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

Percentage Accurate: 97.8% → 97.8%

Time: 7.9s

Alternatives: 11

Speedup: 1.0×

• 24.8% 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: 97.8% 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: 97.8% accurate, 0.1× speedup

Math

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

FPCore

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

C

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

Julia

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

Wolfram

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

Derivation

1. Initial program 98.8%

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

   1. fma-def 98.8%

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

3. Simplified 98.8%

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

4. Final simplification 98.8%

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

Alternative 2: 76.6% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;\frac{x}{y} \leq -2 \cdot 10^{+151}:\\ \;\;\;\;\frac{x}{y} \cdot \left(-t\right)\\ \mathbf{elif}\;\frac{x}{y} \leq 0.0002 \lor \neg \left(\frac{x}{y} \leq 2 \cdot 10^{+67}\right):\\ \;\;\;\;t + \frac{x}{y} \cdot z\\ \mathbf{else}:\\ \;\;\;\;\frac{t}{\frac{-y}{x}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= (/ x y) -2e+151)
   (* (/ x y) (- t))
   (if (or (<= (/ x y) 0.0002) (not (<= (/ x y) 2e+67)))
     (+ t (* (/ x y) z))
     (/ t (/ (- y) x)))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((x / y) <= -2e+151) {
		tmp = (x / y) * -t;
	} else if (((x / y) <= 0.0002) || !((x / y) <= 2e+67)) {
		tmp = t + ((x / y) * z);
	} else {
		tmp = t / (-y / x);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if ((x / y) <= (-2d+151)) then
        tmp = (x / y) * -t
    else if (((x / y) <= 0.0002d0) .or. (.not. ((x / y) <= 2d+67))) then
        tmp = t + ((x / y) * z)
    else
        tmp = t / (-y / x)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if ((x / y) <= -2e+151) {
		tmp = (x / y) * -t;
	} else if (((x / y) <= 0.0002) || !((x / y) <= 2e+67)) {
		tmp = t + ((x / y) * z);
	} else {
		tmp = t / (-y / x);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (x / y) <= -2e+151:
		tmp = (x / y) * -t
	elif ((x / y) <= 0.0002) or not ((x / y) <= 2e+67):
		tmp = t + ((x / y) * z)
	else:
		tmp = t / (-y / x)
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (Float64(x / y) <= -2e+151)
		tmp = Float64(Float64(x / y) * Float64(-t));
	elseif ((Float64(x / y) <= 0.0002) || !(Float64(x / y) <= 2e+67))
		tmp = Float64(t + Float64(Float64(x / y) * z));
	else
		tmp = Float64(t / Float64(Float64(-y) / x));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((x / y) <= -2e+151)
		tmp = (x / y) * -t;
	elseif (((x / y) <= 0.0002) || ~(((x / y) <= 2e+67)))
		tmp = t + ((x / y) * z);
	else
		tmp = t / (-y / x);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[N[(x / y), $MachinePrecision], -2e+151], N[(N[(x / y), $MachinePrecision] * (-t)), $MachinePrecision], If[Or[LessEqual[N[(x / y), $MachinePrecision], 0.0002], N[Not[LessEqual[N[(x / y), $MachinePrecision], 2e+67]], $MachinePrecision]], N[(t + N[(N[(x / y), $MachinePrecision] * z), $MachinePrecision]), $MachinePrecision], N[(t / N[((-y) / x), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if (/.f64 x y) < -2.00000000000000003e151

   1. Initial program 97.5%

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

      1. associate-*l/ 97.5%

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

      2. *-commutative 97.5%

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

      3. associate-*l/ 97.5%

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

      4. *-commutative 97.5%

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

      5. fma-def 97.5%

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

   3. Simplified 97.5%

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

   4. Taylor expanded in z around 0 58.6%

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

      1. mul-1-neg 58.6%

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

      2. unsub-neg 58.6%

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

      3. associate-/l* 61.1%

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

      4. associate-/r/ 58.6%

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

   6. Simplified 58.6%

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

      1. associate-*l/ 58.6%

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

      2. associate-/l* 61.1%

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

   8. Applied egg-rr 61.1%

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

   9. Taylor expanded in y around 0 58.6%

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

       1. mul-1-neg 58.6%

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

       2. associate-*r/ 61.1%

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

       3. distribute-rgt-neg-in 61.1%

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

       4. distribute-neg-frac 61.1%

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

       5. neg-mul-1 61.1%

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

       6. metadata-eval 61.1%

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

       7. associate-/r/ 61.1%

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

       8. associate-/r* 61.0%

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

       9. associate-*l/ 61.0%

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

       10. neg-mul-1 61.0%

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

       11. associate-*r/ 61.1%

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

       12. *-rgt-identity 61.1%

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

       13. associate-/r/ 58.6%

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

       14. *-commutative 58.6%

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

   11. Simplified 58.6%

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

   12. Taylor expanded in x around 0 58.6%

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

       1. associate-*r/ 61.1%

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

       2. associate-*r* 61.1%

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

       3. neg-mul-1 61.1%

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

   14. Simplified 61.1%

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

   if -2.00000000000000003e151 < (/.f64 x y) < 2.0000000000000001e-4 or 1.99999999999999997e67 < (/.f64 x y)

