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

Percentage Accurate: 97.8% → 97.8%

Time: 6.7s

Alternatives: 10

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, 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 97.3%

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

2. Final simplification 97.3%

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

Alternative 2: 92.7% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;\frac{x}{y} \leq -1 \cdot 10^{+35} \lor \neg \left(\frac{x}{y} \leq 10^{-9}\right):\\ \;\;\;\;x \cdot \left(\frac{z}{y} - \frac{t}{y}\right)\\ \mathbf{else}:\\ \;\;\;\;t + \frac{z}{\frac{y}{x}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= (/ x y) -1e+35) (not (<= (/ x y) 1e-9)))
   (* x (- (/ z y) (/ t y)))
   (+ t (/ z (/ y x)))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (((x / y) <= -1e+35) || !((x / y) <= 1e-9)) {
		tmp = x * ((z / y) - (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 (((x / y) <= (-1d+35)) .or. (.not. ((x / y) <= 1d-9))) then
        tmp = x * ((z / y) - (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 (((x / y) <= -1e+35) || !((x / y) <= 1e-9)) {
		tmp = x * ((z / y) - (t / y));
	} else {
		tmp = t + (z / (y / x));
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if ((x / y) <= -1e+35) or not ((x / y) <= 1e-9):
		tmp = x * ((z / y) - (t / y))
	else:
		tmp = t + (z / (y / x))
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((Float64(x / y) <= -1e+35) || !(Float64(x / y) <= 1e-9))
		tmp = Float64(x * Float64(Float64(z / y) - 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 (((x / y) <= -1e+35) || ~(((x / y) <= 1e-9)))
		tmp = x * ((z / y) - (t / y));
	else
		tmp = t + (z / (y / x));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[N[(x / y), $MachinePrecision], -1e+35], N[Not[LessEqual[N[(x / y), $MachinePrecision], 1e-9]], $MachinePrecision]], N[(x * N[(N[(z / y), $MachinePrecision] - 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 (/.f64 x y) < -9.9999999999999997e34 or 1.00000000000000006e-9 < (/.f64 x y)

   1. Initial program 97.5%

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

      1. associate-*l/ 95.1%

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

      2. *-commutative 95.1%

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

      3. associate-*l/ 94.4%

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

      4. *-commutative 94.4%

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

      5. fma-def 94.4%

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

   3. Simplified 94.4%

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

   4. Taylor expanded in x around inf 91.8%

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

   if -9.9999999999999997e34 < (/.f64 x y) < 1.00000000000000006e-9

   1. Initial program 97.2%

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

   2. Taylor expanded in z around inf 94.6%

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

      1. associate-/l* 96.0%

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

   4. Simplified 96.0%

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

4. Final simplification 94.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{x}{y} \leq -1 \cdot 10^{+35} \lor \neg \left(\frac{x}{y} \leq 10^{-9}\right):\\ \;\;\;\;x \cdot \left(\frac{z}{y} - \frac{t}{y}\right)\\ \mathbf{else}:\\ \;\;\;\;t + \frac{z}{\frac{y}{x}}\\ \end{array} \]

Alternative 3: 63.8% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;\frac{x}{y} \leq -2 \cdot 10^{+29} \lor \neg \left(\frac{x}{y} \leq 10\right):\\ \;\;\;\;t \cdot \frac{-x}{y}\\ \mathbf{else}:\\ \;\;\;\;t\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= (/ x y) -2e+29) (not (<= (/ x y) 10.0))) (* t (/ (- x) y)) t))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (((x / y) <= -2e+29) || !((x / y) <= 10.0)) {
		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) <= (-2d+29)) .or. (.not. ((x / y) <= 10.0d0))) 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) <= -2e+29) || !((x / y) <= 10.0)) {
		tmp = t * (-x / y);
	} else {
		tmp = t;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if ((x / y) <= -2e+29) or not ((x / y) <= 10.0):
		tmp = t * (-x / y)
	else:
		tmp = t
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((Float64(x / y) <= -2e+29) || !(Float64(x / y) <= 10.0))
		tmp = Float64(t * Float64(Float64(-x) / y));
	else
		tmp = t;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (((x / y) <= -2e+29) || ~(((x / y) <= 10.0)))
		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], -2e+29], N[Not[LessEqual[N[(x / y), $MachinePrecision], 10.0]], $MachinePrecision]], N[(t * N[((-x) / y), $MachinePrecision]), $MachinePrecision], t]

