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

Percentage Accurate: 97.6% → 97.7%

Time: 8.6s

Alternatives: 13

Speedup: 1.0×

• 24.3% of points produce a very large (infinite) output. You may want to add a precondition.

Specification

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Initial Program: 97.6% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Alternative 1: 97.7% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ t + \frac{z - t}{\frac{y}{x}} \end{array} \]

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 98.3%

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

   1. *-commutative 98.3%

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

   2. clear-num 98.3%

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

   3. un-div-inv 98.6%

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

4. Applied egg-rr 98.6%

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

5. Final simplification 98.6%

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

Alternative 2: 64.3% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;\frac{x}{y} \leq -2000000000 \lor \neg \left(\frac{x}{y} \leq 1\right):\\ \;\;\;\;t \cdot \frac{x}{-y}\\ \mathbf{else}:\\ \;\;\;\;t\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= (/ x y) -2000000000.0) (not (<= (/ x y) 1.0)))
   (* t (/ x (- y)))
   t))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (((x / y) <= -2000000000.0) || !((x / y) <= 1.0)) {
		tmp = t * (x / -y);
	} else {
		tmp = t;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if (((x / y) <= (-2000000000.0d0)) .or. (.not. ((x / y) <= 1.0d0))) then
        tmp = t * (x / -y)
    else
        tmp = t
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if (((x / y) <= -2000000000.0) || !((x / y) <= 1.0)) {
		tmp = t * (x / -y);
	} else {
		tmp = t;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if ((x / y) <= -2000000000.0) or not ((x / y) <= 1.0):
		tmp = t * (x / -y)
	else:
		tmp = t
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((Float64(x / y) <= -2000000000.0) || !(Float64(x / y) <= 1.0))
		tmp = Float64(t * Float64(x / Float64(-y)));
	else
		tmp = t;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (((x / y) <= -2000000000.0) || ~(((x / y) <= 1.0)))
		tmp = t * (x / -y);
	else
		tmp = t;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[N[(x / y), $MachinePrecision], -2000000000.0], N[Not[LessEqual[N[(x / y), $MachinePrecision], 1.0]], $MachinePrecision]], N[(t * N[(x / (-y)), $MachinePrecision]), $MachinePrecision], t]

Derivation

1. Split input into 2 regimes

2. if (/.f64 x y) < -2e9 or 1 < (/.f64 x y)