   1. Initial program 99.0%

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

   2. Taylor expanded in z around inf 83.8%

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

      1. associate-/l* 88.1%

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

   4. Simplified 88.1%

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

      1. clear-num 88.1%

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

      2. associate-/r/ 88.1%

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

      3. clear-num 88.1%

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

   6. Applied egg-rr 88.1%

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

   if 2.0000000000000001e-4 < (/.f64 x y) < 1.99999999999999997e67

   1. Initial program 99.6%

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

      1. associate-*l/ 88.2%

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

      2. *-commutative 88.2%

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

      3. associate-*l/ 88.0%

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

      4. *-commutative 88.0%

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

      5. fma-def 88.0%

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

   3. Simplified 88.0%

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

   4. Taylor expanded in z around 0 63.8%

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

      1. mul-1-neg 63.8%

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

      2. unsub-neg 63.8%

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

      3. associate-/l* 69.6%

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

      4. associate-/r/ 63.9%

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

   6. Simplified 63.9%

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

      1. associate-*l/ 63.8%

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

      2. associate-/l* 69.6%

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

   8. Applied egg-rr 69.6%

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

   9. Taylor expanded in y around 0 61.5%

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

       1. mul-1-neg 61.5%

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

       2. associate-*r/ 63.9%

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

       3. distribute-rgt-neg-in 63.9%

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

       4. distribute-neg-frac 63.9%

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

       5. neg-mul-1 63.9%

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

       6. metadata-eval 63.9%

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

       7. associate-/r/ 63.9%

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

       8. associate-/r* 63.9%

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

       9. associate-*l/ 63.8%

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

       10. neg-mul-1 63.8%

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

       11. associate-*r/ 64.0%

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

       12. *-rgt-identity 64.0%

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

       13. associate-/r/ 58.4%

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

       14. *-commutative 58.4%

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

   11. Simplified 58.4%

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

       1. associate-*r/ 61.5%

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

       2. remove-double-neg 61.5%

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

       3. distribute-rgt-neg-out 61.5%

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

       4. neg-mul-1 61.5%

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

       5. associate-/r* 61.5%

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

       6. distribute-rgt-neg-out 61.5%

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

       7. remove-double-neg 61.5%

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

   13. Applied egg-rr 61.5%

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

       1. associate-/l/ 61.5%

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

       2. *-commutative 61.5%

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

       3. associate-/l* 64.0%

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

       4. *-commutative 64.0%

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

       5. neg-mul-1 64.0%

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

   15. Simplified 64.0%

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

4. Final simplification 82.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{x}{y} \leq -2 \cdot 10^{+151}:\\ \;\;\;\;\frac{x}{y} \cdot \left(-t\right)\\ \mathbf{elif}\;\frac{x}{y} \leq 0.0002 \lor \neg \left(\frac{x}{y} \leq 2 \cdot 10^{+67}\right):\\ \;\;\;\;t + \frac{x}{y} \cdot z\\ \mathbf{else}:\\ \;\;\;\;\frac{t}{\frac{-y}{x}}\\ \end{array} \]

