2neg 8.1%

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

      9. distribute-neg-frac 8.1%

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

      10. add-sqr-sqrt 3.2%

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

      11. sqrt-unprod 33.6%

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

      12. sqr-neg 33.6%

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

      13. sqrt-unprod 31.1%

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

      14. add-sqr-sqrt 52.5%

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

      15. frac-2neg 52.5%

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

   10. Applied egg-rr 52.5%

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

       1. distribute-frac-neg 52.5%

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

       2. associate-/r/ 55.9%

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

       3. add-sqr-sqrt 26.4%

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

       4. sqrt-unprod 22.6%

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

       5. sqr-neg 22.6%

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

       6. sqrt-unprod 2.0%

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

       7. add-sqr-sqrt 6.8%

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

       8. *-commutative 6.8%

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

       9. add-sqr-sqrt 2.0%

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

       10. sqrt-unprod 22.6%

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

       11. sqr-neg 22.6%

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

       12. sqrt-unprod 26.4%

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

       13. add-sqr-sqrt 55.9%

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

   12. Applied egg-rr 55.9%

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

4. Final simplification 61.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{x}{y} \leq -200000:\\ \;\;\;\;t \cdot \frac{-x}{y}\\ \mathbf{elif}\;\frac{x}{y} \leq 10:\\ \;\;\;\;t\\ \mathbf{else}:\\ \;\;\;\;\frac{t}{y} \cdot \left(-x\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 62.9% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;\frac{x}{y} \leq -200000:\\ \;\;\;\;\frac{-t}{\frac{y}{x}}\\ \mathbf{elif}\;\frac{x}{y} \leq 10:\\ \;\;\;\;t\\ \mathbf{else}:\\ \;\;\;\;\frac{t}{y} \cdot \left(-x\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= (/ x y) -200000.0)
   (/ (- t) (/ y x))
   (if (<= (/ x y) 10.0) t (* (/ t y) (- x)))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((x / y) <= -200000.0) {
		tmp = -t / (y / x);
	} else if ((x / y) <= 10.0) {
		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) <= (-200000.0d0)) then
        tmp = -t / (y / x)
    else if ((x / y) <= 10.0d0) 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) <= -200000.0) {
		tmp = -t / (y / x);
	} else if ((x / y) <= 10.0) {
		tmp = t;
	} else {
		tmp = (t / y) * -x;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (x / y) <= -200000.0:
		tmp = -t / (y / x)
	elif (x / y) <= 10.0:
		tmp = t
	else:
		tmp = (t / y) * -x
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (Float64(x / y) <= -200000.0)
		tmp = Float64(Float64(-t) / Float64(y / x));
	elseif (Float64(x / y) <= 10.0)
		tmp = t;
	else
		tmp = Float64(Float64(t / y) * Float64(-x));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((x / y) <= -200000.0)
		tmp = -t / (y / x);
	elseif ((x / y) <= 10.0)
		tmp = t;
	else
		tmp = (t / y) * -x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[N[(x / y), $MachinePrecision], -200000.0], N[((-t) / N[(y / x), $MachinePrecision]), $MachinePrecision], If[LessEqual[N[(x / y), $MachinePrecision], 10.0], t, N[(N[(t / y), $MachinePrecision] * (-x)), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if (/.f64 x y) < -2e5