   1. Initial program 96.7%

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

   3. Taylor expanded in z around 0 47.2%

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

      1. mul-1-neg 47.2%

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

      2. unsub-neg 47.2%

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

      3. *-rgt-identity 47.2%

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

      4. associate-/l* 51.6%

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

      5. distribute-lft-out-- 51.6%

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

   5. Simplified 51.6%

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

   6. Taylor expanded in x around inf 50.7%

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

      1. mul-1-neg 50.7%

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

      2. distribute-frac-neg2 50.7%

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

   8. Simplified 50.7%

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

   if -2e9 < (/.f64 x y) < 1

   1. Initial program 99.8%

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

   3. Taylor expanded in x around 0 74.7%

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

4. Final simplification 63.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{x}{y} \leq -2000000000 \lor \neg \left(\frac{x}{y} \leq 1\right):\\ \;\;\;\;t \cdot \frac{x}{-y}\\ \mathbf{else}:\\ \;\;\;\;t\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 64.3% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;\frac{x}{y} \leq -2000000000:\\ \;\;\;\;t \cdot \frac{x}{-y}\\ \mathbf{elif}\;\frac{x}{y} \leq 1:\\ \;\;\;\;t\\ \mathbf{else}:\\ \;\;\;\;\frac{t}{\frac{y}{-x}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= (/ x y) -2000000000.0)
   (* t (/ x (- y)))
   (if (<= (/ x y) 1.0) t (/ t (/ y (- x))))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((x / y) <= -2000000000.0) {
		tmp = t * (x / -y);
	} else if ((x / y) <= 1.0) {
		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) <= (-2000000000.0d0)) then
        tmp = t * (x / -y)
    else if ((x / y) <= 1.0d0) 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) <= -2000000000.0) {
		tmp = t * (x / -y);
	} else if ((x / y) <= 1.0) {
		tmp = t;
	} else {
		tmp = t / (y / -x);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (x / y) <= -2000000000.0:
		tmp = t * (x / -y)
	elif (x / y) <= 1.0:
		tmp = t
	else:
		tmp = t / (y / -x)
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (Float64(x / y) <= -2000000000.0)
		tmp = Float64(t * Float64(x / Float64(-y)));
	elseif (Float64(x / y) <= 1.0)
		tmp = t;
	else
		tmp = Float64(t / Float64(y / Float64(-x)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((x / y) <= -2000000000.0)
		tmp = t * (x / -y);
	elseif ((x / y) <= 1.0)
		tmp = t;
	else
		tmp = t / (y / -x);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[N[(x / y), $MachinePrecision], -2000000000.0], N[(t * N[(x / (-y)), $MachinePrecision]), $MachinePrecision], If[LessEqual[N[(x / y), $MachinePrecision], 1.0], t, N[(t / N[(y / (-x)), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if (/.f64 x y) < -2e9

   1. Initial program 96.6%

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

   3. Taylor expanded in z around 0 47.0%

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

      1. mul-1-neg 47.0%

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

      2. unsub-neg 47.0%

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

      3. *-rgt-identity 47.0%

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

      4. associate-/l* 49.9%

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

      5. distribute-lft-out-- 49.9%

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

   5. Simplified 49.9%

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

   6. Taylor expanded in x around inf 49.4%

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

      1. mul-1-neg 49.4%

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

      2. distribute-frac-neg2 49.4%

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

   8. Simplified 49.4%

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

   if -2e9 < (/.f64 x y) < 1

   1. Initial program 99.8%

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

   3. Taylor expanded in x around 0 74.7%

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

   if 1 < (/.f64 x y)