Alternative 3: 76.6% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;\frac{x}{y} \leq -2 \cdot 10^{+151}:\\ \;\;\;\;\frac{x}{y} \cdot \left(-t\right)\\ \mathbf{elif}\;\frac{x}{y} \leq 0.0002:\\ \;\;\;\;t + \frac{z}{\frac{y}{x}}\\ \mathbf{elif}\;\frac{x}{y} \leq 2 \cdot 10^{+67}:\\ \;\;\;\;\frac{t}{\frac{-y}{x}}\\ \mathbf{else}:\\ \;\;\;\;t + \frac{x}{y} \cdot z\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= (/ x y) -2e+151)
   (* (/ x y) (- t))
   (if (<= (/ x y) 0.0002)
     (+ t (/ z (/ y x)))
     (if (<= (/ x y) 2e+67) (/ t (/ (- y) x)) (+ t (* (/ x y) z))))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((x / y) <= -2e+151) {
		tmp = (x / y) * -t;
	} else if ((x / y) <= 0.0002) {
		tmp = t + (z / (y / x));
	} else if ((x / y) <= 2e+67) {
		tmp = t / (-y / x);
	} else {
		tmp = t + ((x / y) * z);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if ((x / y) <= (-2d+151)) then
        tmp = (x / y) * -t
    else if ((x / y) <= 0.0002d0) then
        tmp = t + (z / (y / x))
    else if ((x / y) <= 2d+67) then
        tmp = t / (-y / x)
    else
        tmp = t + ((x / y) * z)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if ((x / y) <= -2e+151) {
		tmp = (x / y) * -t;
	} else if ((x / y) <= 0.0002) {
		tmp = t + (z / (y / x));
	} else if ((x / y) <= 2e+67) {
		tmp = t / (-y / x);
	} else {
		tmp = t + ((x / y) * z);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (x / y) <= -2e+151:
		tmp = (x / y) * -t
	elif (x / y) <= 0.0002:
		tmp = t + (z / (y / x))
	elif (x / y) <= 2e+67:
		tmp = t / (-y / x)
	else:
		tmp = t + ((x / y) * z)
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (Float64(x / y) <= -2e+151)
		tmp = Float64(Float64(x / y) * Float64(-t));
	elseif (Float64(x / y) <= 0.0002)
		tmp = Float64(t + Float64(z / Float64(y / x)));
	elseif (Float64(x / y) <= 2e+67)
		tmp = Float64(t / Float64(Float64(-y) / x));
	else
		tmp = Float64(t + Float64(Float64(x / y) * z));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((x / y) <= -2e+151)
		tmp = (x / y) * -t;
	elseif ((x / y) <= 0.0002)
		tmp = t + (z / (y / x));
	elseif ((x / y) <= 2e+67)
		tmp = t / (-y / x);
	else
		tmp = t + ((x / y) * z);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[N[(x / y), $MachinePrecision], -2e+151], N[(N[(x / y), $MachinePrecision] * (-t)), $MachinePrecision], If[LessEqual[N[(x / y), $MachinePrecision], 0.0002], N[(t + N[(z / N[(y / x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[N[(x / y), $MachinePrecision], 2e+67], N[(t / N[((-y) / x), $MachinePrecision]), $MachinePrecision], N[(t + N[(N[(x / y), $MachinePrecision] * z), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 4 regimes