Derivation

1. Split input into 2 regimes

2. if (/.f64 x y) < -1.99999999999999983e29 or 10 < (/.f64 x y)

   1. Initial program 97.5%

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

      1. associate-*l/ 95.8%

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

      2. *-commutative 95.8%

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

      3. associate-*l/ 94.3%

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

      4. *-commutative 94.3%

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

      5. fma-def 94.3%

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

   3. Simplified 94.3%

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

   4. Taylor expanded in z around 0 49.9%

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

      1. mul-1-neg 49.9%

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

      2. unsub-neg 49.9%

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

      3. associate-/l* 54.5%

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

      4. associate-/r/ 50.0%

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

   6. Simplified 50.0%

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

   7. Taylor expanded in t around 0 49.9%

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

      1. associate-*r/ 54.0%

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

   9. Simplified 54.0%

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

   10. Taylor expanded in x around inf 49.9%

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

       1. associate-*l/ 50.0%

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

       2. associate-*r* 50.0%

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

       3. neg-mul-1 50.0%

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

       4. *-commutative 50.0%

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

       5. *-rgt-identity 50.0%

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

       6. *-commutative 50.0%

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

       7. metadata-eval 50.0%

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

       8. times-frac 50.0%

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

       9. neg-mul-1 50.0%

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

       10. neg-mul-1 50.0%

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

       11. distribute-frac-neg 50.0%

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

       12. remove-double-neg 50.0%

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

   12. Simplified 50.0%

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

   13. Taylor expanded in x around 0 49.9%

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

       1. mul-1-neg 49.9%

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

       2. associate-*r/ 54.0%

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

       3. distribute-rgt-neg-in 54.0%

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

       4. distribute-neg-frac 54.0%

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

   15. Simplified 54.0%

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

   if -1.99999999999999983e29 < (/.f64 x y) < 10

   1. Initial program 97.2%

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

      1. associate-*l/ 90.9%

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

      2. *-commutative 90.9%

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

      3. associate-*l/ 93.2%

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

      4. *-commutative 93.2%

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

      5. fma-def 93.2%

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

   3. Simplified 93.2%

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

   4. Taylor expanded in x around 0 69.1%

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

4. Final simplification 62.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{x}{y} \leq -2 \cdot 10^{+29} \lor \neg \left(\frac{x}{y} \leq 10\right):\\ \;\;\;\;t \cdot \frac{-x}{y}\\ \mathbf{else}:\\ \;\;\;\;t\\ \end{array} \]

Alternative 4: 41.8% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;\frac{x}{y} \leq -4 \cdot 10^{+234} \lor \neg \left(\frac{x}{y} \leq 5 \cdot 10^{+30}\right):\\ \;\;\;\;\frac{x}{y} \cdot t\\ \mathbf{else}:\\ \;\;\;\;t\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= (/ x y) -4e+234) (not (<= (/ x y) 5e+30))) (* (/ x y) t) t))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (((x / y) <= -4e+234) || !((x / y) <= 5e+30)) {
		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) <= (-4d+234)) .or. (.not. ((x / y) <= 5d+30))) 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) <= -4e+234) || !((x / y) <= 5e+30)) {
		tmp = (x / y) * t;
	} else {
		tmp = t;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if ((x / y) <= -4e+234) or not ((x / y) <= 5e+30):
		tmp = (x / y) * t
	else:
		tmp = t
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((Float64(x / y) <= -4e+234) || !(Float64(x / y) <= 5e+30))
		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) <= -4e+234) || ~(((x / y) <= 5e+30)))
		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], -4e+234], N[Not[LessEqual[N[(x / y), $MachinePrecision], 5e+30]], $MachinePrecision]], N[(N[(x / y), $MachinePrecision] * t), $MachinePrecision], t]

Derivation

1. Split input into 2 regimes

2. if (/.f64 x y) < -4.00000000000000007e234 or 4.9999999999999998e30 < (/.f64 x y)

   1. Initial program 96.3%

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

      1. associate-*l/ 95.1%

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

      2. *-commutative 95.1%

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

      3. associate-*l/ 96.5%

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

      4. *-commutative 96.5%

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

      5. fma-def 96.5%

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

   3. Simplified 96.5%

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

   4. Taylor expanded in z around 0 47.3%

      \[\leadsto \color{blue}{t + -1 \cdot \frac{t \cdot x}{y}} \]
   5. 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. associate-/l* 52.8%