   1. Initial program 96.8%

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

   3. Taylor expanded in z around 0 47.3%

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

      1. mul-1-neg 47.3%

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

      2. unsub-neg 47.3%

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

      3. *-rgt-identity 47.3%

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

      4. associate-/l* 53.2%

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

      5. distribute-lft-out-- 53.2%

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

   5. Simplified 53.2%

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

   6. Taylor expanded in x around inf 47.3%

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

      1. mul-1-neg 47.3%

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

      2. distribute-frac-neg2 47.3%

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

      3. *-commutative 47.3%

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

      4. associate-/l* 41.8%

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

   8. Simplified 41.8%

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

      1. *-commutative 41.8%

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

      2. add-sqr-sqrt 26.3%

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

      3. sqrt-unprod 33.1%

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

      4. sqr-neg 33.1%

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

      5. sqrt-unprod 6.9%

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

      6. add-sqr-sqrt 14.2%

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

      7. associate-/r/ 14.2%

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

      8. frac-2neg 14.2%

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

      9. distribute-neg-frac 14.2%

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

      10. add-sqr-sqrt 8.8%

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

      11. sqrt-unprod 22.2%

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

      12. sqr-neg 22.2%

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

      13. sqrt-unprod 18.2%

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

      14. add-sqr-sqrt 53.1%

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

   10. Applied egg-rr 53.1%

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

4. Final simplification 63.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{x}{y} \leq -2000000000:\\ \;\;\;\;t \cdot \frac{x}{-y}\\ \mathbf{elif}\;\frac{x}{y} \leq 1:\\ \;\;\;\;t\\ \mathbf{else}:\\ \;\;\;\;\frac{t}{\frac{y}{-x}}\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 43.9% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;\frac{x}{y} \leq -5 \cdot 10^{+29}:\\ \;\;\;\;y \cdot \frac{t}{y}\\ \mathbf{elif}\;\frac{x}{y} \leq 2 \cdot 10^{-8}:\\ \;\;\;\;t\\ \mathbf{else}:\\ \;\;\;\;t \cdot \frac{x}{y}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= (/ x y) -5e+29) (* y (/ t y)) (if (<= (/ x y) 2e-8) t (* t (/ x y)))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((x / y) <= -5e+29) {
		tmp = y * (t / y);
	} else if ((x / y) <= 2e-8) {
		tmp = t;
	} else {
		tmp = t * (x / y);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if ((x / y) <= (-5d+29)) then
        tmp = y * (t / y)
    else if ((x / y) <= 2d-8) then
        tmp = t
    else
        tmp = t * (x / y)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if ((x / y) <= -5e+29) {
		tmp = y * (t / y);
	} else if ((x / y) <= 2e-8) {
		tmp = t;
	} else {
		tmp = t * (x / y);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (x / y) <= -5e+29:
		tmp = y * (t / y)
	elif (x / y) <= 2e-8:
		tmp = t
	else:
		tmp = t * (x / y)
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (Float64(x / y) <= -5e+29)
		tmp = Float64(y * Float64(t / y));
	elseif (Float64(x / y) <= 2e-8)
		tmp = t;
	else
		tmp = Float64(t * Float64(x / y));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((x / y) <= -5e+29)
		tmp = y * (t / y);
	elseif ((x / y) <= 2e-8)
		tmp = t;
	else
		tmp = t * (x / y);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[N[(x / y), $MachinePrecision], -5e+29], N[(y * N[(t / y), $MachinePrecision]), $MachinePrecision], If[LessEqual[N[(x / y), $MachinePrecision], 2e-8], t, N[(t * N[(x / y), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if (/.f64 x y) < -5.0000000000000001e29

   1. Initial program 96.5%

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

   3. Taylor expanded in z around 0 46.9%

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

      1. mul-1-neg 46.9%

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

      2. *-commutative 46.9%

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

      3. associate-/l* 46.8%

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

      4. distribute-rgt-neg-in 46.8%

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

      5. distribute-neg-frac2 46.8%

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

   5. Simplified 46.8%

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

   6. Taylor expanded in y around 0 46.9%

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

      1. neg-mul-1 46.9%

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

      2. +-commutative 46.9%

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

      3. distribute-rgt-neg-in 46.9%

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

      4. distribute-lft-out 46.9%

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

      5. unsub-neg 46.9%

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

   8. Simplified 46.9%

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

   9. Taylor expanded in y around inf 5.1%

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

       1. *-commutative 5.1%

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

   11. Simplified 5.1%

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

       1. associate-/l* 13.1%

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

       2. *-commutative 13.1%

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

   13. Applied egg-rr 13.1%

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

   if -5.0000000000000001e29 < (/.f64 x y) < 2e-8

   1. Initial program 99.8%

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

   3. Taylor expanded in x around 0 74.7%

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

   if 2e-8 < (/.f64 x y)