2. if (/.f64 x y) < -2.00000000000000003e151

   1. Initial program 97.5%

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

      1. associate-*l/ 97.5%

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

      2. *-commutative 97.5%

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

      3. associate-*l/ 97.5%

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

      4. *-commutative 97.5%

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

      5. fma-def 97.5%

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

   3. Simplified 97.5%

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

   4. Taylor expanded in z around 0 58.6%

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

      1. mul-1-neg 58.6%

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

      2. unsub-neg 58.6%

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

      3. associate-/l* 61.1%

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

      4. associate-/r/ 58.6%

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

   6. Simplified 58.6%

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

      1. associate-*l/ 58.6%

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

      2. associate-/l* 61.1%

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

   8. Applied egg-rr 61.1%

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

   9. Taylor expanded in y around 0 58.6%

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

       1. mul-1-neg 58.6%

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

       2. associate-*r/ 61.1%

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

       3. distribute-rgt-neg-in 61.1%

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

       4. distribute-neg-frac 61.1%

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

       5. neg-mul-1 61.1%

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

       6. metadata-eval 61.1%

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

       7. associate-/r/ 61.1%

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

       8. associate-/r* 61.0%

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

       9. associate-*l/ 61.0%

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

       10. neg-mul-1 61.0%

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

       11. associate-*r/ 61.1%

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

       12. *-rgt-identity 61.1%

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

       13. associate-/r/ 58.6%

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

       14. *-commutative 58.6%

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

   11. Simplified 58.6%

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

   12. Taylor expanded in x around 0 58.6%

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

       1. associate-*r/ 61.1%

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

       2. associate-*r* 61.1%

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

       3. neg-mul-1 61.1%

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

   14. Simplified 61.1%

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

   if -2.00000000000000003e151 < (/.f64 x y) < 2.0000000000000001e-4

   1. Initial program 99.3%

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

   2. Taylor expanded in z around inf 90.1%

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

      1. associate-/l* 94.7%

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

   4. Simplified 94.7%

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

   if 2.0000000000000001e-4 < (/.f64 x y) < 1.99999999999999997e67

   1. Initial program 99.6%

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

      1. associate-*l/ 88.2%

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

      2. *-commutative 88.2%

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

      3. associate-*l/ 88.0%

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

      4. *-commutative 88.0%

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

      5. fma-def 88.0%

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

   3. Simplified 88.0%

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

   4. Taylor expanded in z around 0 63.8%

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

      1. mul-1-neg 63.8%

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

      2. unsub-neg 63.8%

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

      3. associate-/l* 69.6%

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

      4. associate-/r/ 63.9%

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

   6. Simplified 63.9%

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

      1. associate-*l/ 63.8%

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

      2. associate-/l* 69.6%

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

   8. Applied egg-rr 69.6%

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

   9. Taylor expanded in y around 0 61.5%

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

       1. mul-1-neg 61.5%

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

       2. associate-*r/ 63.9%

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

       3. distribute-rgt-neg-in 63.9%

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

       4. distribute-neg-frac 63.9%

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

       5. neg-mul-1 63.9%

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

       6. metadata-eval 63.9%

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

       7. associate-/r/ 63.9%

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

       8. associate-/r* 63.9%

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

       9. associate-*l/ 63.8%

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

       10. neg-mul-1 63.8%

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

       11. associate-*r/ 64.0%

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

       12. *-rgt-identity 64.0%

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

       13. associate-/r/ 58.4%

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

       14. *-commutative 58.4%

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

   11. Simplified 58.4%

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

       1. associate-*r/ 61.5%

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

       2. remove-double-neg 61.5%

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

       3. distribute-rgt-neg-out 61.5%

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

       4. neg-mul-1 61.5%

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

       5. associate-/r* 61.5%

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

       6. distribute-rgt-neg-out 61.5%

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

       7. remove-double-neg 61.5%

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

   13. Applied egg-rr 61.5%

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

       1. associate-/l/ 61.5%

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

       2. *-commutative 61.5%

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

       3. associate-/l* 64.0%

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

       4. *-commutative 64.0%

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

       5. neg-mul-1 64.0%

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

   15. Simplified 64.0%

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

   if 1.99999999999999997e67 < (/.f64 x y)

   1. Initial program 98.0%

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

   2. Taylor expanded in z around inf 63.3%

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

      1. associate-/l* 67.2%

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

   4. Simplified 67.2%

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

      1. clear-num 67.2%

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

      2. associate-/r/ 67.2%

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

      3. clear-num 67.2%

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

   6. Applied egg-rr 67.2%

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

4. Final simplification 82.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{x}{y} \leq -2 \cdot 10^{+151}:\\ \;\;\;\;\frac{x}{y} \cdot \left(-t\right)\\ \mathbf{elif}\;\frac{x}{y} \leq 0.0002:\\ \;\;\;\;t + \frac{z}{\frac{y}{x}}\\ \mathbf{elif}\;\frac{x}{y} \leq 2 \cdot 10^{+67}:\\ \;\;\;\;\frac{t}{\frac{-y}{x}}\\ \mathbf{else}:\\ \;\;\;\;t + \frac{x}{y} \cdot z\\ \end{array} \]

Alternative 4: 61.9% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;\frac{x}{y} \leq -2 \cdot 10^{+14} \lor \neg \left(\frac{x}{y} \leq 0.0002\right):\\ \;\;\;\;x \cdot \frac{t}{-y}\\ \mathbf{else}:\\ \;\;\;\;t\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= (/ x y) -2e+14) (not (<= (/ x y) 0.0002))) (* x (/ t (- y))) t))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (((x / y) <= -2e+14) || !((x / y) <= 0.0002)) {
		tmp = x * (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 (((x / y) <= (-2d+14)) .or. (.not. ((x / y) <= 0.0002d0))) then
        tmp = x * (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 (((x / y) <= -2e+14) || !((x / y) <= 0.0002)) {
		tmp = x * (t / -y);
	} else {
		tmp = t;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if ((x / y) <= -2e+14) or not ((x / y) <= 0.0002):
		tmp = x * (t / -y)
	else:
		tmp = t
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((Float64(x / y) <= -2e+14) || !(Float64(x / y) <= 0.0002))
		tmp = Float64(x * Float64(t / Float64(-y)));
	else
		tmp = t;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (((x / y) <= -2e+14) || ~(((x / y) <= 0.0002)))
		tmp = x * (t / -y);
	else
		tmp = t;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[N[(x / y), $MachinePrecision], -2e+14], N[Not[LessEqual[N[(x / y), $MachinePrecision], 0.0002]], $MachinePrecision]], N[(x * N[(t / (-y)), $MachinePrecision]), $MachinePrecision], t]

Derivation

1. Split input into 2 regimes

2. if (/.f64 x y) < -2e14 or 2.0000000000000001e-4 < (/.f64 x y)

