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

Percentage Accurate: 97.8% → 97.8%

Time: 6.0s

Alternatives: 6

Speedup: 1.0×

• 24.7% of points produce a very large (infinite) output. You may want to add a precondition.

Specification

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Initial Program: 97.8% 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 98.6%

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

3. Final simplification 98.6%

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

Alternative 2: 85.1% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -5 \cdot 10^{+49} \lor \neg \left(t \leq 3500\right):\\ \;\;\;\;t \cdot \left(1 - \frac{x}{y}\right)\\ \mathbf{else}:\\ \;\;\;\;t + x \cdot \frac{z}{y}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= t -5e+49) (not (<= t 3500.0)))
   (* t (- 1.0 (/ x y)))
   (+ t (* x (/ z y)))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((t <= -5e+49) || !(t <= 3500.0)) {
		tmp = t * (1.0 - (x / y));
	} else {
		tmp = t + (x * (z / y));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if ((t <= (-5d+49)) .or. (.not. (t <= 3500.0d0))) then
        tmp = t * (1.0d0 - (x / y))
    else
        tmp = t + (x * (z / y))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if ((t <= -5e+49) || !(t <= 3500.0)) {
		tmp = t * (1.0 - (x / y));
	} else {
		tmp = t + (x * (z / y));
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (t <= -5e+49) or not (t <= 3500.0):
		tmp = t * (1.0 - (x / y))
	else:
		tmp = t + (x * (z / y))
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((t <= -5e+49) || !(t <= 3500.0))
		tmp = Float64(t * Float64(1.0 - Float64(x / y)));
	else
		tmp = Float64(t + Float64(x * Float64(z / y)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((t <= -5e+49) || ~((t <= 3500.0)))
		tmp = t * (1.0 - (x / y));
	else
		tmp = t + (x * (z / y));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[t, -5e+49], N[Not[LessEqual[t, 3500.0]], $MachinePrecision]], N[(t * N[(1.0 - N[(x / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(t + N[(x * N[(z / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if t < -5.0000000000000004e49 or 3500 < t

   1. Initial program 99.9%

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

      1. associate-*l/ 89.0%

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

      2. associate-/l* 93.9%

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

      3. fma-define 93.9%

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

   3. Simplified 93.9%

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

   5. Taylor expanded in z around 0 81.4%

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

      1. mul-1-neg 81.4%

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

      2. *-rgt-identity 81.4%

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

      3. associate-/l* 91.7%

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

      4. distribute-rgt-neg-in 91.7%

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

      5. mul-1-neg 91.7%

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

      6. distribute-lft-in 91.7%

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

      7. mul-1-neg 91.7%

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

      8. unsub-neg 91.7%

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

   7. Simplified 91.7%

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

   if -5.0000000000000004e49 < t < 3500

   1. Initial program 97.3%

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

   3. Taylor expanded in z around inf 83.0%

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

      1. associate-/l* 85.2%

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

   5. Simplified 85.2%

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

4. Final simplification 88.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -5 \cdot 10^{+49} \lor \neg \left(t \leq 3500\right):\\ \;\;\;\;t \cdot \left(1 - \frac{x}{y}\right)\\ \mathbf{else}:\\ \;\;\;\;t + x \cdot \frac{z}{y}\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 86.6% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -3.1 \cdot 10^{+49} \lor \neg \left(t \leq 3600000\right):\\ \;\;\;\;t \cdot \left(1 - \frac{x}{y}\right)\\ \mathbf{else}:\\ \;\;\;\;t + \frac{x}{y} \cdot z\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= t -3.1e+49) (not (<= t 3600000.0)))
   (* t (- 1.0 (/ x y)))
   (+ t (* (/ x y) z))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((t <= -3.1e+49) || !(t <= 3600000.0)) {
		tmp = t * (1.0 - (x / y));
	} else {
		tmp = t + ((x / y) * z);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if ((t <= (-3.1d+49)) .or. (.not. (t <= 3600000.0d0))) then
        tmp = t * (1.0d0 - (x / y))
    else
        tmp = t + ((x / y) * z)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if ((t <= -3.1e+49) || !(t <= 3600000.0)) {
		tmp = t * (1.0 - (x / y));
	} else {
		tmp = t + ((x / y) * z);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (t <= -3.1e+49) or not (t <= 3600000.0):
		tmp = t * (1.0 - (x / y))
	else:
		tmp = t + ((x / y) * z)
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((t <= -3.1e+49) || !(t <= 3600000.0))
		tmp = Float64(t * Float64(1.0 - Float64(x / y)));
	else
		tmp = Float64(t + Float64(Float64(x / y) * z));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((t <= -3.1e+49) || ~((t <= 3600000.0)))
		tmp = t * (1.0 - (x / y));
	else
		tmp = t + ((x / y) * z);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[t, -3.1e+49], N[Not[LessEqual[t, 3600000.0]], $MachinePrecision]], N[(t * N[(1.0 - N[(x / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(t + N[(N[(x / y), $MachinePrecision] * z), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if t < -3.09999999999999992e49 or 3.6e6 < t