   1. Initial program 96.1%

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

   3. Taylor expanded in z around 0 48.6%

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

      1. mul-1-neg 48.6%

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

      2. unsub-neg 48.6%

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

      3. *-rgt-identity 48.6%

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

      4. associate-*r/ 50.3%

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

      5. distribute-lft-out-- 50.3%

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

   5. Simplified 50.3%

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

   6. Taylor expanded in x around inf 49.3%

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

      1. mul-1-neg 49.3%

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

      2. distribute-neg-frac 49.3%

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

   8. Simplified 49.3%

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

      1. add-sqr-sqrt 26.6%

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

      2. sqrt-unprod 29.7%

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

      3. sqr-neg 29.7%

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

      4. sqrt-unprod 5.0%

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

      5. add-sqr-sqrt 7.7%

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

      6. clear-num 7.7%

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

      7. div-inv 7.7%

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

      8. frac-2neg 7.7%

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

      9. distribute-neg-frac 7.7%

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

      10. add-sqr-sqrt 5.0%

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

      11. sqrt-unprod 29.7%

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

      12. sqr-neg 29.7%

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

      13. sqrt-unprod 26.6%

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

      14. add-sqr-sqrt 49.5%

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

      15. frac-2neg 49.5%

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

   10. Applied egg-rr 49.5%

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

   if -2e5 < (/.f64 x y) < 10

   1. Initial program 98.7%

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

   3. Taylor expanded in x around 0 69.3%

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

   if 10 < (/.f64 x y)

   1. Initial program 93.2%

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

   3. Taylor expanded in z around 0 54.4%

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

      1. mul-1-neg 54.4%

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

      2. unsub-neg 54.4%

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

      3. *-rgt-identity 54.4%

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

      4. associate-*r/ 54.5%

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

      5. distribute-lft-out-- 54.5%

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

   5. Simplified 54.5%

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

   6. Taylor expanded in x around inf 53.6%

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

      1. mul-1-neg 53.6%

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

      2. distribute-neg-frac 53.6%

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

   8. Simplified 53.6%

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

      1. add-sqr-sqrt 32.4%

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

      2. sqrt-unprod 34.8%

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

      3. sqr-neg 34.8%

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

      4. sqrt-unprod 3.2%

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

      5. add-sqr-sqrt 8.1%

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

      6. clear-num 8.1%

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

      7. div-inv 8.1%

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

      8. frac-2neg 8.1%

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

      9. distribute-neg-frac 8.1%

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

      10. add-sqr-sqrt 3.2%

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

      11. sqrt-unprod 33.6%

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

      12. sqr-neg 33.6%

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

      13. sqrt-unprod 31.1%

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

      14. add-sqr-sqrt 52.5%

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

      15. frac-2neg 52.5%

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

   10. Applied egg-rr 52.5%

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

       1. distribute-frac-neg 52.5%

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

       2. associate-/r/ 55.9%

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

       3. add-sqr-sqrt 26.4%

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

       4. sqrt-unprod 22.6%

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

       5. sqr-neg 22.6%

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

       6. sqrt-unprod 2.0%

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

       7. add-sqr-sqrt 6.8%

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

       8. *-commutative 6.8%

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

       9. add-sqr-sqrt 2.0%

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

       10. sqrt-unprod 22.6%

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

       11. sqr-neg 22.6%

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

       12. sqrt-unprod 26.4%

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

       13. add-sqr-sqrt 55.9%

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

   12. Applied egg-rr 55.9%

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

4. Final simplification 61.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{x}{y} \leq -200000:\\ \;\;\;\;\frac{-t}{\frac{y}{x}}\\ \mathbf{elif}\;\frac{x}{y} \leq 10:\\ \;\;\;\;t\\ \mathbf{else}:\\ \;\;\;\;\frac{t}{y} \cdot \left(-x\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 86.4% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -4 \cdot 10^{+67} \lor \neg \left(t \leq 1.38 \cdot 10^{+54}\right):\\ \;\;\;\;t \cdot \left(1 - \frac{x}{y}\right)\\ \mathbf{else}:\\ \;\;\;\;t + \frac{x}{y} \cdot z\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= t -4e+67) (not (<= t 1.38e+54)))
   (* t (- 1.0 (/ x y)))
   (+ t (* (/ x y) z))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((t <= -4e+67) || !(t <= 1.38e+54)) {
		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 ((t <= (-4d+67)) .or. (.not. (t <= 1.38d+54))) 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 ((t <= -4e+67) || !(t <= 1.38e+54)) {
		tmp = t * (1.0 - (x / y));
	} else {
		tmp = t + ((x / y) * z);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (t <= -4e+67) or not (t <= 1.38e+54):
		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 ((t <= -4e+67) || !(t <= 1.38e+54))
		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 ((t <= -4e+67) || ~((t <= 1.38e+54)))
		tmp = t * (1.0 - (x / y));
	else
		tmp = t + ((x / y) * z);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[t, -4e+67], N[Not[LessEqual[t, 1.38e+54]], $MachinePrecision]], 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 2 regimes