   1. Initial program 96.9%

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

   3. Taylor expanded in z around 0 45.9%

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

      1. mul-1-neg 45.9%

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

      2. *-commutative 45.9%

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

      3. associate-/l* 43.2%

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

      4. distribute-rgt-neg-in 43.2%

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

      5. distribute-neg-frac2 43.2%

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

   5. Simplified 43.2%

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

   6. Taylor expanded in y around 0 41.1%

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

      1. neg-mul-1 41.1%

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

      2. +-commutative 41.1%

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

      3. distribute-rgt-neg-in 41.1%

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

      4. distribute-lft-out 46.0%

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

      5. unsub-neg 46.0%

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

   8. Simplified 46.0%

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

   9. Taylor expanded in y around 0 46.0%

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

       1. associate-*r* 46.0%

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

       2. neg-mul-1 46.0%

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

       3. *-commutative 46.0%

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

   11. Simplified 46.0%

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

       1. frac-2neg 46.0%

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

       2. distribute-rgt-neg-out 46.0%

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

       3. remove-double-neg 46.0%

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

       4. associate-*l/ 50.5%

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

       5. add-sqr-sqrt 32.6%

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

       6. sqrt-unprod 33.5%

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

       7. sqr-neg 33.5%

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

       8. sqrt-unprod 5.5%

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

       9. add-sqr-sqrt 14.1%

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

   13. Applied egg-rr 14.1%

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

4. Final simplification 45.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{x}{y} \leq -5 \cdot 10^{+29}:\\ \;\;\;\;y \cdot \frac{t}{y}\\ \mathbf{elif}\;\frac{x}{y} \leq 2 \cdot 10^{-8}:\\ \;\;\;\;t\\ \mathbf{else}:\\ \;\;\;\;t \cdot \frac{x}{y}\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 43.8% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;\frac{x}{y} \leq -5 \cdot 10^{+29}:\\ \;\;\;\;y \cdot \frac{t}{y}\\ \mathbf{elif}\;\frac{x}{y} \leq 2 \cdot 10^{-8}:\\ \;\;\;\;t\\ \mathbf{else}:\\ \;\;\;\;\frac{t}{\frac{y}{x}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= (/ x y) -5e+29) (* y (/ t y)) (if (<= (/ x y) 2e-8) t (/ t (/ y x)))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((x / y) <= -5e+29) {
		tmp = y * (t / y);
	} else if ((x / y) <= 2e-8) {
		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) <= (-5d+29)) then
        tmp = y * (t / y)
    else if ((x / y) <= 2d-8) 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) <= -5e+29) {
		tmp = y * (t / y);
	} else if ((x / y) <= 2e-8) {
		tmp = t;
	} else {
		tmp = t / (y / x);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (x / y) <= -5e+29:
		tmp = y * (t / y)
	elif (x / y) <= 2e-8:
		tmp = t
	else:
		tmp = t / (y / x)
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (Float64(x / y) <= -5e+29)
		tmp = Float64(y * Float64(t / y));
	elseif (Float64(x / y) <= 2e-8)
		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) <= -5e+29)
		tmp = y * (t / y);
	elseif ((x / y) <= 2e-8)
		tmp = t;
	else
		tmp = t / (y / x);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[N[(x / y), $MachinePrecision], -5e+29], N[(y * N[(t / y), $MachinePrecision]), $MachinePrecision], If[LessEqual[N[(x / y), $MachinePrecision], 2e-8], t, N[(t / N[(y / x), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if (/.f64 x y) < -5.0000000000000001e29

   1. Initial program 96.5%

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

   3. Taylor expanded in z around 0 46.9%

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

      1. mul-1-neg 46.9%

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

      2. *-commutative 46.9%

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

      3. associate-/l* 46.8%

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

      4. distribute-rgt-neg-in 46.8%

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

      5. distribute-neg-frac2 46.8%

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

   5. Simplified 46.8%

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

   6. Taylor expanded in y around 0 46.9%

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

      1. neg-mul-1 46.9%

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

      2. +-commutative 46.9%

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

      3. distribute-rgt-neg-in 46.9%

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

      4. distribute-lft-out 46.9%

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

      5. unsub-neg 46.9%

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

   8. Simplified 46.9%

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

   9. Taylor expanded in y around inf 5.1%

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

       1. *-commutative 5.1%

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

   11. Simplified 5.1%

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

       1. associate-/l* 13.1%

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

       2. *-commutative 13.1%

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

   13. Applied egg-rr 13.1%

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

   if -5.0000000000000001e29 < (/.f64 x y) < 2e-8

   1. Initial program 99.8%

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

   3. Taylor expanded in x around 0 74.7%

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

   if 2e-8 < (/.f64 x y)

