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

Percentage Accurate: 97.5% → 97.5%

Time: 6.0s

Alternatives: 10

Speedup: 1.0×

• 24.0% 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: 97.5% 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: 97.5% 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 96.9%

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

2. Final simplification 96.9%

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

Alternative 2: 64.6% accurate, 0.6× speedup

Math

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

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= (/ x y) -10.0) (not (<= (/ x y) 1e-7))) (* (/ x y) (- t)) t))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (((x / y) <= -10.0) || !((x / y) <= 1e-7)) {
		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) <= (-10.0d0)) .or. (.not. ((x / y) <= 1d-7))) 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) <= -10.0) || !((x / y) <= 1e-7)) {
		tmp = (x / y) * -t;
	} else {
		tmp = t;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if ((x / y) <= -10.0) or not ((x / y) <= 1e-7):
		tmp = (x / y) * -t
	else:
		tmp = t
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((Float64(x / y) <= -10.0) || !(Float64(x / y) <= 1e-7))
		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) <= -10.0) || ~(((x / y) <= 1e-7)))
		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], -10.0], N[Not[LessEqual[N[(x / y), $MachinePrecision], 1e-7]], $MachinePrecision]], N[(N[(x / y), $MachinePrecision] * (-t)), $MachinePrecision], t]

Derivation

1. Split input into 2 regimes

2. if (/.f64 x y) < -10 or 9.9999999999999995e-8 < (/.f64 x y)

   1. Initial program 95.5%

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

      1. fma-def 95.5%

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

   3. Simplified 95.5%

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

   4. Taylor expanded in z around 0 51.6%

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

      1. mul-1-neg 51.6%

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

      2. unsub-neg 51.6%

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

      3. *-rgt-identity 51.6%

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

      4. associate-*r/ 53.7%

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

      5. distribute-lft-out-- 53.7%

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

   6. Simplified 53.7%

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

   7. Taylor expanded in x around inf 53.4%

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

      1. mul-1-neg 53.4%

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

      2. distribute-frac-neg 53.4%

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

   9. Simplified 53.4%

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

   if -10 < (/.f64 x y) < 9.9999999999999995e-8

   1. Initial program 98.4%

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

      1. fma-def 98.4%

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

   3. Simplified 98.4%

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

   4. Taylor expanded in x around 0 66.7%

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

4. Final simplification 59.9%

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

Alternative 3: 63.8% accurate, 0.6× speedup

Math

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

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= (/ x y) -10.0)
   (* (/ x y) (- t))
   (if (<= (/ x y) 1e-7) t (* x (/ t (- y))))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((x / y) <= -10.0) {
		tmp = (x / y) * -t;
	} else if ((x / y) <= 1e-7) {
		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) <= (-10.0d0)) then
        tmp = (x / y) * -t
    else if ((x / y) <= 1d-7) 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) <= -10.0) {
		tmp = (x / y) * -t;
	} else if ((x / y) <= 1e-7) {
		tmp = t;
	} else {
		tmp = x * (t / -y);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (x / y) <= -10.0:
		tmp = (x / y) * -t
	elif (x / y) <= 1e-7:
		tmp = t
	else:
		tmp = x * (t / -y)
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (Float64(x / y) <= -10.0)
		tmp = Float64(Float64(x / y) * Float64(-t));
	elseif (Float64(x / y) <= 1e-7)
		tmp = t;
	else
		tmp = Float64(x * Float64(t / Float64(-y)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((x / y) <= -10.0)
		tmp = (x / y) * -t;
	elseif ((x / y) <= 1e-7)
		tmp = t;
	else
		tmp = x * (t / -y);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[N[(x / y), $MachinePrecision], -10.0], N[(N[(x / y), $MachinePrecision] * (-t)), $MachinePrecision], If[LessEqual[N[(x / y), $MachinePrecision], 1e-7], t, N[(x * N[(t / (-y)), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