2. if t < -3.99999999999999993e67 or 1.38e54 < t

   1. Initial program 99.9%

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

   3. Taylor expanded in z around 0 78.3%

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

      1. mul-1-neg 78.3%

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

      2. unsub-neg 78.3%

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

      3. *-rgt-identity 78.3%

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

      4. associate-*r/ 86.5%

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

      5. distribute-lft-out-- 86.5%

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

   5. Simplified 86.5%

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

   if -3.99999999999999993e67 < t < 1.38e54

   1. Initial program 94.4%

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

   3. Taylor expanded in z around inf 79.3%

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

      1. associate-*l/ 83.7%

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

      2. *-commutative 83.7%

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

   5. Simplified 83.7%

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

4. Final simplification 84.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -4 \cdot 10^{+67} \lor \neg \left(t \leq 1.38 \cdot 10^{+54}\right):\\ \;\;\;\;t \cdot \left(1 - \frac{x}{y}\right)\\ \mathbf{else}:\\ \;\;\;\;t + \frac{x}{y} \cdot z\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 86.4% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -2.1 \cdot 10^{+67}:\\ \;\;\;\;t - \frac{x}{y} \cdot t\\ \mathbf{elif}\;t \leq 6.3 \cdot 10^{+55}:\\ \;\;\;\;t + \frac{x}{y} \cdot z\\ \mathbf{else}:\\ \;\;\;\;t \cdot \left(1 - \frac{x}{y}\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= t -2.1e+67)
   (- t (* (/ x y) t))
   (if (<= t 6.3e+55) (+ t (* (/ x y) z)) (* t (- 1.0 (/ x y))))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (t <= -2.1e+67) {
		tmp = t - ((x / y) * t);
	} else if (t <= 6.3e+55) {
		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 (t <= (-2.1d+67)) then
        tmp = t - ((x / y) * t)
    else if (t <= 6.3d+55) 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 (t <= -2.1e+67) {
		tmp = t - ((x / y) * t);
	} else if (t <= 6.3e+55) {
		tmp = t + ((x / y) * z);
	} else {
		tmp = t * (1.0 - (x / y));
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if t <= -2.1e+67:
		tmp = t - ((x / y) * t)
	elif t <= 6.3e+55:
		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 (t <= -2.1e+67)
		tmp = Float64(t - Float64(Float64(x / y) * t));
	elseif (t <= 6.3e+55)
		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 (t <= -2.1e+67)
		tmp = t - ((x / y) * t);
	elseif (t <= 6.3e+55)
		tmp = t + ((x / y) * z);
	else
		tmp = t * (1.0 - (x / y));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[t, -2.1e+67], N[(t - N[(N[(x / y), $MachinePrecision] * t), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 6.3e+55], 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 3 regimes