   1. Initial program 98.4%

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

      1. associate-*l/ 94.7%

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

      2. *-commutative 94.7%

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

      3. associate-*l/ 94.6%

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

      4. *-commutative 94.6%

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

      5. fma-def 94.6%

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

   3. Simplified 94.6%

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

   4. Taylor expanded in z around 0 47.7%

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

      1. mul-1-neg 47.7%

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

      2. unsub-neg 47.7%

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

      3. associate-/l* 52.1%

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

      4. associate-/r/ 48.4%

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

   6. Simplified 48.4%

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

      1. associate-*l/ 47.7%

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

      2. associate-/l* 52.1%

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

   8. Applied egg-rr 52.1%

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

   9. Taylor expanded in y around 0 47.4%

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

       1. mul-1-neg 47.4%

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

       2. associate-*r/ 51.4%

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

       3. distribute-rgt-neg-in 51.4%

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

       4. distribute-neg-frac 51.4%

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

       5. neg-mul-1 51.4%

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

       6. metadata-eval 51.4%

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

       7. associate-/r/ 51.4%

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

       8. associate-/r* 51.3%

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

       9. associate-*l/ 51.3%

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

       10. neg-mul-1 51.3%

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

       11. associate-*r/ 51.4%

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

       12. *-rgt-identity 51.4%

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

       13. associate-/r/ 47.7%

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

       14. *-commutative 47.7%

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

   11. Simplified 47.7%

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

   if -2e14 < (/.f64 x y) < 2.0000000000000001e-4

   1. Initial program 99.2%

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

      1. associate-*l/ 91.5%

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

      2. *-commutative 91.5%

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

      3. associate-*l/ 90.4%

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

      4. *-commutative 90.4%

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

      5. fma-def 90.4%

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

   3. Simplified 90.4%

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

   4. Taylor expanded in x around 0 73.5%

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

4. Final simplification 60.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{x}{y} \leq -2 \cdot 10^{+14} \lor \neg \left(\frac{x}{y} \leq 0.0002\right):\\ \;\;\;\;x \cdot \frac{t}{-y}\\ \mathbf{else}:\\ \;\;\;\;t\\ \end{array} \]

Alternative 5: 63.8% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;\frac{x}{y} \leq -2 \cdot 10^{+14} \lor \neg \left(\frac{x}{y} \leq 0.0002\right):\\ \;\;\;\;\frac{x}{y} \cdot \left(-t\right)\\ \mathbf{else}:\\ \;\;\;\;t\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= (/ x y) -2e+14) (not (<= (/ x y) 0.0002))) (* (/ x y) (- t)) t))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (((x / y) <= -2e+14) || !((x / y) <= 0.0002)) {
		tmp = (x / y) * -t;
	} else {
		tmp = t;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if (((x / y) <= (-2d+14)) .or. (.not. ((x / y) <= 0.0002d0))) then
        tmp = (x / y) * -t
    else
        tmp = t
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if (((x / y) <= -2e+14) || !((x / y) <= 0.0002)) {
		tmp = (x / y) * -t;
	} else {
		tmp = t;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if ((x / y) <= -2e+14) or not ((x / y) <= 0.0002):
		tmp = (x / y) * -t
	else:
		tmp = t
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((Float64(x / y) <= -2e+14) || !(Float64(x / y) <= 0.0002))
		tmp = Float64(Float64(x / y) * Float64(-t));
	else
		tmp = t;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (((x / y) <= -2e+14) || ~(((x / y) <= 0.0002)))
		tmp = (x / y) * -t;
	else
		tmp = t;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[N[(x / y), $MachinePrecision], -2e+14], N[Not[LessEqual[N[(x / y), $MachinePrecision], 0.0002]], $MachinePrecision]], N[(N[(x / y), $MachinePrecision] * (-t)), $MachinePrecision], t]

Derivation

1. Split input into 2 regimes

2. if (/.f64 x y) < -2e14 or 2.0000000000000001e-4 < (/.f64 x y)

   1. Initial program 98.4%

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

      1. associate-*l/ 94.7%

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

      2. *-commutative 94.7%

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

      3. associate-*l/ 94.6%

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

      4. *-commutative 94.6%

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

      5. fma-def 94.6%

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

   3. Simplified 94.6%

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

   4. Taylor expanded in z around 0 47.7%

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

      1. mul-1-neg 47.7%

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

      2. unsub-neg 47.7%

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

      3. associate-/l* 52.1%

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

      4. associate-/r/ 48.4%

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

   6. Simplified 48.4%

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

      1. associate-*l/ 47.7%

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

      2. associate-/l* 52.1%

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

   8. Applied egg-rr 52.1%

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

   9. Taylor expanded in y around 0 47.4%

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

       1. mul-1-neg 47.4%

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

       2. associate-*r/ 51.4%

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

       3. distribute-rgt-neg-in 51.4%

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

       4. distribute-neg-frac 51.4%

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

       5. neg-mul-1 51.4%

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

       6. metadata-eval 51.4%

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

       7. associate-/r/ 51.4%

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

       8. associate-/r* 51.3%

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

       9. associate-*l/ 51.3%

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

       10. neg-mul-1 51.3%

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

       11. associate-*r/ 51.4%

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

       12. *-rgt-identity 51.4%

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

       13. associate-/r/ 47.7%

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

       14. *-commutative 47.7%

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

   11. Simplified 47.7%

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

   12. Taylor expanded in x around 0 47.4%

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

       1. associate-*r/ 51.4%

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

       2. associate-*r* 51.4%

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

       3. neg-mul-1 51.4%

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

   14. Simplified 51.4%

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

   if -2e14 < (/.f64 x y) < 2.0000000000000001e-4

   1. Initial program 99.2%

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

      1. associate-*l/ 91.5%

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

      2. *-commutative 91.5%

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

      3. associate-*l/ 90.4%

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

      4. *-commutative 90.4%

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

      5. fma-def 90.4%

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

   3. Simplified 90.4%

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

   4. Taylor expanded in x around 0 73.5%

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

4. Final simplification 62.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{x}{y} \leq -2 \cdot 10^{+14} \lor \neg \left(\frac{x}{y} \leq 0.0002\right):\\ \;\;\;\;\frac{x}{y} \cdot \left(-t\right)\\ \mathbf{else}:\\ \;\;\;\;t\\ \end{array} \]