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

   1. Initial program 96.4%

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

      1. fma-def 96.4%

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

   3. Simplified 96.4%

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

   4. Taylor expanded in z around 0 52.0%

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

      1. mul-1-neg 52.0%

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

      2. unsub-neg 52.0%

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

      3. *-rgt-identity 52.0%

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

      4. associate-*r/ 60.1%

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

      5. distribute-lft-out-- 60.1%

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

   6. Simplified 60.1%

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

   7. Taylor expanded in x around inf 60.1%

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

      1. mul-1-neg 60.1%

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

      2. distribute-frac-neg 60.1%

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

   9. Simplified 60.1%

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

   if -10 < (/.f64 x y) < 9.9999999999999995e-8

   1. Initial program 98.4%

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

      1. fma-def 98.4%

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

   3. Simplified 98.4%

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

   4. Taylor expanded in x around 0 66.7%

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

   if 9.9999999999999995e-8 < (/.f64 x y)

   1. Initial program 94.8%

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

      1. fma-def 94.8%

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

   3. Simplified 94.8%

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

   4. Taylor expanded in z around 0 51.2%

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

      1. mul-1-neg 51.2%

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

      2. unsub-neg 51.2%

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

      3. *-rgt-identity 51.2%

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

      4. associate-*r/ 48.7%

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

      5. distribute-lft-out-- 48.7%

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

   6. Simplified 48.7%

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

   7. Taylor expanded in x around inf 48.2%

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

      1. mul-1-neg 48.2%

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

      2. distribute-frac-neg 48.2%

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

   9. Simplified 48.2%

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

       1. *-commutative 48.2%

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

       2. frac-2neg 48.2%

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

       3. remove-double-neg 48.2%

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

       4. associate-*l/ 50.7%

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

   11. Applied egg-rr 50.7%

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

       1. *-commutative 50.7%

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

       2. associate-/l* 48.1%

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

       3. associate-/r/ 48.2%

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

       4. *-commutative 48.2%

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

   13. Simplified 48.2%

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

4. Final simplification 59.9%

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

Alternative 4: 63.9% accurate, 0.6× speedup

Math

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

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= (/ x y) -10.0)
   (* (/ x y) (- t))
   (if (<= (/ x y) 1e-7) t (/ x (/ (- y) t)))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((x / y) <= -10.0) {
		tmp = (x / y) * -t;
	} else if ((x / y) <= 1e-7) {
		tmp = t;
	} else {
		tmp = x / (-y / t);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if ((x / y) <= (-10.0d0)) then
        tmp = (x / y) * -t
    else if ((x / y) <= 1d-7) then
        tmp = t
    else
        tmp = x / (-y / t)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if ((x / y) <= -10.0) {
		tmp = (x / y) * -t;
	} else if ((x / y) <= 1e-7) {
		tmp = t;
	} else {
		tmp = x / (-y / t);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (x / y) <= -10.0:
		tmp = (x / y) * -t
	elif (x / y) <= 1e-7:
		tmp = t
	else:
		tmp = x / (-y / t)
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (Float64(x / y) <= -10.0)
		tmp = Float64(Float64(x / y) * Float64(-t));
	elseif (Float64(x / y) <= 1e-7)
		tmp = t;
	else
		tmp = Float64(x / Float64(Float64(-y) / t));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((x / y) <= -10.0)
		tmp = (x / y) * -t;
	elseif ((x / y) <= 1e-7)
		tmp = t;
	else
		tmp = x / (-y / t);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[N[(x / y), $MachinePrecision], -10.0], N[(N[(x / y), $MachinePrecision] * (-t)), $MachinePrecision], If[LessEqual[N[(x / y), $MachinePrecision], 1e-7], t, N[(x / N[((-y) / t), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