2. if t < -2.1000000000000001e67

   1. Initial program 99.9%

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

      1. *-commutative 99.9%

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

      2. clear-num 99.9%

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

      3. un-div-inv 99.9%

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

   4. Applied egg-rr 99.9%

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

   5. Taylor expanded in z around 0 73.5%

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

      1. associate-*r/ 80.9%

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

      2. neg-mul-1 80.9%

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

      3. sub-neg 80.9%

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

   7. Simplified 80.9%

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

   if -2.1000000000000001e67 < t < 6.2999999999999996e55

   1. Initial program 94.4%

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

   3. Taylor expanded in z around inf 79.3%

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

      1. associate-*l/ 83.7%

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

      2. *-commutative 83.7%

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

   5. Simplified 83.7%

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

   if 6.2999999999999996e55 < t

   1. Initial program 100.0%

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

   3. Taylor expanded in z around 0 83.8%

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

      1. mul-1-neg 83.8%

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

      2. unsub-neg 83.8%

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

      3. *-rgt-identity 83.8%

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

      4. associate-*r/ 92.9%

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

      5. distribute-lft-out-- 92.9%

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

   5. Simplified 92.9%

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

4. Final simplification 84.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -2.1 \cdot 10^{+67}:\\ \;\;\;\;t - \frac{x}{y} \cdot t\\ \mathbf{elif}\;t \leq 6.3 \cdot 10^{+55}:\\ \;\;\;\;t + \frac{x}{y} \cdot z\\ \mathbf{else}:\\ \;\;\;\;t \cdot \left(1 - \frac{x}{y}\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 98.2% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq 1.5 \cdot 10^{-7}:\\ \;\;\;\;t + \frac{x}{y} \cdot \left(z - t\right)\\ \mathbf{else}:\\ \;\;\;\;t + x \cdot \frac{z - t}{y}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= x 1.5e-7) (+ t (* (/ x y) (- z t))) (+ t (* x (/ (- z t) y)))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (x <= 1.5e-7) {
		tmp = t + ((x / y) * (z - t));
	} 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 (x <= 1.5d-7) then
        tmp = t + ((x / y) * (z - t))
    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 (x <= 1.5e-7) {
		tmp = t + ((x / y) * (z - t));
	} else {
		tmp = t + (x * ((z - t) / y));
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if x <= 1.5e-7:
		tmp = t + ((x / y) * (z - t))
	else:
		tmp = t + (x * ((z - t) / y))
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (x <= 1.5e-7)
		tmp = Float64(t + Float64(Float64(x / y) * Float64(z - t)));
	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 (x <= 1.5e-7)
		tmp = t + ((x / y) * (z - t));
	else
		tmp = t + (x * ((z - t) / y));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[x, 1.5e-7], N[(t + N[(N[(x / y), $MachinePrecision] * N[(z - t), $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 x < 1.4999999999999999e-7

   1. Initial program 98.5%

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

   if 1.4999999999999999e-7 < x

   1. Initial program 91.6%

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

   3. Taylor expanded in x around 0 83.5%

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

      1. associate-*r/ 99.5%

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

   5. Simplified 99.5%

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

4. Final simplification 98.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq 1.5 \cdot 10^{-7}:\\ \;\;\;\;t + \frac{x}{y} \cdot \left(z - t\right)\\ \mathbf{else}:\\ \;\;\;\;t + x \cdot \frac{z - t}{y}\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 39.8% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;\frac{x}{y} \leq 10^{+109}:\\ \;\;\;\;t\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{y} \cdot t\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t) :precision binary64 (if (<= (/ x y) 1e+109) t (* (/ x y) t)))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((x / y) <= 1e+109) {
		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) <= 1d+109) 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) <= 1e+109) {
		tmp = t;
	} else {
		tmp = (x / y) * t;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (x / y) <= 1e+109:
		tmp = t
	else:
		tmp = (x / y) * t
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (Float64(x / y) <= 1e+109)
		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) <= 1e+109)
		tmp = t;
	else
		tmp = (x / y) * t;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[N[(x / y), $MachinePrecision], 1e+109], t, N[(N[(x / y), $MachinePrecision] * t), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if (/.f64 x y) < 9.99999999999999982e108

   1. Initial program 98.1%

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

   3. Taylor expanded in x around 0 47.8%

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

   if 9.99999999999999982e108 < (/.f64 x y)

   1. Initial program 91.7%

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

   3. Taylor expanded in z around 0 55.2%

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

      1. mul-1-neg 55.2%

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

      2. unsub-neg 55.2%

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

      3. *-rgt-identity 55.2%

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

      4. associate-*r/ 52.6%

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

      5. distribute-lft-out-- 52.6%

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

   5. Simplified 52.6%

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

   6. Taylor expanded in x around inf 52.6%

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

      1. mul-1-neg 52.6%

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

      2. distribute-neg-frac 52.6%

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

   8. Simplified 52.6%

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

      1. expm1-log1p-u 28.6%

         \[\leadsto \color{blue}{\mathsf{expm1}\left(\mathsf{log1p}\left(t \cdot \frac{-x}{y}\right)\right)} \]

      2. expm1-udef 28.6%

         \[\leadsto \color{blue}{e^{\mathsf{log1p}\left(t \cdot \frac{-x}{y}\right)} - 1} \]