   1. Initial program 96.9%

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

   3. Taylor expanded in z around 0 45.9%

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

      1. mul-1-neg 45.9%

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

      2. unsub-neg 45.9%

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

      3. *-rgt-identity 45.9%

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

      4. associate-/l* 53.1%

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

      5. distribute-lft-out-- 53.1%

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

   5. Simplified 53.1%

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

   6. Taylor expanded in x around inf 50.5%

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

      1. mul-1-neg 50.5%

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

      2. distribute-frac-neg2 50.5%

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

   8. Simplified 50.5%

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

      1. clear-num 50.5%

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

      2. un-div-inv 51.5%

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

      3. add-sqr-sqrt 33.6%

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

      4. sqrt-unprod 34.6%

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

      5. sqr-neg 34.6%

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

      6. sqrt-unprod 5.5%

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

      7. add-sqr-sqrt 14.1%

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

   10. Applied egg-rr 14.1%

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

4. Final simplification 45.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{x}{y} \leq -5 \cdot 10^{+29}:\\ \;\;\;\;y \cdot \frac{t}{y}\\ \mathbf{elif}\;\frac{x}{y} \leq 2 \cdot 10^{-8}:\\ \;\;\;\;t\\ \mathbf{else}:\\ \;\;\;\;\frac{t}{\frac{y}{x}}\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 83.7% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -2.6 \cdot 10^{-53} \lor \neg \left(z \leq 5.8 \cdot 10^{-109}\right):\\ \;\;\;\;t + x \cdot \frac{z}{y}\\ \mathbf{else}:\\ \;\;\;\;t \cdot \left(1 - \frac{x}{y}\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= z -2.6e-53) (not (<= z 5.8e-109)))
   (+ t (* x (/ z y)))
   (* t (- 1.0 (/ x y)))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((z <= -2.6e-53) || !(z <= 5.8e-109)) {
		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 <= (-2.6d-53)) .or. (.not. (z <= 5.8d-109))) 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 <= -2.6e-53) || !(z <= 5.8e-109)) {
		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 <= -2.6e-53) or not (z <= 5.8e-109):
		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 <= -2.6e-53) || !(z <= 5.8e-109))
		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 <= -2.6e-53) || ~((z <= 5.8e-109)))
		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, -2.6e-53], N[Not[LessEqual[z, 5.8e-109]], $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 < -2.59999999999999996e-53 or 5.8e-109 < z

   1. Initial program 99.7%

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

   3. Taylor expanded in z around inf 78.1%

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

      1. associate-/l* 79.4%

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

   5. Simplified 79.4%

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

   if -2.59999999999999996e-53 < z < 5.8e-109

   1. Initial program 96.3%

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

   3. Taylor expanded in z around 0 85.2%

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

      1. mul-1-neg 85.2%

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

      2. unsub-neg 85.2%

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

      3. *-rgt-identity 85.2%

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

      4. associate-/l* 92.1%

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

      5. distribute-lft-out-- 92.1%

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

   5. Simplified 92.1%

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

4. Final simplification 84.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -2.6 \cdot 10^{-53} \lor \neg \left(z \leq 5.8 \cdot 10^{-109}\right):\\ \;\;\;\;t + x \cdot \frac{z}{y}\\ \mathbf{else}:\\ \;\;\;\;t \cdot \left(1 - \frac{x}{y}\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 85.9% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -2.8 \cdot 10^{-53} \lor \neg \left(z \leq 2 \cdot 10^{-109}\right):\\ \;\;\;\;t + z \cdot \frac{x}{y}\\ \mathbf{else}:\\ \;\;\;\;t \cdot \left(1 - \frac{x}{y}\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= z -2.8e-53) (not (<= z 2e-109)))
   (+ t (* z (/ x y)))
   (* t (- 1.0 (/ x y)))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((z <= -2.8e-53) || !(z <= 2e-109)) {
		tmp = t + (z * (x / 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 <= (-2.8d-53)) .or. (.not. (z <= 2d-109))) then
        tmp = t + (z * (x / 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 <= -2.8e-53) || !(z <= 2e-109)) {
		tmp = t + (z * (x / y));
	} else {
		tmp = t * (1.0 - (x / y));
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (z <= -2.8e-53) or not (z <= 2e-109):
		tmp = t + (z * (x / y))
	else:
		tmp = t * (1.0 - (x / y))
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((z <= -2.8e-53) || !(z <= 2e-109))
		tmp = Float64(t + Float64(z * Float64(x / 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 <= -2.8e-53) || ~((z <= 2e-109)))
		tmp = t + (z * (x / y));
	else
		tmp = t * (1.0 - (x / y));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[z, -2.8e-53], N[Not[LessEqual[z, 2e-109]], $MachinePrecision]], N[(t + N[(z * N[(x / 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 < -2.79999999999999985e-53 or 2e-109 < z