   1. Initial program 99.9%

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

      1. associate-*l/ 89.0%

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

      2. associate-/l* 93.9%

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

      3. fma-define 93.9%

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

   3. Simplified 93.9%

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

   5. Taylor expanded in z around 0 81.4%

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

      1. mul-1-neg 81.4%

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

      2. *-rgt-identity 81.4%

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

      3. associate-/l* 91.7%

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

      4. distribute-rgt-neg-in 91.7%

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

      5. mul-1-neg 91.7%

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

      6. distribute-lft-in 91.7%

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

      7. mul-1-neg 91.7%

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

      8. unsub-neg 91.7%

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

   7. Simplified 91.7%

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

   if -3.09999999999999992e49 < t < 3.6e6

   1. Initial program 97.3%

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

   3. Taylor expanded in z around inf 83.0%

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

      1. *-commutative 83.0%

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

      2. associate-/l* 87.2%

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

   5. Applied egg-rr 87.2%

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

4. Final simplification 89.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -3.1 \cdot 10^{+49} \lor \neg \left(t \leq 3600000\right):\\ \;\;\;\;t \cdot \left(1 - \frac{x}{y}\right)\\ \mathbf{else}:\\ \;\;\;\;t + \frac{x}{y} \cdot z\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 86.6% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -3.1 \cdot 10^{+49}:\\ \;\;\;\;t - \frac{t}{\frac{y}{x}}\\ \mathbf{elif}\;t \leq 23000000:\\ \;\;\;\;t + \frac{x}{y} \cdot z\\ \mathbf{else}:\\ \;\;\;\;t \cdot \left(1 - \frac{x}{y}\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= t -3.1e+49)
   (- t (/ t (/ y x)))
   (if (<= t 23000000.0) (+ t (* (/ x y) z)) (* t (- 1.0 (/ x y))))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (t <= -3.1e+49) {
		tmp = t - (t / (y / x));
	} else if (t <= 23000000.0) {
		tmp = t + ((x / y) * z);
	} else {
		tmp = t * (1.0 - (x / y));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if (t <= (-3.1d+49)) then
        tmp = t - (t / (y / x))
    else if (t <= 23000000.0d0) then
        tmp = t + ((x / y) * z)
    else
        tmp = t * (1.0d0 - (x / y))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if (t <= -3.1e+49) {
		tmp = t - (t / (y / x));
	} else if (t <= 23000000.0) {
		tmp = t + ((x / y) * z);
	} else {
		tmp = t * (1.0 - (x / y));
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if t <= -3.1e+49:
		tmp = t - (t / (y / x))
	elif t <= 23000000.0:
		tmp = t + ((x / y) * z)
	else:
		tmp = t * (1.0 - (x / y))
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (t <= -3.1e+49)
		tmp = Float64(t - Float64(t / Float64(y / x)));
	elseif (t <= 23000000.0)
		tmp = Float64(t + Float64(Float64(x / y) * z));
	else
		tmp = Float64(t * Float64(1.0 - Float64(x / y)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (t <= -3.1e+49)
		tmp = t - (t / (y / x));
	elseif (t <= 23000000.0)
		tmp = t + ((x / y) * z);
	else
		tmp = t * (1.0 - (x / y));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[t, -3.1e+49], N[(t - N[(t / N[(y / x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 23000000.0], N[(t + N[(N[(x / y), $MachinePrecision] * z), $MachinePrecision]), $MachinePrecision], N[(t * N[(1.0 - N[(x / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if t < -3.09999999999999992e49