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

      4. associate-/r/ 47.5%

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

   6. Simplified 47.5%

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

   7. Taylor expanded in t around 0 47.3%

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

      1. associate-*r/ 52.1%

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

   9. Simplified 52.1%

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

   10. Taylor expanded in x around inf 47.3%

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

       1. associate-*l/ 47.5%

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

       2. associate-*r* 47.5%

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

       3. neg-mul-1 47.5%

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

       4. *-commutative 47.5%

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

       5. *-rgt-identity 47.5%

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

       6. *-commutative 47.5%

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

       7. metadata-eval 47.5%

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

       8. times-frac 47.5%

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

       9. neg-mul-1 47.5%

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

       10. neg-mul-1 47.5%

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

       11. distribute-frac-neg 47.5%

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

       12. remove-double-neg 47.5%

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

   12. Simplified 47.5%

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

       1. expm1-log1p-u 20.1%

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

       2. expm1-udef 20.1%

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

       3. log1p-udef 20.1%

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

       4. add-exp-log 47.5%

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

       5. add-sqr-sqrt 14.2%

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

       6. sqrt-unprod 22.6%

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

       7. sqr-neg 22.6%

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

       8. sqrt-unprod 8.4%

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

       9. add-sqr-sqrt 14.3%

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

   14. Applied egg-rr 14.3%

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

       1. +-commutative 14.3%

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

       2. associate--l+ 14.4%

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

       3. metadata-eval 14.4%

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

       4. +-rgt-identity 14.4%

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

       5. *-commutative 14.4%

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

       6. associate-*l/ 16.5%

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

       7. associate-*r/ 16.6%

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

   16. Simplified 16.6%

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

   if -4.00000000000000007e234 < (/.f64 x y) < 4.9999999999999998e30

   1. Initial program 97.8%

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

      1. associate-*l/ 92.2%

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

      2. *-commutative 92.2%

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

      3. associate-*l/ 92.4%

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

      4. *-commutative 92.4%

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

      5. fma-def 92.4%

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

   3. Simplified 92.4%

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

   4. Taylor expanded in x around 0 55.6%

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

4. Final simplification 43.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{x}{y} \leq -4 \cdot 10^{+234} \lor \neg \left(\frac{x}{y} \leq 5 \cdot 10^{+30}\right):\\ \;\;\;\;\frac{x}{y} \cdot t\\ \mathbf{else}:\\ \;\;\;\;t\\ \end{array} \]

Alternative 5: 41.2% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;\frac{x}{y} \leq -4 \cdot 10^{+234}:\\ \;\;\;\;\frac{x}{y} \cdot t\\ \mathbf{elif}\;\frac{x}{y} \leq 10^{-9}:\\ \;\;\;\;t\\ \mathbf{else}:\\ \;\;\;\;\frac{x \cdot t}{y}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= (/ x y) -4e+234)
   (* (/ x y) t)
   (if (<= (/ x y) 1e-9) t (/ (* x t) y))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((x / y) <= -4e+234) {
		tmp = (x / y) * t;
	} else if ((x / y) <= 1e-9) {
		tmp = t;
	} else {
		tmp = (x * t) / y;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if ((x / y) <= (-4d+234)) then
        tmp = (x / y) * t
    else if ((x / y) <= 1d-9) then
        tmp = t
    else
        tmp = (x * t) / y
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if ((x / y) <= -4e+234) {
		tmp = (x / y) * t;
	} else if ((x / y) <= 1e-9) {
		tmp = t;
	} else {
		tmp = (x * t) / y;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (x / y) <= -4e+234:
		tmp = (x / y) * t
	elif (x / y) <= 1e-9:
		tmp = t
	else:
		tmp = (x * t) / y
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (Float64(x / y) <= -4e+234)
		tmp = Float64(Float64(x / y) * t);
	elseif (Float64(x / y) <= 1e-9)
		tmp = t;
	else
		tmp = Float64(Float64(x * t) / y);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((x / y) <= -4e+234)
		tmp = (x / y) * t;
	elseif ((x / y) <= 1e-9)
		tmp = t;
	else
		tmp = (x * t) / y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[N[(x / y), $MachinePrecision], -4e+234], N[(N[(x / y), $MachinePrecision] * t), $MachinePrecision], If[LessEqual[N[(x / y), $MachinePrecision], 1e-9], t, N[(N[(x * t), $MachinePrecision] / y), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if (/.f64 x y) < -4.00000000000000007e234