      3. add-sqr-sqrt 15.9%

         \[\leadsto e^{\mathsf{log1p}\left(t \cdot \frac{\color{blue}{\sqrt{-x} \cdot \sqrt{-x}}}{y}\right)} - 1 \]

      4. sqrt-unprod 18.2%

         \[\leadsto e^{\mathsf{log1p}\left(t \cdot \frac{\color{blue}{\sqrt{\left(-x\right) \cdot \left(-x\right)}}}{y}\right)} - 1 \]

      5. sqr-neg 18.2%

         \[\leadsto e^{\mathsf{log1p}\left(t \cdot \frac{\sqrt{\color{blue}{x \cdot x}}}{y}\right)} - 1 \]

      6. sqrt-unprod 3.7%

         \[\leadsto e^{\mathsf{log1p}\left(t \cdot \frac{\color{blue}{\sqrt{x} \cdot \sqrt{x}}}{y}\right)} - 1 \]

      7. add-sqr-sqrt 5.8%

         \[\leadsto e^{\mathsf{log1p}\left(t \cdot \frac{\color{blue}{x}}{y}\right)} - 1 \]

      8. clear-num 5.8%

         \[\leadsto e^{\mathsf{log1p}\left(t \cdot \color{blue}{\frac{1}{\frac{y}{x}}}\right)} - 1 \]

      9. div-inv 5.8%

         \[\leadsto e^{\mathsf{log1p}\left(\color{blue}{\frac{t}{\frac{y}{x}}}\right)} - 1 \]

      10. div-inv 5.8%

          \[\leadsto e^{\mathsf{log1p}\left(\color{blue}{t \cdot \frac{1}{\frac{y}{x}}}\right)} - 1 \]

      11. clear-num 5.8%

          \[\leadsto e^{\mathsf{log1p}\left(t \cdot \color{blue}{\frac{x}{y}}\right)} - 1 \]

   10. Applied egg-rr 5.8%

       \[\leadsto \color{blue}{e^{\mathsf{log1p}\left(t \cdot \frac{x}{y}\right)} - 1} \]
   11. Step-by-step derivation

       1. expm1-def 5.8%

          \[\leadsto \color{blue}{\mathsf{expm1}\left(\mathsf{log1p}\left(t \cdot \frac{x}{y}\right)\right)} \]

       2. expm1-log1p 9.8%

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

   12. Simplified 9.8%

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

4. Final simplification 39.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{x}{y} \leq 10^{+109}:\\ \;\;\;\;t\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{y} \cdot t\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 39.8% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;\frac{x}{y} \leq 10^{+109}:\\ \;\;\;\;t\\ \mathbf{else}:\\ \;\;\;\;\frac{t}{\frac{y}{x}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t) :precision binary64 (if (<= (/ x y) 1e+109) t (/ t (/ y x))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((x / y) <= 1e+109) {
		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) <= 1d+109) 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) <= 1e+109) {
		tmp = t;
	} else {
		tmp = t / (y / x);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (x / y) <= 1e+109:
		tmp = t
	else:
		tmp = t / (y / x)
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (Float64(x / y) <= 1e+109)
		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) <= 1e+109)
		tmp = t;
	else
		tmp = t / (y / x);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[N[(x / y), $MachinePrecision], 1e+109], t, N[(t / N[(y / x), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if (/.f64 x y) < 9.99999999999999982e108

   1. Initial program 98.1%

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

   3. Taylor expanded in x around 0 47.8%

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

   if 9.99999999999999982e108 < (/.f64 x y)