Alternative 6: 63.8% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;\frac{x}{y} \leq -2 \cdot 10^{+14} \lor \neg \left(\frac{x}{y} \leq 0.0002\right):\\ \;\;\;\;\frac{t}{\frac{-y}{x}}\\ \mathbf{else}:\\ \;\;\;\;t\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= (/ x y) -2e+14) (not (<= (/ x y) 0.0002))) (/ t (/ (- y) x)) t))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (((x / y) <= -2e+14) || !((x / y) <= 0.0002)) {
		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) <= (-2d+14)) .or. (.not. ((x / y) <= 0.0002d0))) 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) <= -2e+14) || !((x / y) <= 0.0002)) {
		tmp = t / (-y / x);
	} else {
		tmp = t;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if ((x / y) <= -2e+14) or not ((x / y) <= 0.0002):
		tmp = t / (-y / x)
	else:
		tmp = t
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((Float64(x / y) <= -2e+14) || !(Float64(x / y) <= 0.0002))
		tmp = Float64(t / Float64(Float64(-y) / x));
	else
		tmp = t;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (((x / y) <= -2e+14) || ~(((x / y) <= 0.0002)))
		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], -2e+14], N[Not[LessEqual[N[(x / y), $MachinePrecision], 0.0002]], $MachinePrecision]], N[(t / N[((-y) / x), $MachinePrecision]), $MachinePrecision], t]

Derivation

1. Split input into 2 regimes

2. if (/.f64 x y) < -2e14 or 2.0000000000000001e-4 < (/.f64 x y)

   1. Initial program 98.4%

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

      1. associate-*l/ 94.7%

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

      2. *-commutative 94.7%

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

      3. associate-*l/ 94.6%

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

      4. *-commutative 94.6%

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

      5. fma-def 94.6%

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

   3. Simplified 94.6%

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

   4. Taylor expanded in z around 0 47.7%

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

      1. mul-1-neg 47.7%

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

      2. unsub-neg 47.7%

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

      3. associate-/l* 52.1%

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

      4. associate-/r/ 48.4%

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

   6. Simplified 48.4%

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

      1. associate-*l/ 47.7%

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

      2. associate-/l* 52.1%

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

   8. Applied egg-rr 52.1%

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

   9. Taylor expanded in y around 0 47.4%

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

       1. mul-1-neg 47.4%

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

       2. associate-*r/ 51.4%

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

       3. distribute-rgt-neg-in 51.4%

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

       4. distribute-neg-frac 51.4%

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

       5. neg-mul-1 51.4%

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

       6. metadata-eval 51.4%

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

       7. associate-/r/ 51.4%

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

       8. associate-/r* 51.3%

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

       9. associate-*l/ 51.3%

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

       10. neg-mul-1 51.3%

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

       11. associate-*r/ 51.4%

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

       12. *-rgt-identity 51.4%

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

       13. associate-/r/ 47.7%

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

       14. *-commutative 47.7%

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

   11. Simplified 47.7%

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

       1. associate-*r/ 47.4%

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

       2. remove-double-neg 47.4%

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

       3. distribute-rgt-neg-out 47.4%

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

       4. neg-mul-1 47.4%

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

       5. associate-/r* 47.4%

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

       6. distribute-rgt-neg-out 47.4%

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

       7. remove-double-neg 47.4%

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

   13. Applied egg-rr 47.4%

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

       1. associate-/l/ 47.4%

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

       2. *-commutative 47.4%

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

       3. associate-/l* 51.4%

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

       4. *-commutative 51.4%

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

       5. neg-mul-1 51.4%

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

   15. Simplified 51.4%

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

   if -2e14 < (/.f64 x y) < 2.0000000000000001e-4

   1. Initial program 99.2%

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

      1. associate-*l/ 91.5%

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

      2. *-commutative 91.5%

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

      3. associate-*l/ 90.4%

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

      4. *-commutative 90.4%

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

      5. fma-def 90.4%

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

   3. Simplified 90.4%

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

   4. Taylor expanded in x around 0 73.5%

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

4. Final simplification 62.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{x}{y} \leq -2 \cdot 10^{+14} \lor \neg \left(\frac{x}{y} \leq 0.0002\right):\\ \;\;\;\;\frac{t}{\frac{-y}{x}}\\ \mathbf{else}:\\ \;\;\;\;t\\ \end{array} \]