   1. Initial program 89.5%

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

      1. associate-*l/ 99.8%

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

      2. *-commutative 99.8%

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

      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 56.1%

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

      1. mul-1-neg 56.1%

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

      2. unsub-neg 56.1%

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

      3. associate-/l* 58.4%

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

      4. associate-/r/ 56.2%

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

   6. Simplified 56.2%

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

   7. Taylor expanded in t around 0 56.1%

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

      1. associate-*r/ 56.3%

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

   9. Simplified 56.3%

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

   10. Taylor expanded in x around inf 56.1%

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

       1. associate-*l/ 56.2%

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

       2. associate-*r* 56.2%

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

       3. neg-mul-1 56.2%

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

       4. *-commutative 56.2%

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

       5. *-rgt-identity 56.2%

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

       6. *-commutative 56.2%

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

       7. metadata-eval 56.2%

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

       8. times-frac 56.2%

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

       9. neg-mul-1 56.2%

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

       10. neg-mul-1 56.2%

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

       11. distribute-frac-neg 56.2%

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

       12. remove-double-neg 56.2%

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

   12. Simplified 56.2%

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

       1. expm1-log1p-u 35.9%

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

       2. expm1-udef 35.9%

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

       3. log1p-udef 35.9%

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

       4. add-exp-log 56.2%

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

       5. add-sqr-sqrt 19.1%

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

       6. sqrt-unprod 34.1%

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

       7. sqr-neg 34.1%

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

       8. sqrt-unprod 8.5%

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

       9. add-sqr-sqrt 16.5%

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

   14. Applied egg-rr 16.5%

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

       1. +-commutative 16.5%

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

       2. associate--l+ 16.5%

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

       3. metadata-eval 16.5%

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

       4. +-rgt-identity 16.5%

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

       5. *-commutative 16.5%

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

       6. associate-*l/ 16.5%

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

       7. associate-*r/ 23.1%

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

   16. Simplified 23.1%

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

   if -4.00000000000000007e234 < (/.f64 x y) < 1.00000000000000006e-9

   1. Initial program 97.7%

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

      1. associate-*l/ 92.5%

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

      2. *-commutative 92.5%

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

      3. associate-*l/ 92.2%

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

      4. *-commutative 92.2%

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

      5. fma-def 92.2%

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

   3. Simplified 92.2%

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

   4. Taylor expanded in x around 0 57.5%

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

   if 1.00000000000000006e-9 < (/.f64 x y)

   1. Initial program 99.8%

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

      1. associate-*l/ 91.8%

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

      2. *-commutative 91.8%

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

      3. associate-*l/ 95.2%

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

      4. *-commutative 95.2%

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

      5. fma-def 95.2%

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

   3. Simplified 95.2%

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

   4. Taylor expanded in z around 0 41.9%

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

      1. mul-1-neg 41.9%

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

      2. unsub-neg 41.9%

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

      3. associate-/l* 48.5%

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

      4. associate-/r/ 42.2%

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

   6. Simplified 42.2%

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

   7. Taylor expanded in t around 0 41.9%

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

      1. associate-*r/ 48.5%

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

   9. Simplified 48.5%

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

   10. Taylor expanded in x around inf 41.9%

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

       1. associate-*l/ 42.2%

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

       2. associate-*r* 42.2%

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

       3. neg-mul-1 42.2%

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

       4. *-commutative 42.2%

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

       5. *-rgt-identity 42.2%

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

       6. *-commutative 42.2%

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

       7. metadata-eval 42.2%

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

       8. times-frac 42.2%

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

       9. neg-mul-1 42.2%

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

       10. neg-mul-1 42.2%

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

       11. distribute-frac-neg 42.2%

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

       12. remove-double-neg 42.2%

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

   12. Simplified 42.2%

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

       1. associate-*r/ 41.9%

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

       2. add-sqr-sqrt 9.1%

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

       3. sqrt-unprod 13.7%

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

       4. sqr-neg 13.7%

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

       5. sqrt-unprod 7.8%

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

       6. add-sqr-sqrt 15.2%

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

   14. Applied egg-rr 15.2%

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

4. Final simplification 44.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{x}{y} \leq -4 \cdot 10^{+234}:\\ \;\;\;\;\frac{x}{y} \cdot t\\ \mathbf{elif}\;\frac{x}{y} \leq 10^{-9}:\\ \;\;\;\;t\\ \mathbf{else}:\\ \;\;\;\;\frac{x \cdot t}{y}\\ \end{array} \]