   1. Initial program 99.7%

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

   3. Taylor expanded in z around inf 78.1%

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

      1. associate-/l* 79.4%

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

   5. Simplified 79.4%

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

      1. *-commutative 79.4%

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

      2. associate-/r/ 85.9%

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

   7. Applied egg-rr 85.9%

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

      1. div-inv 85.8%

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

      2. clear-num 85.8%

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

      3. *-commutative 85.8%

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

   9. Applied egg-rr 85.8%

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

   if -2.79999999999999985e-53 < z < 2e-109

   1. Initial program 96.3%

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

   3. Taylor expanded in z around 0 85.2%

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

      1. mul-1-neg 85.2%

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

      2. unsub-neg 85.2%

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

      3. *-rgt-identity 85.2%

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

      4. associate-/l* 92.1%

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

      5. distribute-lft-out-- 92.1%

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

   5. Simplified 92.1%

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

4. Final simplification 88.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -2.8 \cdot 10^{-53} \lor \neg \left(z \leq 2 \cdot 10^{-109}\right):\\ \;\;\;\;t + z \cdot \frac{x}{y}\\ \mathbf{else}:\\ \;\;\;\;t \cdot \left(1 - \frac{x}{y}\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 85.9% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -7.4 \cdot 10^{-54} \lor \neg \left(z \leq 6.6 \cdot 10^{-110}\right):\\ \;\;\;\;t + \frac{z}{\frac{y}{x}}\\ \mathbf{else}:\\ \;\;\;\;t \cdot \left(1 - \frac{x}{y}\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= z -7.4e-54) (not (<= z 6.6e-110)))
   (+ t (/ z (/ y x)))
   (* t (- 1.0 (/ x y)))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((z <= -7.4e-54) || !(z <= 6.6e-110)) {
		tmp = t + (z / (y / x));
	} 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 <= (-7.4d-54)) .or. (.not. (z <= 6.6d-110))) then
        tmp = t + (z / (y / x))
    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 <= -7.4e-54) || !(z <= 6.6e-110)) {
		tmp = t + (z / (y / x));
	} else {
		tmp = t * (1.0 - (x / y));
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (z <= -7.4e-54) or not (z <= 6.6e-110):
		tmp = t + (z / (y / x))
	else:
		tmp = t * (1.0 - (x / y))
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((z <= -7.4e-54) || !(z <= 6.6e-110))
		tmp = Float64(t + Float64(z / Float64(y / x)));
	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 <= -7.4e-54) || ~((z <= 6.6e-110)))
		tmp = t + (z / (y / x));
	else
		tmp = t * (1.0 - (x / y));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[z, -7.4e-54], N[Not[LessEqual[z, 6.6e-110]], $MachinePrecision]], N[(t + N[(z / N[(y / x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(t * N[(1.0 - N[(x / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -7.4000000000000006e-54 or 6.5999999999999998e-110 < z