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

   1. Initial program 96.4%

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

      1. fma-def 96.4%

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

   3. Simplified 96.4%

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

   4. Taylor expanded in z around 0 52.0%

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

      1. mul-1-neg 52.0%

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

      2. unsub-neg 52.0%

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

      3. *-rgt-identity 52.0%

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

      4. associate-*r/ 60.1%

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

      5. distribute-lft-out-- 60.1%

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

   6. Simplified 60.1%

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

   7. Taylor expanded in x around inf 60.1%

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

      1. mul-1-neg 60.1%

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

      2. distribute-frac-neg 60.1%

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

   9. Simplified 60.1%

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

   if -10 < (/.f64 x y) < 9.9999999999999995e-8

   1. Initial program 98.4%

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

      1. fma-def 98.4%

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

   3. Simplified 98.4%

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

   4. Taylor expanded in x around 0 66.7%

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

   if 9.9999999999999995e-8 < (/.f64 x y)

   1. Initial program 94.8%

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

      1. fma-def 94.8%

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

   3. Simplified 94.8%

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

   4. Taylor expanded in z around 0 51.2%

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

      1. mul-1-neg 51.2%

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

      2. unsub-neg 51.2%

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

      3. *-rgt-identity 51.2%

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

      4. associate-*r/ 48.7%

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

      5. distribute-lft-out-- 48.7%

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

   6. Simplified 48.7%

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

   7. Taylor expanded in x around inf 48.2%

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

      1. mul-1-neg 48.2%

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

      2. distribute-frac-neg 48.2%

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

   9. Simplified 48.2%

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

       1. *-commutative 48.2%

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

       2. frac-2neg 48.2%

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

       3. remove-double-neg 48.2%

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

       4. associate-*l/ 50.7%

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

   11. Applied egg-rr 50.7%

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

       1. associate-/l* 48.2%

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

   13. Simplified 48.2%

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

4. Final simplification 59.9%

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

Alternative 5: 63.7% accurate, 0.6× speedup

Math

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

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= (/ x y) -10.0)
   (* (/ x y) (- t))
   (if (<= (/ x y) 1e-7) t (/ (* x t) (- y)))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((x / y) <= -10.0) {
		tmp = (x / y) * -t;
	} else if ((x / y) <= 1e-7) {
		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) <= (-10.0d0)) then
        tmp = (x / y) * -t
    else if ((x / y) <= 1d-7) 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) <= -10.0) {
		tmp = (x / y) * -t;
	} else if ((x / y) <= 1e-7) {
		tmp = t;
	} else {
		tmp = (x * t) / -y;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (x / y) <= -10.0:
		tmp = (x / y) * -t
	elif (x / y) <= 1e-7:
		tmp = t
	else:
		tmp = (x * t) / -y
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (Float64(x / y) <= -10.0)
		tmp = Float64(Float64(x / y) * Float64(-t));
	elseif (Float64(x / y) <= 1e-7)
		tmp = t;
	else
		tmp = Float64(Float64(x * t) / Float64(-y));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((x / y) <= -10.0)
		tmp = (x / y) * -t;
	elseif ((x / y) <= 1e-7)
		tmp = t;
	else
		tmp = (x * t) / -y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[N[(x / y), $MachinePrecision], -10.0], N[(N[(x / y), $MachinePrecision] * (-t)), $MachinePrecision], If[LessEqual[N[(x / y), $MachinePrecision], 1e-7], t, N[(N[(x * t), $MachinePrecision] / (-y)), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

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

   1. Initial program 96.4%

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

      1. fma-def 96.4%

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

   3. Simplified 96.4%

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

   4. Taylor expanded in z around 0 52.0%

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

      1. mul-1-neg 52.0%

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

      2. unsub-neg 52.0%

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

      3. *-rgt-identity 52.0%

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

      4. associate-*r/ 60.1%

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

      5. distribute-lft-out-- 60.1%

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

   6. Simplified 60.1%

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

   7. Taylor expanded in x around inf 60.1%

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

      1. mul-1-neg 60.1%

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

      2. distribute-frac-neg 60.1%

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

   9. Simplified 60.1%

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

   if -10 < (/.f64 x y) < 9.9999999999999995e-8

   1. Initial program 98.4%

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

      1. fma-def 98.4%

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

   3. Simplified 98.4%

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

   4. Taylor expanded in x around 0 66.7%

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

   if 9.9999999999999995e-8 < (/.f64 x y)