Alternative 6: 86.1% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -15200:\\ \;\;\;\;t + \frac{z}{\frac{y}{x}}\\ \mathbf{elif}\;z \leq 1.1:\\ \;\;\;\;t - \frac{x}{y} \cdot t\\ \mathbf{else}:\\ \;\;\;\;t + \frac{x}{y} \cdot z\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= z -15200.0)
   (+ t (/ z (/ y x)))
   (if (<= z 1.1) (- t (* (/ x y) t)) (+ t (* (/ x y) z)))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (z <= -15200.0) {
		tmp = t + (z / (y / x));
	} else if (z <= 1.1) {
		tmp = t - ((x / y) * t);
	} else {
		tmp = t + ((x / y) * z);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if (z <= (-15200.0d0)) then
        tmp = t + (z / (y / x))
    else if (z <= 1.1d0) then
        tmp = t - ((x / y) * t)
    else
        tmp = t + ((x / y) * z)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if (z <= -15200.0) {
		tmp = t + (z / (y / x));
	} else if (z <= 1.1) {
		tmp = t - ((x / y) * t);
	} else {
		tmp = t + ((x / y) * z);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if z <= -15200.0:
		tmp = t + (z / (y / x))
	elif z <= 1.1:
		tmp = t - ((x / y) * t)
	else:
		tmp = t + ((x / y) * z)
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (z <= -15200.0)
		tmp = Float64(t + Float64(z / Float64(y / x)));
	elseif (z <= 1.1)
		tmp = Float64(t - Float64(Float64(x / y) * t));
	else
		tmp = Float64(t + Float64(Float64(x / y) * z));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (z <= -15200.0)
		tmp = t + (z / (y / x));
	elseif (z <= 1.1)
		tmp = t - ((x / y) * t);
	else
		tmp = t + ((x / y) * z);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[z, -15200.0], N[(t + N[(z / N[(y / x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 1.1], N[(t - N[(N[(x / y), $MachinePrecision] * t), $MachinePrecision]), $MachinePrecision], N[(t + N[(N[(x / y), $MachinePrecision] * z), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if z < -15200

   1. Initial program 96.1%

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

   2. Taylor expanded in z around inf 86.6%

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

      1. associate-/l* 88.1%

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

   4. Simplified 88.1%

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

   if -15200 < z < 1.1000000000000001

   1. Initial program 97.5%

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

      1. associate-*l/ 95.1%

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

      2. *-commutative 95.1%

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

      3. associate-*l/ 95.4%

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

      4. *-commutative 95.4%

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

      5. fma-def 95.4%

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

   3. Simplified 95.4%

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

   4. Taylor expanded in z around 0 82.3%

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

      1. mul-1-neg 82.3%

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

      2. unsub-neg 82.3%

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

      3. associate-/l* 86.8%

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

      4. associate-/r/ 83.9%

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

   6. Simplified 83.9%

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

   7. Taylor expanded in t around 0 82.3%

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

      1. associate-*r/ 86.3%

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

   9. Simplified 86.3%

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

   if 1.1000000000000001 < z

   1. Initial program 98.4%

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

   2. Taylor expanded in z around inf 89.9%

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

      1. associate-/l* 94.6%

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

   4. Simplified 94.6%

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

      1. clear-num 94.5%

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

      2. associate-/r/ 94.6%

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

      3. clear-num 94.7%

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

   6. Applied egg-rr 94.7%

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

4. Final simplification 88.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -15200:\\ \;\;\;\;t + \frac{z}{\frac{y}{x}}\\ \mathbf{elif}\;z \leq 1.1:\\ \;\;\;\;t - \frac{x}{y} \cdot t\\ \mathbf{else}:\\ \;\;\;\;t + \frac{x}{y} \cdot z\\ \end{array} \]