   1. Initial program 99.7%

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

   3. Taylor expanded in z around inf 78.1%

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

      1. associate-/l* 79.4%

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

   5. Simplified 79.4%

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

      1. *-commutative 79.4%

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

      2. associate-/r/ 85.9%

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

   7. Applied egg-rr 85.9%

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

   if -7.4000000000000006e-54 < z < 6.5999999999999998e-110

   1. Initial program 96.3%

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

   3. Taylor expanded in z around 0 85.2%

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

      1. mul-1-neg 85.2%

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

      2. unsub-neg 85.2%

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

      3. *-rgt-identity 85.2%

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

      4. associate-/l* 92.1%

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

      5. distribute-lft-out-- 92.1%

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

   5. Simplified 92.1%

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

4. Final simplification 88.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -7.4 \cdot 10^{-54} \lor \neg \left(z \leq 6.6 \cdot 10^{-110}\right):\\ \;\;\;\;t + \frac{z}{\frac{y}{x}}\\ \mathbf{else}:\\ \;\;\;\;t \cdot \left(1 - \frac{x}{y}\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 86.0% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -7.5 \cdot 10^{-54} \lor \neg \left(z \leq 8.8 \cdot 10^{-110}\right):\\ \;\;\;\;t + \frac{z}{\frac{y}{x}}\\ \mathbf{else}:\\ \;\;\;\;t - \frac{t}{\frac{y}{x}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= z -7.5e-54) (not (<= z 8.8e-110)))
   (+ t (/ z (/ y x)))
   (- t (/ t (/ y x)))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((z <= -7.5e-54) || !(z <= 8.8e-110)) {
		tmp = t + (z / (y / x));
	} else {
		tmp = t - (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 ((z <= (-7.5d-54)) .or. (.not. (z <= 8.8d-110))) then
        tmp = t + (z / (y / x))
    else
        tmp = t - (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 ((z <= -7.5e-54) || !(z <= 8.8e-110)) {
		tmp = t + (z / (y / x));
	} else {
		tmp = t - (t / (y / x));
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (z <= -7.5e-54) or not (z <= 8.8e-110):
		tmp = t + (z / (y / x))
	else:
		tmp = t - (t / (y / x))
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((z <= -7.5e-54) || !(z <= 8.8e-110))
		tmp = Float64(t + Float64(z / Float64(y / x)));
	else
		tmp = Float64(t - Float64(t / Float64(y / x)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((z <= -7.5e-54) || ~((z <= 8.8e-110)))
		tmp = t + (z / (y / x));
	else
		tmp = t - (t / (y / x));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[z, -7.5e-54], N[Not[LessEqual[z, 8.8e-110]], $MachinePrecision]], N[(t + N[(z / N[(y / x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(t - N[(t / N[(y / x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -7.5000000000000005e-54 or 8.7999999999999997e-110 < z

   1. Initial program 99.7%

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

   3. Taylor expanded in z around inf 78.1%

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

      1. associate-/l* 79.4%

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

   5. Simplified 79.4%

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

      1. *-commutative 79.4%

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

      2. associate-/r/ 85.9%

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

   7. Applied egg-rr 85.9%

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

   if -7.5000000000000005e-54 < z < 8.7999999999999997e-110

   1. Initial program 96.3%

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

   3. Taylor expanded in z around 0 85.2%

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

      1. mul-1-neg 85.2%

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

      2. *-commutative 85.2%

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

      3. associate-/l* 87.7%

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

      4. distribute-rgt-neg-in 87.7%

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

      5. distribute-neg-frac2 87.7%

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

   5. Simplified 87.7%

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

      1. *-commutative 34.2%

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

      2. add-sqr-sqrt 21.6%

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

      3. sqrt-unprod 20.1%

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

      4. sqr-neg 20.1%

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

      5. sqrt-unprod 1.5%

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

      6. add-sqr-sqrt 3.1%

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

      7. associate-/r/ 3.9%

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

      8. frac-2neg 3.9%

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

      9. distribute-neg-frac 3.9%

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

      10. add-sqr-sqrt 2.4%

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

      11. sqrt-unprod 11.0%

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

      12. sqr-neg 11.0%

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

      13. sqrt-unprod 13.3%

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

      14. add-sqr-sqrt 36.5%

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

   7. Applied egg-rr 92.7%

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

4. Final simplification 88.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -7.5 \cdot 10^{-54} \lor \neg \left(z \leq 8.8 \cdot 10^{-110}\right):\\ \;\;\;\;t + \frac{z}{\frac{y}{x}}\\ \mathbf{else}:\\ \;\;\;\;t - \frac{t}{\frac{y}{x}}\\ \end{array} \]
5. Add Preprocessing