   1. Initial program 94.8%

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

      1. fma-def 94.8%

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

   3. Simplified 94.8%

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

   4. Taylor expanded in z around 0 51.2%

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

      1. mul-1-neg 51.2%

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

      2. unsub-neg 51.2%

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

      3. *-rgt-identity 51.2%

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

      4. associate-*r/ 48.7%

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

      5. distribute-lft-out-- 48.7%

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

   6. Simplified 48.7%

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

   7. Taylor expanded in x around inf 48.2%

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

      1. mul-1-neg 48.2%

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

      2. distribute-frac-neg 48.2%

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

   9. Simplified 48.2%

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

       1. *-commutative 48.2%

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

       2. frac-2neg 48.2%

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

       3. remove-double-neg 48.2%

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

       4. associate-*l/ 50.7%

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

   11. Applied egg-rr 50.7%

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

4. Final simplification 60.6%

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

Alternative 6: 84.0% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -3.1 \cdot 10^{+85} \lor \neg \left(z \leq 4.2 \cdot 10^{-86}\right):\\ \;\;\;\;t + \frac{x}{y} \cdot z\\ \mathbf{else}:\\ \;\;\;\;t \cdot \left(1 - \frac{x}{y}\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= z -3.1e+85) (not (<= z 4.2e-86)))
   (+ t (* (/ x y) z))
   (* t (- 1.0 (/ x y)))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((z <= -3.1e+85) || !(z <= 4.2e-86)) {
		tmp = t + ((x / y) * z);
	} else {
		tmp = t * (1.0 - (x / y));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if ((z <= (-3.1d+85)) .or. (.not. (z <= 4.2d-86))) then
        tmp = t + ((x / y) * z)
    else
        tmp = t * (1.0d0 - (x / y))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if ((z <= -3.1e+85) || !(z <= 4.2e-86)) {
		tmp = t + ((x / y) * z);
	} else {
		tmp = t * (1.0 - (x / y));
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (z <= -3.1e+85) or not (z <= 4.2e-86):
		tmp = t + ((x / y) * z)
	else:
		tmp = t * (1.0 - (x / y))
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((z <= -3.1e+85) || !(z <= 4.2e-86))
		tmp = Float64(t + Float64(Float64(x / y) * z));
	else
		tmp = Float64(t * Float64(1.0 - Float64(x / y)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((z <= -3.1e+85) || ~((z <= 4.2e-86)))
		tmp = t + ((x / y) * z);
	else
		tmp = t * (1.0 - (x / y));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[z, -3.1e+85], N[Not[LessEqual[z, 4.2e-86]], $MachinePrecision]], N[(t + N[(N[(x / y), $MachinePrecision] * z), $MachinePrecision]), $MachinePrecision], N[(t * N[(1.0 - N[(x / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -3.10000000000000011e85 or 4.2e-86 < z

   1. Initial program 98.4%

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

   2. Taylor expanded in z around inf 84.6%

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

      1. associate-/l* 85.4%

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

      2. associate-/r/ 91.3%

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

   4. Applied egg-rr 91.3%

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

   if -3.10000000000000011e85 < z < 4.2e-86

   1. Initial program 95.1%

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

      1. fma-def 95.1%

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

   3. Simplified 95.1%

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

   4. Taylor expanded in z around 0 85.0%

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

      1. mul-1-neg 85.0%

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

      2. unsub-neg 85.0%

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

      3. *-rgt-identity 85.0%

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

      4. associate-*r/ 87.4%

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

      5. distribute-lft-out-- 87.4%

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

   6. Simplified 87.4%

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

4. Final simplification 89.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -3.1 \cdot 10^{+85} \lor \neg \left(z \leq 4.2 \cdot 10^{-86}\right):\\ \;\;\;\;t + \frac{x}{y} \cdot z\\ \mathbf{else}:\\ \;\;\;\;t \cdot \left(1 - \frac{x}{y}\right)\\ \end{array} \]