Alternative 7: 82.5% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -3 \cdot 10^{-26} \lor \neg \left(t \leq 1.4 \cdot 10^{+93}\right):\\ \;\;\;\;t - x \cdot \frac{t}{y}\\ \mathbf{else}:\\ \;\;\;\;t + \frac{z}{\frac{y}{x}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= t -3e-26) (not (<= t 1.4e+93)))
   (- t (* x (/ t y)))
   (+ t (/ z (/ y x)))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((t <= -3e-26) || !(t <= 1.4e+93)) {
		tmp = t - (x * (t / y));
	} else {
		tmp = t + (z / (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 ((t <= (-3d-26)) .or. (.not. (t <= 1.4d+93))) then
        tmp = t - (x * (t / y))
    else
        tmp = t + (z / (y / x))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if ((t <= -3e-26) || !(t <= 1.4e+93)) {
		tmp = t - (x * (t / y));
	} else {
		tmp = t + (z / (y / x));
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (t <= -3e-26) or not (t <= 1.4e+93):
		tmp = t - (x * (t / y))
	else:
		tmp = t + (z / (y / x))
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((t <= -3e-26) || !(t <= 1.4e+93))
		tmp = Float64(t - Float64(x * Float64(t / y)));
	else
		tmp = Float64(t + Float64(z / Float64(y / x)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((t <= -3e-26) || ~((t <= 1.4e+93)))
		tmp = t - (x * (t / y));
	else
		tmp = t + (z / (y / x));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[t, -3e-26], N[Not[LessEqual[t, 1.4e+93]], $MachinePrecision]], N[(t - N[(x * N[(t / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(t + N[(z / N[(y / x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if t < -3.00000000000000012e-26 or 1.39999999999999994e93 < t

   1. Initial program 99.9%

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

      1. associate-*l/ 89.4%

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

      2. *-commutative 89.4%

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

      3. associate-*l/ 92.9%

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

      4. *-commutative 92.9%

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

      5. fma-def 92.9%

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

   3. Simplified 92.9%

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

   4. Taylor expanded in z around 0 82.2%

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

      1. mul-1-neg 82.2%

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

      2. unsub-neg 82.2%

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

      3. associate-/l* 91.1%

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

      4. associate-/r/ 89.4%

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

   6. Simplified 89.4%

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

   if -3.00000000000000012e-26 < t < 1.39999999999999994e93

   1. Initial program 98.0%

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

   2. Taylor expanded in z around inf 85.6%

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

      1. associate-/l* 88.8%

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

   4. Simplified 88.8%

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

4. Final simplification 89.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -3 \cdot 10^{-26} \lor \neg \left(t \leq 1.4 \cdot 10^{+93}\right):\\ \;\;\;\;t - x \cdot \frac{t}{y}\\ \mathbf{else}:\\ \;\;\;\;t + \frac{z}{\frac{y}{x}}\\ \end{array} \]

Alternative 8: 83.9% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -1.2 \cdot 10^{-24}:\\ \;\;\;\;t - x \cdot \frac{t}{y}\\ \mathbf{elif}\;t \leq 440000:\\ \;\;\;\;t + \frac{z}{\frac{y}{x}}\\ \mathbf{else}:\\ \;\;\;\;t - \frac{t}{\frac{y}{x}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= t -1.2e-24)
   (- t (* x (/ t y)))
   (if (<= t 440000.0) (+ t (/ z (/ y x))) (- t (/ t (/ y x))))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (t <= -1.2e-24) {
		tmp = t - (x * (t / y));
	} else if (t <= 440000.0) {
		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 (t <= (-1.2d-24)) then
        tmp = t - (x * (t / y))
    else if (t <= 440000.0d0) 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 (t <= -1.2e-24) {
		tmp = t - (x * (t / y));
	} else if (t <= 440000.0) {
		tmp = t + (z / (y / x));
	} else {
		tmp = t - (t / (y / x));
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if t <= -1.2e-24:
		tmp = t - (x * (t / y))
	elif t <= 440000.0:
		tmp = t + (z / (y / x))
	else:
		tmp = t - (t / (y / x))
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (t <= -1.2e-24)
		tmp = Float64(t - Float64(x * Float64(t / y)));
	elseif (t <= 440000.0)
		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 (t <= -1.2e-24)
		tmp = t - (x * (t / y));
	elseif (t <= 440000.0)
		tmp = t + (z / (y / x));
	else
		tmp = t - (t / (y / x));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[t, -1.2e-24], N[(t - N[(x * N[(t / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 440000.0], 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 3 regimes