Alternative 10: 41.2% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -3 \cdot 10^{-116}:\\ \;\;\;\;t\\ \mathbf{elif}\;y \leq 7 \cdot 10^{-220}:\\ \;\;\;\;y \cdot \frac{t}{y}\\ \mathbf{else}:\\ \;\;\;\;t\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= y -3e-116) t (if (<= y 7e-220) (* y (/ t y)) t)))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (y <= -3e-116) {
		tmp = t;
	} else if (y <= 7e-220) {
		tmp = y * (t / y);
	} else {
		tmp = t;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if (y <= (-3d-116)) then
        tmp = t
    else if (y <= 7d-220) then
        tmp = y * (t / y)
    else
        tmp = t
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if (y <= -3e-116) {
		tmp = t;
	} else if (y <= 7e-220) {
		tmp = y * (t / y);
	} else {
		tmp = t;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if y <= -3e-116:
		tmp = t
	elif y <= 7e-220:
		tmp = y * (t / y)
	else:
		tmp = t
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (y <= -3e-116)
		tmp = t;
	elseif (y <= 7e-220)
		tmp = Float64(y * Float64(t / y));
	else
		tmp = t;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (y <= -3e-116)
		tmp = t;
	elseif (y <= 7e-220)
		tmp = y * (t / y);
	else
		tmp = t;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[y, -3e-116], t, If[LessEqual[y, 7e-220], N[(y * N[(t / y), $MachinePrecision]), $MachinePrecision], t]]

Derivation

1. Split input into 2 regimes

2. if y < -3.00000000000000026e-116 or 6.99999999999999975e-220 < y

   1. Initial program 98.3%

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

   3. Taylor expanded in x around 0 51.9%

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

   if -3.00000000000000026e-116 < y < 6.99999999999999975e-220

   1. Initial program 98.3%

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

   3. Taylor expanded in z around 0 50.1%

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

      1. mul-1-neg 50.1%

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

      2. *-commutative 50.1%

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

      3. associate-/l* 39.7%

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

      4. distribute-rgt-neg-in 39.7%

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

      5. distribute-neg-frac2 39.7%

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

   5. Simplified 39.7%

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

   6. Taylor expanded in y around 0 50.0%

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

      1. neg-mul-1 50.0%

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

      2. +-commutative 50.0%

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

      3. distribute-rgt-neg-in 50.0%

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

      4. distribute-lft-out 50.0%

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

      5. unsub-neg 50.0%

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

   8. Simplified 50.0%

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

   9. Taylor expanded in y around inf 3.0%

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

       1. *-commutative 3.0%

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

   11. Simplified 3.0%

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

       1. associate-/l* 19.4%

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

       2. *-commutative 19.4%

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

   13. Applied egg-rr 19.4%

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

4. Final simplification 43.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -3 \cdot 10^{-116}:\\ \;\;\;\;t\\ \mathbf{elif}\;y \leq 7 \cdot 10^{-220}:\\ \;\;\;\;y \cdot \frac{t}{y}\\ \mathbf{else}:\\ \;\;\;\;t\\ \end{array} \]
5. Add Preprocessing

Alternative 11: 97.6% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 98.3%

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

3. Final simplification 98.3%

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

Alternative 12: 65.5% 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 98.3%

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

3. Taylor expanded in z around 0 59.1%

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

   1. mul-1-neg 59.1%

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

   2. unsub-neg 59.1%

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

   3. *-rgt-identity 59.1%

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

   4. associate-/l* 64.6%

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

   5. distribute-lft-out-- 64.6%

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

5. Simplified 64.6%

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

6. Final simplification 64.6%

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

Alternative 13: 38.5% 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 98.3%

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

3. Taylor expanded in x around 0 39.8%

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

4. Final simplification 39.8%

   \[\leadsto t \]
5. Add Preprocessing

Developer target: 97.1% 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 2024067 
(FPCore (x y z t)
  :name "Numeric.Signal.Multichannel:$cget from hsignal-0.2.7.1"
  :precision binary64

  :alt
  (if (< z 2.759456554562692e-282) (+ (* (/ x y) (- z t)) t) (if (< z 2.326994450874436e-110) (+ (* x (/ (- z t) y)) t) (+ (* (/ x y) (- z t)) t)))

  (+ (* (/ x y) (- z t)) t))