Alternative 7: 86.1% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -8000:\\ \;\;\;\;t + \frac{z}{\frac{y}{x}}\\ \mathbf{elif}\;z \leq 61000:\\ \;\;\;\;t - \frac{t}{\frac{y}{x}}\\ \mathbf{else}:\\ \;\;\;\;t + \frac{x}{y} \cdot z\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= z -8000.0)
   (+ t (/ z (/ y x)))
   (if (<= z 61000.0) (- t (/ t (/ y x))) (+ t (* (/ x y) z)))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (z <= -8000.0) {
		tmp = t + (z / (y / x));
	} else if (z <= 61000.0) {
		tmp = t - (t / (y / x));
	} else {
		tmp = t + ((x / y) * z);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if (z <= (-8000.0d0)) then
        tmp = t + (z / (y / x))
    else if (z <= 61000.0d0) then
        tmp = t - (t / (y / x))
    else
        tmp = t + ((x / y) * z)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if (z <= -8000.0) {
		tmp = t + (z / (y / x));
	} else if (z <= 61000.0) {
		tmp = t - (t / (y / x));
	} else {
		tmp = t + ((x / y) * z);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if z <= -8000.0:
		tmp = t + (z / (y / x))
	elif z <= 61000.0:
		tmp = t - (t / (y / x))
	else:
		tmp = t + ((x / y) * z)
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (z <= -8000.0)
		tmp = Float64(t + Float64(z / Float64(y / x)));
	elseif (z <= 61000.0)
		tmp = Float64(t - Float64(t / Float64(y / x)));
	else
		tmp = Float64(t + Float64(Float64(x / y) * z));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (z <= -8000.0)
		tmp = t + (z / (y / x));
	elseif (z <= 61000.0)
		tmp = t - (t / (y / x));
	else
		tmp = t + ((x / y) * z);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[z, -8000.0], N[(t + N[(z / N[(y / x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 61000.0], N[(t - N[(t / N[(y / x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(t + N[(N[(x / y), $MachinePrecision] * z), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if z < -8e3

   1. Initial program 96.1%

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

   2. Taylor expanded in z around inf 86.6%

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

      1. associate-/l* 88.1%

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

   4. Simplified 88.1%

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

   if -8e3 < z < 61000

   1. Initial program 97.5%

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

      1. associate-*l/ 95.1%

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

      2. *-commutative 95.1%

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

      3. associate-*l/ 95.4%

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

      4. *-commutative 95.4%

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

      5. fma-def 95.4%

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

   3. Simplified 95.4%

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

   4. Taylor expanded in z around 0 82.3%

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

      1. mul-1-neg 82.3%

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

      2. unsub-neg 82.3%

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

      3. associate-/l* 86.8%

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

      4. associate-/r/ 83.9%

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

   6. Simplified 83.9%

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

      1. associate-/r/ 86.8%

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

   8. Applied egg-rr 86.8%

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

   if 61000 < z

   1. Initial program 98.4%

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

   2. Taylor expanded in z around inf 89.9%

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

      1. associate-/l* 94.6%

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

   4. Simplified 94.6%

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

      1. clear-num 94.5%

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

      2. associate-/r/ 94.6%

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

      3. clear-num 94.7%

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

   6. Applied egg-rr 94.7%

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

4. Final simplification 89.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -8000:\\ \;\;\;\;t + \frac{z}{\frac{y}{x}}\\ \mathbf{elif}\;z \leq 61000:\\ \;\;\;\;t - \frac{t}{\frac{y}{x}}\\ \mathbf{else}:\\ \;\;\;\;t + \frac{x}{y} \cdot z\\ \end{array} \]

Alternative 8: 77.0% accurate, 1.3× speedup

Math

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

FPCore

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

C

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

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)
end function

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 97.3%

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

2. Taylor expanded in z around inf 78.5%

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

   1. associate-/l* 80.5%

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

4. Simplified 80.5%

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

   1. clear-num 80.4%

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

   2. associate-/r/ 80.4%

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

   3. clear-num 80.5%

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

6. Applied egg-rr 80.5%

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

7. Final simplification 80.5%

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

Alternative 9: 76.7% accurate, 1.3× speedup

Math

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

FPCore

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

C

double code(double x, double y, double z, double t) {
	return t + (z / (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 / (y / x))
end function

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 97.3%

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

2. Taylor expanded in z around inf 78.5%

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

   1. associate-/l* 80.5%

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

4. Simplified 80.5%

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

5. Final simplification 80.5%

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

Alternative 10: 38.8% accurate, 9.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 97.3%

   \[\frac{x}{y} \cdot \left(z - t\right) + t \]
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/ 93.7%

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

   4. *-commutative 93.7%

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

   5. fma-def 93.7%

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

3. Simplified 93.7%

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

4. Taylor expanded in x around 0 38.9%

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

5. Final simplification 38.9%

   \[\leadsto t \]

Developer target: 97.3% 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 2023230 
(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))