2. if t < -1.1999999999999999e-24

   1. Initial program 100.0%

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

      1. associate-*l/ 88.2%

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

      2. *-commutative 88.2%

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

      3. associate-*l/ 97.0%

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

      4. *-commutative 97.0%

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

      5. fma-def 97.0%

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

   3. Simplified 97.0%

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

   4. Taylor expanded in z around 0 81.4%

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

      1. mul-1-neg 81.4%

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

      2. unsub-neg 81.4%

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

      3. associate-/l* 91.7%

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

      4. associate-/r/ 93.1%

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

   6. Simplified 93.1%

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

   if -1.1999999999999999e-24 < t < 4.4e5

   1. Initial program 97.8%

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

   2. Taylor expanded in z around inf 87.8%

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

      1. associate-/l* 90.6%

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

   4. Simplified 90.6%

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

   if 4.4e5 < t

   1. Initial program 99.9%

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

      1. associate-*l/ 93.2%

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

      2. *-commutative 93.2%

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

      3. associate-*l/ 88.4%

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

      4. *-commutative 88.4%

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

      5. fma-def 88.4%

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

   3. Simplified 88.4%

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

   4. Taylor expanded in z around 0 81.7%

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

      1. mul-1-neg 81.7%

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

      2. unsub-neg 81.7%

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

      3. associate-/l* 86.8%

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

      4. associate-/r/ 80.3%

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

   6. Simplified 80.3%

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

      1. associate-*l/ 81.7%

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

      2. associate-/l* 86.8%

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

   8. Applied egg-rr 86.8%

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

4. Final simplification 90.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -1.2 \cdot 10^{-24}:\\ \;\;\;\;t - x \cdot \frac{t}{y}\\ \mathbf{elif}\;t \leq 440000:\\ \;\;\;\;t + \frac{z}{\frac{y}{x}}\\ \mathbf{else}:\\ \;\;\;\;t - \frac{t}{\frac{y}{x}}\\ \end{array} \]

Alternative 9: 39.4% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;\frac{x}{y} \leq -1 \cdot 10^{+239}:\\ \;\;\;\;\frac{x}{y} \cdot t\\ \mathbf{else}:\\ \;\;\;\;t\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= (/ x y) -1e+239) (* (/ x y) t) t))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((x / y) <= -1e+239) {
		tmp = (x / y) * t;
	} else {
		tmp = t;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if ((x / y) <= (-1d+239)) then
        tmp = (x / y) * t
    else
        tmp = t
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if ((x / y) <= -1e+239) {
		tmp = (x / y) * t;
	} else {
		tmp = t;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (x / y) <= -1e+239:
		tmp = (x / y) * t
	else:
		tmp = t
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (Float64(x / y) <= -1e+239)
		tmp = Float64(Float64(x / y) * t);
	else
		tmp = t;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((x / y) <= -1e+239)
		tmp = (x / y) * t;
	else
		tmp = t;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[N[(x / y), $MachinePrecision], -1e+239], N[(N[(x / y), $MachinePrecision] * t), $MachinePrecision], t]

Derivation

1. Split input into 2 regimes

2. if (/.f64 x y) < -9.99999999999999991e238

   1. Initial program 96.1%

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

      1. associate-*l/ 99.9%

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

      2. *-commutative 99.9%

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

      3. associate-*l/ 99.9%

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

      4. *-commutative 99.9%

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

      5. fma-def 99.9%

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

   3. Simplified 99.9%

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

   4. Taylor expanded in z around 0 50.3%

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

      1. mul-1-neg 50.3%

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

      2. unsub-neg 50.3%

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

      3. associate-/l* 50.3%

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

      4. associate-/r/ 50.2%

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

   6. Simplified 50.2%

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

      1. associate-*l/ 50.3%

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

      2. associate-/l* 50.3%

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

   8. Applied egg-rr 50.3%

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

   9. Taylor expanded in y around 0 50.3%

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

       1. associate-*r/ 50.3%

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

       2. *-commutative 50.3%

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

       3. neg-mul-1 50.3%

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

       4. distribute-rgt-neg-in 50.3%

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

   11. Simplified 50.3%

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

       1. associate-/l* 50.3%

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

       2. associate-/r/ 50.3%

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

       3. add-sqr-sqrt 25.3%

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

       4. sqrt-unprod 42.3%

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

       5. sqr-neg 42.3%

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

       6. sqrt-unprod 25.2%

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

       7. add-sqr-sqrt 30.0%

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

   13. Applied egg-rr 30.0%

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

   if -9.99999999999999991e238 < (/.f64 x y)

   1. Initial program 99.1%

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

      1. associate-*l/ 92.3%

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

      2. *-commutative 92.3%

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

      3. associate-*l/ 91.7%

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

      4. *-commutative 91.7%

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

      5. fma-def 91.7%

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

   3. Simplified 91.7%

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

   4. Taylor expanded in x around 0 42.3%

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

4. Final simplification 41.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{x}{y} \leq -1 \cdot 10^{+239}:\\ \;\;\;\;\frac{x}{y} \cdot t\\ \mathbf{else}:\\ \;\;\;\;t\\ \end{array} \]

Alternative 10: 97.8% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 98.8%

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

2. Final simplification 98.8%

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

Alternative 11: 38.2% accurate, 9.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 98.8%

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

   1. associate-*l/ 93.1%

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

   2. *-commutative 93.1%

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

   3. associate-*l/ 92.5%

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

   4. *-commutative 92.5%

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

   5. fma-def 92.5%

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

3. Simplified 92.5%

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

4. Taylor expanded in x around 0 38.6%

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

5. Final simplification 38.6%

   \[\leadsto t \]

Developer target: 97.6% accurate, 0.7× 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 2023185 
(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))