   1. Initial program 99.9%

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

   3. Taylor expanded in x around 0 87.5%

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

      1. associate-/l* 90.2%

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

      2. *-commutative 90.2%

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

      3. associate-/r/ 99.9%

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

   5. Simplified 99.9%

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

   6. Taylor expanded in z around 0 81.1%

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

      1. associate-*l/ 82.4%

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

      2. associate-*l* 82.4%

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

      3. mul-1-neg 82.4%

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

      4. distribute-frac-neg2 82.4%

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

      5. associate-/r/ 92.0%

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

   8. Simplified 92.0%

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

   if -3.09999999999999992e49 < t < 2.3e7

   1. Initial program 97.3%

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

   3. Taylor expanded in z around inf 83.0%

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

      1. *-commutative 83.0%

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

      2. associate-/l* 87.2%

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

   5. Applied egg-rr 87.2%

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

   if 2.3e7 < t

   1. Initial program 99.9%

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

      1. associate-*l/ 90.3%

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

      2. associate-/l* 97.1%

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

      3. fma-define 97.1%

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

   3. Simplified 97.1%

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

   5. Taylor expanded in z around 0 81.7%

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

      1. mul-1-neg 81.7%

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

      2. *-rgt-identity 81.7%

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

      3. associate-/l* 91.3%

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

      4. distribute-rgt-neg-in 91.3%

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

      5. mul-1-neg 91.3%

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

      6. distribute-lft-in 91.4%

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

      7. mul-1-neg 91.4%

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

      8. unsub-neg 91.4%

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

   7. Simplified 91.4%

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

4. Final simplification 89.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -3.1 \cdot 10^{+49}:\\ \;\;\;\;t - \frac{t}{\frac{y}{x}}\\ \mathbf{elif}\;t \leq 23000000:\\ \;\;\;\;t + \frac{x}{y} \cdot z\\ \mathbf{else}:\\ \;\;\;\;t \cdot \left(1 - \frac{x}{y}\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 65.3% accurate, 1.3× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 98.6%

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

   1. associate-*l/ 91.2%

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

   2. associate-/l* 95.0%

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

   3. fma-define 95.0%

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

3. Simplified 95.0%

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

5. Taylor expanded in z around 0 61.5%

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

   1. mul-1-neg 61.5%

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

   2. *-rgt-identity 61.5%

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

   3. associate-/l* 66.9%

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

   4. distribute-rgt-neg-in 66.9%

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

   5. mul-1-neg 66.9%

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

   6. distribute-lft-in 66.9%

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

   7. mul-1-neg 66.9%

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

   8. unsub-neg 66.9%

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

7. Simplified 66.9%

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

8. Final simplification 66.9%

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

Alternative 6: 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 98.6%

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

   1. associate-*l/ 91.2%

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

   2. associate-/l* 95.0%

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

   3. fma-define 95.0%

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

3. Simplified 95.0%

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

5. Taylor expanded in x around 0 41.3%

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

6. Final simplification 41.3%

   \[\leadsto t \]
7. Add Preprocessing

Developer target: 97.4% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{x}{y} \cdot \left(z - t\right) + t\\ \mathbf{if}\;z < 2.759456554562692 \cdot 10^{-282}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z < 2.326994450874436 \cdot 10^{-110}:\\ \;\;\;\;x \cdot \frac{z - t}{y} + t\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Reproduce

herbie shell --seed 2024055 
(FPCore (x y z t)
  :name "Numeric.Signal.Multichannel:$cget from hsignal-0.2.7.1"
  :precision binary64

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

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