   1. Initial program 91.7%

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

   3. Taylor expanded in z around 0 55.2%

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

      1. mul-1-neg 55.2%

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

      2. unsub-neg 55.2%

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

      3. *-rgt-identity 55.2%

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

      4. associate-*r/ 52.6%

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

      5. distribute-lft-out-- 52.6%

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

   5. Simplified 52.6%

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

   6. Taylor expanded in x around inf 52.6%

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

      1. mul-1-neg 52.6%

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

      2. distribute-neg-frac 52.6%

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

   8. Simplified 52.6%

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

      1. add-sqr-sqrt 30.5%

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

      2. sqrt-unprod 36.0%

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

      3. sqr-neg 36.0%

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

      4. sqrt-unprod 3.9%

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

      5. add-sqr-sqrt 9.8%

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

      6. clear-num 9.8%

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

      7. div-inv 9.8%

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

   10. Applied egg-rr 9.8%

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

4. Final simplification 39.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{x}{y} \leq 10^{+109}:\\ \;\;\;\;t\\ \mathbf{else}:\\ \;\;\;\;\frac{t}{\frac{y}{x}}\\ \end{array} \]
5. Add Preprocessing

Alternative 10: 65.0% 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 96.6%

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

3. Taylor expanded in z around 0 59.4%

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

   1. mul-1-neg 59.4%

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

   2. unsub-neg 59.4%

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

   3. *-rgt-identity 59.4%

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

   4. associate-*r/ 62.3%

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

   5. distribute-lft-out-- 62.3%

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

5. Simplified 62.3%

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

6. Final simplification 62.3%

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

Alternative 11: 38.1% accurate, 9.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 96.6%

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

3. Taylor expanded in x around 0 37.5%

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

4. Final simplification 37.5%

   \[\leadsto t \]
5. Add Preprocessing

Developer target: 97.5% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{x}{y} \cdot \left(z - t\right) + t\\ \mathbf{if}\;z < 2.759456554562692 \cdot 10^{-282}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z < 2.326994450874436 \cdot 10^{-110}:\\ \;\;\;\;x \cdot \frac{z - t}{y} + t\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (+ (* (/ x y) (- z t)) t)))
   (if (< z 2.759456554562692e-282)
     t_1
     (if (< z 2.326994450874436e-110) (+ (* x (/ (- z t) y)) t) t_1))))

C

double code(double x, double y, double z, double t) {
	double t_1 = ((x / y) * (z - t)) + t;
	double tmp;
	if (z < 2.759456554562692e-282) {
		tmp = t_1;
	} else if (z < 2.326994450874436e-110) {
		tmp = (x * ((z - t) / y)) + t;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: t_1
    real(8) :: tmp
    t_1 = ((x / y) * (z - t)) + t
    if (z < 2.759456554562692d-282) then
        tmp = t_1
    else if (z < 2.326994450874436d-110) then
        tmp = (x * ((z - t) / y)) + t
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double t_1 = ((x / y) * (z - t)) + t;
	double tmp;
	if (z < 2.759456554562692e-282) {
		tmp = t_1;
	} else if (z < 2.326994450874436e-110) {
		tmp = (x * ((z - t) / y)) + t;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = ((x / y) * (z - t)) + t
	tmp = 0
	if z < 2.759456554562692e-282:
		tmp = t_1
	elif z < 2.326994450874436e-110:
		tmp = (x * ((z - t) / y)) + t
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(Float64(Float64(x / y) * Float64(z - t)) + t)
	tmp = 0.0
	if (z < 2.759456554562692e-282)
		tmp = t_1;
	elseif (z < 2.326994450874436e-110)
		tmp = Float64(Float64(x * Float64(Float64(z - t) / y)) + t);
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = ((x / y) * (z - t)) + t;
	tmp = 0.0;
	if (z < 2.759456554562692e-282)
		tmp = t_1;
	elseif (z < 2.326994450874436e-110)
		tmp = (x * ((z - t) / y)) + t;
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(N[(N[(x / y), $MachinePrecision] * N[(z - t), $MachinePrecision]), $MachinePrecision] + t), $MachinePrecision]}, If[Less[z, 2.759456554562692e-282], t$95$1, If[Less[z, 2.326994450874436e-110], N[(N[(x * N[(N[(z - t), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision] + t), $MachinePrecision], t$95$1]]]

Reproduce

herbie shell --seed 2024019 
(FPCore (x y z t)
  :name "Numeric.Signal.Multichannel:$cget from hsignal-0.2.7.1"
  :precision binary64

  :herbie-target
  (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))