Alternative 7: 82.5% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -9.2 \cdot 10^{+80} \lor \neg \left(z \leq 4.2 \cdot 10^{-86}\right):\\ \;\;\;\;t + \frac{x}{y} \cdot z\\ \mathbf{else}:\\ \;\;\;\;t - x \cdot \frac{t}{y}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= z -9.2e+80) (not (<= z 4.2e-86)))
   (+ t (* (/ x y) z))
   (- t (* x (/ t y)))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((z <= -9.2e+80) || !(z <= 4.2e-86)) {
		tmp = t + ((x / y) * z);
	} else {
		tmp = t - (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 ((z <= (-9.2d+80)) .or. (.not. (z <= 4.2d-86))) then
        tmp = t + ((x / y) * z)
    else
        tmp = t - (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 ((z <= -9.2e+80) || !(z <= 4.2e-86)) {
		tmp = t + ((x / y) * z);
	} else {
		tmp = t - (x * (t / y));
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (z <= -9.2e+80) or not (z <= 4.2e-86):
		tmp = t + ((x / y) * z)
	else:
		tmp = t - (x * (t / y))
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((z <= -9.2e+80) || !(z <= 4.2e-86))
		tmp = Float64(t + Float64(Float64(x / y) * z));
	else
		tmp = Float64(t - Float64(x * Float64(t / y)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((z <= -9.2e+80) || ~((z <= 4.2e-86)))
		tmp = t + ((x / y) * z);
	else
		tmp = t - (x * (t / y));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[z, -9.2e+80], N[Not[LessEqual[z, 4.2e-86]], $MachinePrecision]], N[(t + N[(N[(x / y), $MachinePrecision] * z), $MachinePrecision]), $MachinePrecision], N[(t - N[(x * N[(t / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -9.20000000000000016e80 or 4.2e-86 < z

   1. Initial program 98.5%

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

   2. Taylor expanded in z around inf 84.7%

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

      1. associate-/l* 85.5%

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

      2. associate-/r/ 91.4%

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

   4. Applied egg-rr 91.4%

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

   if -9.20000000000000016e80 < z < 4.2e-86

   1. Initial program 95.0%

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

   2. Taylor expanded in z around 0 85.7%

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

      1. associate-*r/ 85.7%

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

      2. mul-1-neg 85.7%

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

      3. *-commutative 85.7%

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

      4. distribute-rgt-neg-out 85.7%

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

      5. associate-*r/ 87.4%

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

   4. Simplified 87.4%

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

4. Final simplification 89.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -9.2 \cdot 10^{+80} \lor \neg \left(z \leq 4.2 \cdot 10^{-86}\right):\\ \;\;\;\;t + \frac{x}{y} \cdot z\\ \mathbf{else}:\\ \;\;\;\;t - x \cdot \frac{t}{y}\\ \end{array} \]

Alternative 8: 39.9% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;\frac{x}{y} \leq 5 \cdot 10^{+17}:\\ \;\;\;\;t\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{y} \cdot t\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t) :precision binary64 (if (<= (/ x y) 5e+17) t (* (/ x y) t)))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((x / y) <= 5e+17) {
		tmp = t;
	} else {
		tmp = (x / y) * t;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if ((x / y) <= 5d+17) then
        tmp = t
    else
        tmp = (x / y) * t
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if ((x / y) <= 5e+17) {
		tmp = t;
	} else {
		tmp = (x / y) * t;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (x / y) <= 5e+17:
		tmp = t
	else:
		tmp = (x / y) * t
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (Float64(x / y) <= 5e+17)
		tmp = t;
	else
		tmp = Float64(Float64(x / y) * t);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((x / y) <= 5e+17)
		tmp = t;
	else
		tmp = (x / y) * t;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[N[(x / y), $MachinePrecision], 5e+17], t, N[(N[(x / y), $MachinePrecision] * t), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if (/.f64 x y) < 5e17

   1. Initial program 97.8%

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

      1. fma-def 97.8%

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

   3. Simplified 97.8%

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

   4. Taylor expanded in x around 0 45.5%

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

   if 5e17 < (/.f64 x y)

   1. Initial program 94.3%

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

      1. fma-def 94.3%

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

   3. Simplified 94.3%

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

   4. Taylor expanded in z around 0 51.3%

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

      1. mul-1-neg 51.3%

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

      2. unsub-neg 51.3%

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

      3. *-rgt-identity 51.3%

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

      4. associate-*r/ 48.6%

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

      5. distribute-lft-out-- 48.6%

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

   6. Simplified 48.6%

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

   7. Taylor expanded in x around inf 48.6%

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

      1. mul-1-neg 48.6%

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

      2. distribute-frac-neg 48.6%

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

   9. Simplified 48.6%

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

       1. associate-*r/ 51.3%

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

       2. expm1-log1p-u 26.6%

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

       3. expm1-udef 25.9%

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

       4. associate-/l* 25.0%

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

       5. associate-/r/ 25.9%

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

       6. add-sqr-sqrt 10.4%

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

       7. sqrt-unprod 11.2%

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

       8. sqr-neg 11.2%

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

       9. sqrt-unprod 0.4%

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

       10. add-sqr-sqrt 2.4%

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

   11. Applied egg-rr 2.4%

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

       1. expm1-def 2.4%

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

       2. expm1-log1p 4.6%

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

       3. associate-*l/ 4.7%

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

       4. associate-*r/ 11.4%

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

   13. Simplified 11.4%

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

4. Final simplification 36.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{x}{y} \leq 5 \cdot 10^{+17}:\\ \;\;\;\;t\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{y} \cdot t\\ \end{array} \]

Alternative 9: 65.9% accurate, 1.3× speedup

Math

\[\begin{array}{l} \\ t \cdot \left(1 - \frac{x}{y}\right) \end{array} \]

FPCore

(FPCore (x y z t) :precision binary64 (* t (- 1.0 (/ x y))))

C

double code(double x, double y, double z, double t) {
	return t * (1.0 - (x / y));
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    code = t * (1.0d0 - (x / y))
end function

Java

public static double code(double x, double y, double z, double t) {
	return t * (1.0 - (x / y));
}

Python

def code(x, y, z, t):
	return t * (1.0 - (x / y))

Julia

function code(x, y, z, t)
	return Float64(t * Float64(1.0 - Float64(x / y)))
end

MATLAB

function tmp = code(x, y, z, t)
	tmp = t * (1.0 - (x / y));
end

Wolfram

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

Derivation

1. Initial program 96.9%

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

   1. fma-def 96.9%

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

3. Simplified 96.9%

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

4. Taylor expanded in z around 0 58.1%

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

   1. mul-1-neg 58.1%

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

   2. unsub-neg 58.1%

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

   3. *-rgt-identity 58.1%

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

   4. associate-*r/ 60.8%

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

   5. distribute-lft-out-- 60.7%

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

6. Simplified 60.7%

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

7. Final simplification 60.7%

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

Alternative 10: 38.3% accurate, 9.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 96.9%

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

   1. fma-def 96.9%

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

3. Simplified 96.9%

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

4. Taylor expanded in x around 0 33.8%

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

5. Final simplification 33.8%

   \[\leadsto t \]

Developer target: 97.1% 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 2023334 
(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))